



	S

TER VERKRIJGING VAN DEN GRAAD VAN DOCTOR
IN DE WIS- EN NATUURKUNDE AAN DE RIJKS-
UNIVERSITEIT TE UTRECHT, OP GEZAG VAN DEN
RECTOR-MAGNIFICUS Dr TH. M. VAN LEEUWEN,
HOOGLEERAAR IN DE FACULTEIT DER GENEES-
KUNDE, VOLGENS BESLUIT VAN DEN SENAAT DER
UNIVERSITEIT TEGEN DE BEDENKINGEN VAN DE
FACULTEIT DER WIS- EN NATUURKUNDE TE VER-
DEDIGEN OP MAANDAG 3 JULI 1939, DES NAMIDDAGS
TE 4 UUR
DOOR

„Triebt in der Hube des Besitzes sondern in
der steten Vermebrun^ der Erkenntnis Ue0 die
Befriedigung und das Qlück des Jorschers.quot;

De techniek van het schrijven brengt met zich mede dat wat voor U als
lezer het voorwoord is, voor mij als schrijver het slot vormt van de redactie
van het onderzoek waarop mijn aandacht langen tijd is geconcentreerd
geweest. Het schrijven van deze regels richt onze blik achterwaarts en
bij het als in vogelvlucht overzien van de periode die met dit proefschrift
afgesloten wordt dringen zich gedachten op waarvan een enkele hier een
plaats moge vinden.

Het onderzoek dat in de volgende pagina's behandeld wordt heeft, met
mij, eenige malen van domicilie gewisseld, doch waar de voorbereiding
er toe, en de afsluiting er van, onafscheidelijk met Utrecht verbonden zijn
kan ik niet nalaten uitdrukking te geven aan een gevoel van diepe dank-
baarheid jegens de Alma Mater voor het vele dat mij het verblijf binnen
Hare muren geschonken heeft; een gevoel van dankbaarheid dat, naar mij
in het afgeloopen jaar duidelijk geworden is, in intensiteit toeneemt naar-
mate de afstand in de tijd die ons scheidt van de periode van dagelijksch
contact met de Universiteit toeneemt, waarbij weliswaar de details van
het beeld in onze herinnering vager worden, doch waarbij wij ons tevens
scherper bewust worden van de resultante van alle invloeden die in de
studententijd in bonte mengeling op ons ingewerkt hebben.

Zoozeer valt voor mij hierbij de nadruk op de invloed die wij onder-
vonden hebben van de Academie als geheel dat ik er van wil afzien het
aandeel dat verschillende personen hiertoe bijgedragen hebben nader te
analyseeren. Een enkele uitzondering zij het mij vergund hierop te maken.

Dat ik U, Hooggeleerde K r u y t, Hooggeachte Promotor, daarbij in de
eerste plaats wil noemen moge U geen verwondering baren. Aan weinigen
Uwer leerlingen zal het in dier mate vergund geweest zijn met U in contact

te komen, zoowel binnen als buiten de muren van het Laboratorium, als
voor mij het geval was. Een qualitatieve uitdrukking te vinden voor de
groote waarde die dit contact met U voor mij gehad heeft is een te om-
vangrijke taak om binnen het kader van deze regels adequaat ten uitvoer
gebracht te kunnen worden; hoeveel te zwaarder derhalve de taak deze
grootheid ook quantitatief te benaderen en onder woorden te brengen!
Zoozeer dringt zich de mate van Uw vermogen om uit een veelheid van
materiaal de essentieele elementen uit te lichten op aan diegenen wien het
gegeven is onder Uw leiding zich een weg te banen tot het begrijpen van
hetgeen zich binnen de grenzen der chemische verschijnselen kan afspelen,
dat geen Uwer leerlingen, en wel in de laatste plaats de schrijver van deze
regels, zich kan onttrekken aan het streven te trachten zich Uw werkwijze
eigen te maken en het door U gegeven voorbeeld als ideaal voor oogen te
houden.

Dear Professor Freundlich, the more ardently I attempt to give
expression to the feeling of gratitude towards you which has steadily grown
during the period in which I was engaged in these investigations, the less
I fear I shall succeed in doing so. The bare fact that your presence in
London enabled me to combine carrying out research under your super-
vision with a prolongued visit to England, would in itself have been
sufficient to make me feel deeply indebted to you. How much more so
where in addition you have displayed towards me such a continuous and
stimulating interest in the results of these investigations; an interest
interrupted neither by distance nor by time. Please accept the expres-
sion of my sincere gratitude for the invaluable guidance which you lent
to my steps in the domain of the intricate systems under discussion and
for the generous way in which you have never ceased to put at my disposal
your extensive knowledge of colloid-chemical phenomena.

Dear Professor Donnan, I feel sincerely indebted to you for the hos-
pitality which I experienced in the Sir William Ramsay Laboratories and
for the encouraging interest which you have shown in the progress of my
work.

my stay in England, without whose continuous sympathy I should have
found it difficult, if not impossible, to complete the drafting of this in-
vestigation in its present form that I can not refrain from tendering these
few lines to all of them as a token of cordial gratitude. Our contacts,
though for the moment interrupted, remain a perpetual source of the most
pleasant souvenirs to me, and will, I am sure, never cease to do so.

My sincere thanks are due to Mrs. D. K u e n e n-W i c k s t e e d for
kindly having revised the manuscript.

CHAPTER VI - DISCUSSION OF THE REPORTED FACTS AND
CHECKING OF THE CONCLUSIONS ARRIVED AT

It has been our aim to investigate the properties of systems which show
the phenomenon of dilatancy i, in particular the relations between dilatant
and thixotropic systems. In this form the problem originally formed a subject
of investigation undertaken by the author under the supervision of Prof.
H. Freundlich at 7he Sir William Ramsey and Ralph Torster Caho-
ratories, University College, London.

From the beginning it has been our intention to develop a technique
which should enable us to reduce the measurements of dilatant as well
as thixotropic phenomena to the appropriate units, pince it has been in
particular the lack of an adequate technique for quantitative investigation
which has increasingly hampered the extension of our knowledge of
thixotropic phenomena.

However valuable the quot;time of solidificationquot; may have been for the
development of a schematic knowledge of thixotropic systems, and still
may be for a qualitative characterisation of such systems, it has been
the authors aim to correlate dilatant as well as thixotropic systems only
with their behaviour in connection with flow.

After preliminary investigations had supplied us with sufficient in-
formation to outline the scope of the experimental method to be applied,
a design was made of an apparatus for the measurement of the systems
in the required way.

This apparatus was constructed at the Instrument workshop of the van
't Tioff Laboratorium, Utrecht, and all further experimental work has been
carried out in this laboratory.

In chapter I a short summary will be given of the principles underlying
the measuring of flow in general; chapter II will deal with the apparatus
above referred to, while in chapter III and IV the measurements of dilatant
and thixotropic systems respectively will be reported and examined. In
chapter V thixotropic systems will be subjected to a somewhat broader
^ For a description of the phenomenon c.f. page 29.

treatment, whereas chapter VI aims at providing a coordinating discussion
of all the various phenomena involved. Eventually a concise summary of
relevant papers in the contemporary literature will be offered in chap-
ter VII.

For literature, books as well as papers, concerning the subjects which are
dealt with in the following pages we refer to the list of literature at
page 85.

As has been pointed out in the introduction, we decided to look for an
unambiguous criterion for the degree of dilatancy and the degree of thixo-
tropy of our systems in their behaviour under various conditions of
shearing stress. In the literature dealing with thixotropic systems again
and again the terms quot;highly thixotropicquot; or quot;weakly dilatantquot; are met with,
but, unfortunately, the criterion according to which these qualifications are
attributed to the systems under observation seems to vary from one author
to another.

Now the whole subject of the behaviour of systems under various con-
ditions of flow can ultimately be reduced to the relation between rate of
shear and the shearing stress exerted on the system under observation.
The various possibilities which are met with in practice are shown in

Fig. 1. and Fig. 2. Curve a represents a system in which the rate of shear
is linearly proportional to the shearing stress. This type of flow will be

referred to as quot;viscous flowquot;. The tangent of the angle between this
curve and the abscissa represents the mobility of the system i.e. the re-
ciprocal value of the viscosity. Curve b represents a system which behaves
differently according to the value of the shearing stress; for stresses below
f J (the lower yield value) ^ no flow occurs at all. For stresses larger
than ordinary quot;viscousquot; flow takes place, while for intermediate
stresses the mobility shows a strong dependance upon the shearing stress,

Attention must be drawn in particular to the characteristic values on
the abscissa denoted by fj, and f„j, each of which is called a yield
value. The lower yield value fj and the maximum' yield value f^, were
mentioned above. The yield value fe (Bingham's yield value) re-
presents the (purely theoretical) value of the shearing stress which would
be necessary to just produce flow of the system in case this should exhibit
quot;viscous flowquot; at each value of the rate of shear. The type of flow re-
presented by curve b will be referred to as quot;plastic flowquot;.

represents a case in which a lower yield value is not present, while curve
d represents a case which can be characterised as quot;ideal plastic flowquot;; in
this case the three yield values coincide at f.

^ Throughout the following pages we will use the nomenclature suggested — and applied —
in the First Report on Viscosity and Plasticity of the Academy of Sciences, Amsterdam,
1935.

Eventually a third type of curve must be taken into consideration, which
is drawn in Fig. 3, showing a curvature concave to the abscissa. From the

theoretical point of view we may distinguish between curve e and g,
according to the abscence of a yield value or not.

§ 2 - RELATION BETWEEN GRAPHIC REPRESENTATION AND PHYSICAL
PROPERTIES OF VARIOUS SYSTEMS

The question arises which is the physical meaning of the curves of the
preceding section, i.e. which systems exhibit curves like the ones just
shown and what is the interpretation of the physical mechanism causing
either one type of flow or the other?

Curve a represents the properties of an ordinary — a so called quot;New-
tonianquot; — liquid which is characterised by the abscence of any yield
value while its D/r relation is a perfectly straight line. A Newtonian
liquid is entirely characterised by the angle « i.e. by its mobility. By a
simple calculation the rate of shear and the shearing stress can be calcu-
lated from the experimental data, from which the viscosity i.e. the reciprocal
value of the mobility can be enumerated.

Curve d Fig. 2, represents a system which over a certain range of shearing
stresses shows no flow at all, i.e. behaves as a solid. From f onwards,
however, purely viscous flow suddenly sets in. It is not so easy, from the
physical point of view to understand what kind of system would behave
as represented by this type of curve which shows such an abrupt change
in behaviour from a solid to a Newtonian liquid at one particular shearing

Stress. In addition it is often doubted whether systems showing this type
of D/r relation do really exist, the difficulty being to determine a D/z
relation for very small values of the rate of shear. So it is often supposed
that in actual practice curves like d will always tend to degenerate into
the type of curve shown in b. Fig. 1. We will not enter into a discussion
of this point here. Let it be sufficient to say that curve d may be considered
as an idealised form of curve b.

The curve b represents the behaviour of a large number of systems
which are all characterised by their more of'less pronounced character of
a quot;plasticquot; substance. This is readily understood from the form of this
curve. During the moulding of a plastic substance a relatively high shearing
stress is exerted on it and the substance exhibits a comparatively low
viscosity; as soon, however, as the stress is released the substance regains
its high viscosity corresponding to the lower part of the curve subsequently
an infinitely great viscosity represented by the part of the curve which
coincides with the abscissa for stresses below fj. This means that after
the stress has ceased to act the substance will retain the shape it had
adopted during the moulding. In order to characterise a plastic substance
four quantities should be specified, namely, f], fg, f^ and the angle « i.e.
a quantity proportional to the viscosity of the linear part of the curve.

Let us try to realise the physical meaning of these various yield values.
The lower yield value fj (c.f. curve b, Fig. 1) apparently is the minimum
stress necessary to cause the system to break somewhere; since the system
will contain bonds of different strength the lower yield value apparently
corresponds to the weakest of these bonds. The maximum yield value,
on the other hand characterises that stress onward from which the force
applied to the system is consumed to produce viscous flow only, i.e. that
type of flow which occurs in systems with relatively independent rheologi-
cal units like a Newtonian liquid.

For any value f^ of the stress between fj and the force applied to
the system is apparently consumed for two purposes, an amount equal to
to fi is used for breaking the weakest bonds which are present in the
system while an amount equal to fx—f i is available for the mutual shearing
of the lumps into which the system has been broken down. Since these

lumps themselves are liable to be further reduced in size during this
shearing-process the total force applied to the system will at any value
of the shearing stress be consumed for these two purposes: breaking down
of bonds, thus producing lumps of system, and shearing of the lumps of
system. At any point of the D/r curve these two amounts may be graphi-

cally determined as it has been done for the point P in Fig. 4, which
shows a curve similar to the curve b of Fig. 1. The tangent in P has been
drawn (P—fg). In this Fig. O—fg represents the part of the stress con-
sumed for the breaking down process (consists of part fj for breaking
down of the weekest bonds plus fg—fj for breaking down of further
bonds), while the part of the force equal to fA—fg produces the flow
of the remnants of the system.

On continually increasing the shearing stress applied to the system a
value must be reached at which no further breaking down of the system
is possible, since it has been reduced to the smallest possible particles.
This is the value indicated by f^,, curve b, fig 1. At the same time we
can now realise the meaning of fg, this being the stress necessary to reduce
the system to the smallest possible rheologically active units at a rate of
shear of zero, provided such a condition were possible. The remaining
part of the stress fm—ffi, Fig. 1, curve b is the force necessary to produce
that rheological condition at which the smallest possible active units mu-
tually influence each other as if they were the quot;moleculesquot; of an ordinary
liquid.

down no tendency whatever to reunite should be present in the dis-
integrated remnants of the system. If, however, in a particular type of
system such a tendency should actually exist then the aspect will neces-
sarily be affected. Let us consider, in addition to the two tendencies taken
into account in the preceding lines, n.1. the breaking down action of the
stress and the mutual resistance against shear of the lumps of
system, a third factor, namely the tendency of the lumps of the
system to reunite after the shearing has ceased. In that case each point
of the D/r curve represents the equilibrium between a breaking down
action of the shear, a reuniting tendency of the lumps of system and a
certain quot;viscous-flow-resistancequot;. What this means in terms of the D/t

curve may be discussed in connection with Fig. 5. Let curve a represent a
D/r curve for a system, the particles of which do not exhibit the ten-
dency to reunite after having been broken down by the action of a stress
greater than fj. Let us for instance take the point p at a shearing stress f;
now let us endow the particles of the same system with a vigourous tendency
to reunite after having been disunited. In that case the same force f will
result in a smaller rate of shear of the system. Let us assume a rate of
shear p' to be reached in this case; a similar kind of reasoning may be
applied to the other points of the curve and in this way the whole curve a
shifts to curve h. Each point of curve h now represents the equilibrium
between: rate of break down by shear, rate of reunion and quot;viscous
resistancequot;. In curve b the value of f^, represents that shearing stress which

produces a rate of shear at which the rate of break down to the smallest
possible particles is just balanced by their tendency to reunite.

Now if we ask under which conditions a curve like h of Fig. 1 will
pass into a curve like d of Fig. 1 the answer automatically follows from
the preceding discussion. Since we have considered the portion of the
curve between fj and f^j to be an indication of the breaking down of bonds
of different strength it must be reduced to a single point if only one type
of bonds should exist in the system. If such a system might be discovered
it would show the behaviour of an ideal plastic substance. On the other
hand we will consider the amount of divergence of any curve from that
of an ideal plastic curve as an indication of the degree of complexity of
the bonds which keep the system together.

Eventually, a few words must be devoted to curves of the type which
is represented by the curves e and ^ of Fig. 3; in the literature curves of
this type are seldom met with. Their shape, however, in the case of curve e
suggests a behaviour just the opposite to that of a plastic substance, since
in the former case at low shearing stresses the system will show similarity
with a Newtonian liquid, i.e. will flow spontaneously, while at higher
shearing stresses an increasing quot;viscosityquot;, i-e. an increasing resistance against
change of shape will occur. Curve g represents a system which exhibits
the character of an ideal plastic substance at small values of the shearing
stress while at higher shearing stresses an opposite tendency is exhibited
similar to that of curve e. This type of systems will be dealt with more
extensively in § 9.

Having dealt with the graphic representation of the properties of various
systems in the preceding section, a few lines should be devoted to a
description of the measuring apparatus by means of which such graphs
may be obtained in practice. Since the object of all such measurements is
the establishment of a relation between a rate of shear and a shearing
stress two ways are open from the start: either a certain rate of shear can
be specified and the shearing stress propagated by the system under
observation registered, or the shearing stress can be given and the rate
of shear recorded. So with an apparatus of the first group the method
comes down to the measurement of a force, while with the second group a

speed is recorded, i.e. the method is reduced to the measurement of a
time interval. All the different viscometers, plastometers etc. which are
used in practice do belong to either of these two groups. The best known
representatives of the first group are: The Couette viscometer and its
various modifications.

1 - The Searle viscometer, and its modifications (Mc. Michael visco-
meter, Stormer viscometer, Wolffs turboviscometer).

Neither the measurement of a force nor that of a speed offers insuperable
difficulties in practice. Difficulties, however, arise in the evaluation of the
numerical data in terms of a rate of shear. The dimension of rate of
shear is (T—1) i.e. a difference of two speeds divided by the distance
separating the two planes of different speed. (This applies to laminar flow).
With systems consisting of rheological units which are very small compared
with the dimensions of the measuring apparatus, as in the case of ordinary
liquids, the distance between the two planes can be made very small, namely
of the order of magnitude of 1—2 millimeter, as is the case in an ordinary
Couette viscometer. In that case the rate of shear in one plane is the speed
at which the rotating part of the apparatus revolves while the speed of
the other plane is assumed to be zero, and calculation of the rate of shear
is easy.

Owing to the fact that it was dilatant systems, which formed the starting
point of our investigations any apparatus we intended to make use of
must be appropriate to cope with the properties characteristic for these
systems. In chapter III these particular properties will be dealt with com-
prehensively, but at this place we will mention only those few points
which narrowed our choice of the type of apparatus to be used. The
greatest difficulty we had to deal with was the tendency of the systems
to settle. It seemed most appropriate to us to use an instrument of the
Stormer-viscometer type, which allows a determination of the speed of
a cylinder, rotated by a specified force, to be made, since it is just the
change in behaviour resulting from a variation of the speed which cha-
racterises dilatant systems. In its earliest form the apparatus we used
consisted of a glass rod kept in position by a piece of glass tube; at the
lower end of the rod a paddle — made of wood — was fixed while at
the upper end a kind of drum was fixed upon which a string had been
wound; at the end of the string, which ran over a pulley a pan had been
fixed on which weights could be placed. In course of time this type of
instrument was developed to a slightly higher state of craftmanship, the
apparatus being made of brass, while a ball-bearing provided adequate
guiding of the axis. By means of a screw paddles of various size could
be fixed at the lower end of the axis; the system itself was contained
in a beaker kept in position by a contrivance allowing the beaker to be
removed and replaced in the same position; a scala on top of the axis
allowed the number of revolutions during a certain time to be determined.

Apparatus of a similar type, though of varying shape of the paddle are
occasionally met with in the literature; c.f. the Turboviscosimeter of Droste

When the angular speed of the rotating paddle was determined it was
found that this speed increased during the first rotations and finally
reached a constant value. At a slightly higher weight this constant speed
was reached after a larger number of revolutions. Only the constant value
of the speed was considered as a criterion for the rheological behaviour
of the system under observation. On increasing the weight, however, an
increasing number of rotations was required in order to reach this con-
stant speed. Since the number of rotations of the apparatus is determined
by the length of the thread the apparatus was altered in so far that it
could be worked continually by employing two pans, one of which went
up while the other descended.

In Fig. 6 measurements of a 40,5 % dispersion of starch in a mixture
of 70 % glycerine and 30 % of water have been reproduced. The angular

speed has been plotted against the number of revolutions of the paddle
for various weights. The lenght of the thread allowed the paddle to make
about 16 revolutions; then the weight was transferred to the other pan and
another 26 revolutions were examined. It is seen that at a force of 15 g a

1 Droste und Wollf, Z. angew. Chem. 43, 1002 and 1022 (1930) Kolloid-Z. 55, 81 (1931).
^ Kämpf, Kolloid-Z. 51, 165 (1930).
ä Elliot Mc Millen, Ind. Eng. Chem. 23, 676, (1931).

perfectly constant speed is reached after about 10 revolutions; at 25 g
about 20 revolutions are required for this stage to be reached but then
the speed remains quite constant. About the same speed is attained at a
weight of 35 g; at 45 g, however, a constant speed is not reached even
after 80 revolutions. The determinations can be repeated at will.

We asked ourselves what might be the meaning of this slow increase
of the speed at consecutive rotations. Apparently the conditions are
slightly different after each rotation of the paddle, i.e. the system is
seriously affected by the measuring method itself.

So the conclusions we have come to are obviously this: that in order
to obtain a reliable impression of the rheological behaviour of a dilatant
system the measurement should be carried out in such a way as to allow
the system to be subjected to a shearing motion only once; each following
shearing of the system will bring it in a different condition and should
therefore be discarded.

The most obvious solution for this problem seemed to be the
construction of some type of apparatus which should enable us to
closely imitate the test by which hitherto dilatant systems used to be
tested qualitatively, namely the moving of a spatula through a few cc's of
the system on a watch glass. Two more conditions which should be fulfilled
by the apparatus were: 1 - the container of the system should allow the
system to be easily accessible to being stirred just before starting the
measurement, since dilatant systems show a strong tendency to settle;
2 - the container should be as long as possible in order to secure sufficient
length for reaching the constant speed while its content should not be too
large in order to avoid the necessity of a large quantity of system for each
determination.

The form in which the apparatus, embodying these various requirements
has eventually taken shape is shown in pictures I to V, and figures 7, 8,
9, 10 and 11.

Essentially the instrument consists of a quot;canalquot;-shaped container which
can be closed by a cover on top of which a small quot;carquot; moves, guided by
two grooves; a slot in the cover allows a metal sphere, fixed underneath
the car to be drawn through the centre of the container. This sphere acted
as the spatula in our qualitative test and therefore forms the essential part
of the instrument. The force required to draw the sphere through the

system after this has beeti introduced into the quot;canar is provided by
weighquot; which are placed on a scale connected to the quot;carquot; by means of

' \n pfcture 1 the apparatus is shown ready for making a measurement;
th quot;Squot; may be seen on the extreme left, while the scale is visible on
the extreme right of the apparatus. Picture II shows the container empty,
while rcover separately is shown in picture IV; in this picture the cover
Tsuspended in a special frame which we used in later experiments (c.f^
par'6). The pictLs III and V give further details of the position o
the quot;carquot; on top of the cover, of the construction o the pulley and of
the quot;carquot; itself. The small hook on top of the car (ci. picture V) served
o attaching the thread, by means of a small ring at the end of the thread,
whicLllowed the thread to be easily detachable from the car if necessary.

Cross-section of part of the apparatus, showing the situation of the
quot;canalquot;, the cover and the quot;carquot; when in operation.

Figure 7 shows a cross section of the container with the coyer and the
car in the position for carrying out a measurement. Origmally the con-

tainer consisted of a brass U shaped tube with the two oblique brims
attached to it. Since the structure in this way was too weak to sustain

Cross-section of total apparatus, showing the quot;canalquot; suspended in iron frame.

the cover the tube was suspended in a H shaped profile iron; this is shown
in the cross section of figure 8.
The oblique brims are attached to the side-walls of the container by the

aid of supporting clamps (6 of them on either side soldered to the walls).
Additional clamps secured the container to be firmly fixed inside the
profile iron, details of which, including the dimensions may be gained
from figure 8. The cross section of the quot;canalquot; amounted to 17X17 mm,
while its total length was 85 cm.

Figure 9 shows the cover of the apparatus. On the left a small lever is
shown which allowed the car to be started after weights had been placed
on the scale. A ruler was attached to the cover for determining the distance
over which the speed of the car was timed. By means of a chalk mark we
used to fix the portions over which the speed was determined. The arrow
attached to the car moved just over the ruler.

Figure 10 shows the car; the frame was made of brass, the wheels and
the guiding of the axles are of aluminium; the axles are of steel while the
conical-topped screws which provided the bearing were also made of
steel. Details of this construction may be gained from figure 11. The weight
of the car was 54 g.

Originally the dilatant systems were directly introduced into the canal;
later glass cuvets were made fitting inside the container since thixotropic
systems are very sensitive to traces of electrolytes. This apparatus allows
us to investigate the behaviour of any kind of fluid system upon déforma-

tion, the properties of the system being the decisive factors which determine
the speed at which the sphere moves through the system under the action

of a specified force. In actual fact our apparatus
represents a kind of quot;horizontalquot; modification of
the falling-ball type of viscometer, the difference
being that in our apparatus the force acting on the
system can be modified by simply adding weights
to the scale while the shearing surface — i.e. the
sphere — remains constant. At first a circular plate
was used instead of a sphere of the same radius but
it was found that there was hardly any difference
between the effect of either of these, so the sphere
was chosen. Another point of difference is the fact

that it was the aim of this apparatus to let the sphere move in an quot;infinitequot;
quantity of system, the motive being that if we should try to determine
the resistance against shear of a system consisting of particles of 1 — 10
micron, dispersed in a liquid, in any kind of the usual viscometers a certain
amount of slip at the walls would be inevitable.

In order to check the apparatus a Newtonian liquid was introduced into
it and the speed was determined at various weights. Table I gives the data
obtained for glycerine while Fig. 12 gives the graphic records of the speed

This graph shows that a straight line
is obtained, intersecting the abscissa
at the point 660 mg; this means that
660 mg is the minimum weight required
to just overcome the resistance of fric-
tion of the car when moving over the
cover of the apparatus. This value is not
constant since the friction of the car is
not a perfectly reproducable magnitude,
owing to the craftmanship of the axle
bearings; Had these been of agate in-
stead of ordinary steel then a smaller
and more constant value would no doubt
have been attained. In practice the fric-
tion turned out to have a fairly stationary
value of circa 600 mg.

In connection with table I we should
like to remark that each value of the
speed for one particular weight is the
Fig. 12nbsp;average value of 10 single determinations.

been inserted in this table; On page 17, however, an example in detail will
be given of this way in which each measurement was carried out.

From the data of Fig. \1 the viscosity of glycerine may be roughly
calculated if certain assumptions are made. The dimensions of the appa-
ratus under the conditions of the above mentioned determinations were:
cross section glass cuvet 14 mm; diameter sphere 8 mm. From fig. 12
we see that a weight of 2000—660 1340 mg is required to give the

glycerine at 18° is 12 poise this results proves that the apparatus gives us
data of the correct order of magnitude for substances of a viscosity of
10 poise or larger. If water is introduced into the apparatus a very steep
curve is obtained, while it is by no means certain that the recorded speed
actually is the constant speed at that particular weight. A value is found
of about 1, i.e. about 100 times too large. This is very probably due to
the fact that the sphere does not move in a cylindrical shaped container
— as was assumed in the calculation — but in a glass cuvet, while in
addition it is even inprobable that in the case of a highly mobile liquid
as water the shear should reach from the surface of the sphere to the walls
of the cuvet.

For a highly viscous syrup a viscosity of 1800 poise was found.
These numerical data have been inserted as a rough quantitative guide
rather than a rigorously reliable method for the determination of viscosity.
The main point we want to emphasize is the fact that Newtonian liquids
are characterised by a straight speed/weight relation in this apparatus, the
curves of which intersect the origin. Further results of our measurements
will be used for a qualitative and semi-quantitative interpretation respec-
tively of the phenomena under observation in such a way that any deviation
of a speed/weight curve from a straight line will be attributed to the
pecularities of the system under observation.

The limits of the measuring capacity of our apparatus can be summed
up as follows: The maximum speed which could be recorded was about
20 cm/sec. At larger speeds it was not possible to time the passing of a

certain mark by the car without making appreciable errors. Towards the
smaller speeds, there is no limit in principle, since the slower the motion
of the car the easier it is to obtain accurate readings of the time needed
to cover a specified portion of the apparatus. In practice, however, a
difficulty arose; namely that, when the car moves at small weights at
a small speed the slightest resistance may seriously affect the speed of
the car, causing it to stop. Because of the fact that the weights are small
the force exerted on the car will in such a case be insufficient to overcome
the initial frictional resistance of the car, in consequence of which the
sphere will persist to stop. With systems of higher viscosity this limit
lies at a much lower rate of shear since in that case a relatively high weight
is required for even moving the sphere with a relatively small speed. Any
resistance which in such a case may occur will be more easily overcome.
The following figure may serve to illustrate this:

right, region A is limited by the strength of the thread connecting the car
with the pan supporting the weights; the second factor limiting the region
on this side being the fact that at high weights the torque acting on the

sphere becomes so large that the sphere is partially lifted out of the
system; this turned out to occur at weights over ± 50 g. The situation
of curve a is determined purely by the mechanical qualities of the apparatus.
Reduction of the weight of the car and of the friction would displace the
situation of the curve to the left, i.e. enhance the accuracy of the appa-
ratus.

An impression of the accuracy of the readings obtained with our
apparatus may be gained from the following lines. In order to justly
appreciate the accuracy a number of considerations have to be taken into
account. First of all, the frictional resistance met by the car varies over
each portion of the cover of the apparatus owing to imperfections of the
grooves which keep the car in position. By systematic experiments we were

able to trace those parts of the quot;trackquot; which apparently offered a some-
what higher resistance to the car. These experiments were made by
checking the speed over varying portions of the track at a specified weight:
e.g. the portion from 20—30 cm, 20—40 cm, 20—50 cm etc. Then the
same procedure was repeated at a different weight. Table II gives the
values thus obtained, for glycerine. The time was measured with a quot;three
seconds stopwatchquot;, allowing i/ioo of a second to be read.

Column I shows the weight, col. II represents the portion of the track
over which the car was allowed to move before the speed was checked,

col. Ill represents the portion over which readings of tb;' speed were made,
while col. IV shows the time — in seconds — and col.' ^ the speed calcu-
lated from these data. From these data two conclusionsquot;^i- ay be drawn:
first, that with this particular system a quot;runquot; of about 10 cm is sufficient
to guarantee a constant speed up to a value of the speed of about 9 cm/sec.;
at higher speeds at least 20 cm is required before a constant speed is
reached. Second: the portion of the grooves from cm 40—50 exerts a
resistance larger than that of the rest of the track.

In col. VI the average values of the speed are recorded, in the calculation
of which the values for a quot;runquot; of 0—10 cm and those including the portion
of the track from 40—50 cm have been left out of consideration. The
data of Col. VI have been plotted in Fig. 15 against the weights.

ness of the layer of substance between the sphere and the walls a some-
what larger cuvet was made measuring 25X25 mm cross-section.This cuvet
filled with glycerine yielded the data of table III while the curve represen-
ting these data is shown in Fig. 16. This curve practically coincides with
the curve representing the behaviour of glycerine in the small cuvet as
shown in Fig. 12.

Of course it was not possible to fix
the large cuvet inside the container
which measured only 17X17 mm. In
order to overcome this difficulty a frame
was made in which the cover of the
apparatus could be suspended. This
frame is shown in Picture IV (pag. 14).
This frame in combination with the cover
and a glass cuvet provides a complete
equipment for carrying out measurements
in the way we have described.

Sffect of diameter of sphere.
The effect of the distance between the
sphere and the wall of the apparatus was
also checked by recording curves with
spheres of various diameters while the
dimensions of the cuvet remained un-
altered. Table IV represents the data ob-
tained in this way while the curves repre-
pjgnbsp;senting these figures are shown in Fig. 17.

polated values on the abscissa are different from each other, which means
that the friction of the car was different in each case. One explanation for
the differences in frictional resistance may be found in differences in
weight owing to the increasing weight of the car with increasing size of
the sphere. In Fig. 18 the curves are shown after reduction on the same
origin.

F.S. means: Final Speed, calculated from second portion of 25 cm.
* means: 30 cm instead of 25 cm.

Speed/weight curves of glycerine with various spheres.
From these data may be computed whether our apparatus agrees with

Stokes' law. According to Stokes' law the product of speed X radius of the
sphere should be constant at a constant force. From Fig. 18 the values
of the speed for one constant force — i.e. 1,00 g — have been graphically
determined. In Table V the result is shown.

The values are fairly constant, within 10 % of the mean value which
is as good as might be expected under the given conditions.

However we did not consider the agreement sufficient to allow us to
convert values of different spheres to the unit of surface; thus, when curves
for different systems are compared they will always have been determined
with the same sphere.

An investigation of the properties of various samples of quicksand by
Freundlich and Juliusburgeri drew the investigators' attention to
the peculiar behaviour of some of the samples of sea sand wich had been
taken from the neighbourhood of places where the quicksand samples had
been collected. This behaviour can be easily demonstrated by the following
experiment: 20 g quartz powder of an average particle size of 1—5 fx
which is carefully freed from electrolyte by prolonged treatment with
hydrochloric acid and subsequent washing with water, is mixed with 8,5 cm^
of water on a watch glass.

When stirred with a spatula the system exhibits the following pecu-
larities: when undisturbed, the system will spread out like a drop of an
ordinary liquid. When slowly stirred it will behave in the same way; as
soon, however, as the spatula is moved through the system quickly a
disproportionately high resistance sets in while the system becomes quot;dryquot;
and ceases to behave like a drop of liquid. Immediately after the stress is
released the system will recover its previous appearance and flow easily; it is
possible in this way to cut out a piece of the system with a spatula, but
as soon as this has been done the quot;solid piecequot; will return to its fluid state
again and trickle down the spatula like a viscous liquid. The phenomenon
is entirely reversible and can be repeated at will.

It was found by the investigators that the peculiar behaviour of systems
consisting of sandgrains and water have been the subject of an investiga-
tion bij Osborne Reynolds as early as the year 18852. This author

^ H Freundlich and F. Juliusburger, Quicksand as a thixotropic system, Trans. Faraday
Soc. 168, 31, 769, (1935).

describes the following experiment which is highly instructive as well as
puzzling at the first sight: A rubber ball, which is fitted with a glass tube
on top of it is filled with ordinary sand of an average particle size of 1 —2 mm
after which water is added until the whole ball is completely filled. Now
if the ball is softly squeezed at the place indicated by the arrows — c.f.
Fig. 19 — the water level will immediately fall, the meniscus being lowered
proportionally to the squeezing. The explanation of
this startling phenomenon should be this that the con-
tent of the rubber ball, when filled with sand and
water does not decrease upon squeezing — as it does
when filled with water only — but increases, in con-
sequence of wich the water level wil fall. The reason
why the volume of the rubber ball increases upon
squeezing is this: at the beginning the sand grains in-
side the ball will be in a condition of close packing,
each particle touching a number of other particles.
Upon squeezing, however, this condition of close
packing will be disturbed, the particles are removed
from each other, causing the interstices to increase.
This will result in an increase of the total volume of
grains and water and water will be drawn into the en-
larged interstices. It was this behaviour which Osborne
Reynolds characteristically denoted as quot;dilatancyquot;, owing
to the dilating effect of the sand-water system on
f O b R Idnbsp;rubber ball. Since the mechanism responsible for

the behaviour of the quartz in the experiment of
Freundlich and Juliusburger is obviously the same as the
one in the experiment of Osborne Reynolds the term quot;dilatancyquot;
(adiectiv: dilatant) was reintroduced by the former authors.

It must be mentioned that there is a difference between the experiment
of Freundlich and Juliusburger and the one of Osborne Rey-
nolds in so far that the former experiment can be done only with small
particles while the latter can be carried out with large sand grains only. If a
rubber ball is filled with quartz powder of 1—5 micron it is impossible to
squeeze the ball since the system is far too consistent. On the other hand no
effect will be noted when sand grains of 1—2 mm diameter are stirred with
water on a watch glass.

markable properties of dilatant systems: when a beaker of 100 c.c. is
partly filled with a dilatant paste the mass can be easily stirred with a
glass rod by gently moving it through the mass. When, however, the glass
rod is dropped into the system the mass will solidify at the sudden impact
of the rod, thus reducing the speed of the rod to almost zero, after which
the rod will quietly sink to the bottom of the beaker. Whether dropped
from one or ten feet height does not make any difference, in no case will
the bottom of the beaker be broken by the falling rod.

At the start of our investigations a number of dilatant systems had
already been traced; in the first place a number of powdered minerals were
examined by Freundlich and Jones^ who mention the following
substances to show dilatancy in a marked degree:

while dilatancy in a somewhat lesser degree was observed in the following
cases:

An interesting system, which turned out to be a case of dilatancy was
found to be reported bij Bon^ who described the behaviour of a paste of
wheat starch with a mixture of glycerine and water; we found that a
mixture of rice starch and water exhibits the phenomenon equally well as
quartz and water. Recently a system consisting of carbonyl iron suspended
in carbon tetrachloride which exhibits dilatancy on addition of a drop of
oleic acid has been described by V e r w e y and D e B o e r

investigate the properties of these dilatant systems and it was decided to
start with an investigation of the influence of particle size upon the pheno-
menon. As our object we choose quartz-water, later rice starch-water
suspensions. A quantity of Kahlbaum quartz powder (Quarz, geglüht und
gepulvert) was chosen as the material for these experiments. The crude
material does not show dilatancy on addition of water, obviously owing
to its content of electrolyte. In order to purify the quartz it was treated
with concentrated chloric acid on a water bath until no more iron could
be extracted and subsequently washed with water until the washing water
showed no acid reaction to lacmoid. The quartz was then separated into
various fractions by allowing the particles to settle during various periods.
The average size of the particles in the various fractions was checked by
measurement under the microscope. Fractions were obtained containing
particles of:

smaller than 1,5 micron
1,5-5 „
5-10 „
15—30 „
30—55 „
larger than 50 „

In addition we had at our disposition samples of larger quartz particles
namely: quartz sand, which was obtained by grinding of big particles in
a mechanical agate mortar. These portions were purified in the same way
as mentioned above, and subsequently divided in various fractions by
sieving through cotton sieves. The fractions thus obtained ranged from

Qualitative experiments showed us that dilatancy was exhibited in a
different degree according to the size of the particles. The following
summary may give some idea of this:

The difference between the behaviour of particles of and 50 n is
very marked; the system consisting of the 5/^ particles becomes quite dry
and hard upon quick stirring while it turns liquid immediately after the
stress is released. In the 50^ system, however, dilatancy is much less
pronounced; Upon stirring the increase in consistency is considerably less
than with the 5fi particles while after release of the stress the mass does
not reacquire the fluid character until the watch glass has been slightly
tapped. It was this behaviour which was indicated as quot;passive dilatancyquot;
by Freundlich and Jones (loc. cit. pag. 31).

From these experiments it was learnt that the range of 1,5—5/j. shows
dilatancy the most obviously, so it was decided to first investigate the
properties of this system in detail. In the first place we wished to examine
the flowing properties of quartz suspensions as a function of the con-
centration. To that purpose to 90,5 g of quartz 42,3 c.c. of water was
added, and the system well mixed — conc. 44,7 % by volume —. The
system behaves as a consistent mass; after having been transferred into
the apparatus determinations were made of the speed at various weights.
The same procedure was repeated after addition of water to final con-
centrations of 42,9 and 41,6 %. The data are shown in Table VI. The
speed was determined over portions of 14 cm; each determination was
repeated two or three times. Fig. 20 shows the curves representing the
data of Table VI.

Speed at various weights for suspensions of quartz (1%—5 /lt;) in water; cm/sec.

From these graphs we see that at small speeds there is proportionality
between the speed and the weight but at a certain speed no further in-
crease in the speed is obtained on increasing the weights. This quot;maximumquot;
speed is higher the lower the concentration of the suspension. At 41,6 %
this maximum speed is so high that it can not be registered anymore under

application of the sphere of 4 mm diameter. When this system was
investigated by means of the sphere of 8 mm diameter the curve B8
(Fig. 20) was obtained. On dilution to 40,6 % this system gave the curve
of Fig. 20 a.

For rice starch similar curves were obtained. Fig. 21 shows a curve for
a 44 % — by volume — suspension of rice starch in water. The curves

which are reproduced are just a few examples of the many dozens of
curves of quarz and starch systems which have been determined with
various spheres in course of time. They all exhibit the same shape as the
curves of Fig. 20 and Fig. 21.

In order to understand what they mean attention should be drawn to one
pecularity which does not find adequate expression in the curves. It is
this: Let the diagrammatic shape of the curves be as shown in Fig. 22.
Now if we observe the motion of the sphere at small speeds, i.e. the
points of part a. of the curve then the motion is perfectly smooth. At the
speed of the horizontal part b. of the curve, however, the sphere does
not move smoothly but with periodical variations of speed. Since the
speed was always measured over a distance of 15—25 cm each point of
the part b of the curve represents the mean value of this periodically varying

however, will be piled up in front of the sphere and so reduce its speed
to almost zero. The system will then flow out again, after which the
sphere regains it speed etc.

In this section we will attempt to deduce the meaning of the curves
which have been reported in the preceding one. It seems reasonable to us
to emphasize three points:

2nd: Dilatancy is confined to a rather narrow range of concentrations-
for quartz-water ±41-45 % by vol.; for rice starch-water ± 38-44%!

3rd: Dilatant systems are characterized by a speed/weight curve which
is concave to the weight axis.

On close inspection of the speed/weight curves we come to the con-
clusion that two different mechanisms must give rise to the two sharply
distinguished parts a and b. During the slow motion, represented by part
a the particles apparently are able to slide along each other. When a
certain speed is reached, however, they are forced against each other and
thus form a solid obstacle; immediately after the stress is released they

retake their original position. The predominant condition for allowing this
behaviour being that the particles do not show the least tendency to adhere
to each other, but remain absolutely individual.

These results having been obtained, let us return to our initial problem,
being the question how to find an unambiguous criterion for the degree of
dilatancy of a system. Apparently it is not quite correct to consider the
value of the speed of the horizontal part of the curves as a measure of
the degree of dilatancy; since we must consider a 40 % quartz-water
mixture qualitatively just as dilatant as a 44 % system, — though quan-
titavely different according to the different values of the horizontal part
of the curves — it seems obvious to consider as the correct criterion for
dilatancy the angle between parts a and b of the speed/weight curve. The
more pronounced the difference in direction of these two parts the stronger
the dilatant tendencies of the system. Apparently this angle represents a
criterion for the degree of stability of the particles in suspension.

The next step to be taken should have been a measurement of a suspen-
sion of quartz particles of say 10—15 /jl average size. Unfortunately,
however, it turned out to be practically impossible to make any measure-
ment of such a system since the particles immediately settle down, thus
preventing the possibility of making any determination of the theological
behaviour of the system.

In this connection it may be well to say a few words about the expres-
sion, hitherto used of: quot;a 45 % quarz suspensionquot;. It would be quite wrong
to think of such a system in terms of a 45 % solution of sugar in water
for instance. The latter is a homogeneous system while the former is quasi-
homogeneous only when it is kept in vigorous stirring motion and during a
number of seconds after the stirring has ceased; a number which depends
entirely upon the size of the particles. With particles of 1—5// it may be
for 30—60 seconds while it may be 1—2 seconds for 15—30// particles.
It is this circumstance which seriously interfered with our attempts to
establish a ratio between speed and weight with particles larger than 5 /x.

Another point of importance with dilatant systems is the fact that there
is no influence of time apart from the tendency to settle. Other changes
do not seem to occur. A dilatant system exhibits its behaviour indepen-
dently of the time elapsed since its preparation.

Originally the word quot;thixotropyquot; was chosen to characterize those
systems which are liable to an isothermal gel-sol transformation by the
influence of shaking, while the gel condition redevelops on standing i.

In course of time, however, the conception was extended to all those
systems which are liable to a temporary change of consistency upon me-
chamcal deformation. During the last decade an appreciable amount of
research has been carried out on the nature of the phenomenon and the
optimum conditions under which thixotropy occurs. After the first extensive
investigations of the ferrice-oxyde sol by Freundlich and coworkers
dealing with the influence of electrolytes on the rigidity of the systems
under investigation, numerous other systems have been described showing
the phenomenon in all varying grades of intensity and inconspiciousness
These many substances may be classified, roughly, within a few classes
of kindred systems e.g.

fl - systems which show real sol-gel transition (FegOs sol; copper-
ferrocyanide sol, aluminiumhydroxide)

b - suspensions of small distinct particles in various vehicles (bentonite
clays, paints, ceramic masses)nbsp;'

Numerous investigations have taught us that the thixotropic condition
is intermediate between the sol condition and the condition of a flocculated
system. Naturally the concentration is a factor of decisive importance.
Most of the investigators have made their experiments on the basis of

For a comprehensive treatment of various systems c.f. Scott Blair's book mentioned on
page 85.

the quot;time of solidificationquot;, i.e. the time required by a certain system to
reach such solidity as to just prevent the system from flowing down the
walls of a testtube, upon turning it upside down. It need hardly be said
that this criterion is a relative one, in consequence of which it is quite
usefull for comparing differences brought about in one system, but hardly
suitable for comparison of different systems. The reason why measurement
of the time of solidification must be considered insufficient for completely
caracterizing a thixotropic system is this: Apparently thixotropy is cha-
racterized by the increase of consistency in course of time; So, from the
start only the increase of some magnitude proportional to the consistency
of the system as a function of time will be able to convey a complete
picture of the properties of the system under observation. The time of
solidification can be considered as just one point of this imaginary con-
sistency-time curve, namely the time at which the consistency of the
system is just sufficient to overcome the tendency of the system to flow
down the walls of the tube in which the system happens to be contained.

Now the difficulty of finding a suitable criterion for the consistency of
a thixotropic system is this: apparently the increase in consistency of the
liquified system only effects an increase in the viscosity of the system.
Viscosity, however, can only be measured by shearing the system, while
this very shearing reduces the consistency of the system. So, whatever
determination of the viscosity is made the measuring method itself will
always interfere with the condition of the system. For this reason all
measurements of thixotropic systems with the Couette type of viscometer
are rendered doubtful. In a few cases only authors have tried to circum-
vent the difficulty hinted at; Pryce Jones^ constructed an apparatus in
which the movement over a small angle of a cylinder immersed in the
system under observation is registered, while observations are made as
a function of the time elapsed after stirring of the system has ceased. This
method of observation is undoubtedly able to provide some information
concerning the changes occurring in thixotropic systems, the difficulty
being, however, to translate the results obtained in this way in terms of
a D/ T relation. The movement of the cylinder namely is produced by the
recoil of a torsion wire; which implies that the shearing stress continually
decreases during the movement of the cylinder. Even though it is theo-
retically not impossible to obtain by calculation the concurring values of
shearing stress and rate of shear, this method hardly seems suitable to give
1 Pryce Jones, J. Oil and Colour Chem. Assoc., 19, 295 (1936).

more than qualitative results. Various authors have made investigations on
similar lines, thus compromising between the determination of viscosity
according to the Couette method and the requirement of the thixotrolc
systen. of not being altered by a disturbing shearing motion. We ref

behaviour of thixotropic system in our apparatus. This apparatus namely
enabled us to measure a system at any time after shaking of the system
had ceased, while the breaking down of the system owing to the shearing
motion of the moving sphere does not affect the results since the sphere
moves continually through a fresh - i.e. an undisturbed - portion of
the systo. This however, implies that the sphere should be allowed to
move through the system only one time; after it has travelled through
the system from one end of the apparatus to the other the apparatus
should be emptied, the content thouroughly stirred, the apparatus refilled
and allowed to stand for the same specified time as with the previous
measurement, and then a second measurement could be made with a
different weight on the scale.

This method could be carried out in practice by making use of glass
cuvets which just fitted inside the canal-shaped container of the apparLs
Cuvets of 45 and 65 cm length at an inside cross section of 1 4X1 4 cm
were constructed by cementing together long strips of object-glass'with
de Khotinsky cement. In this way even electrolyte-sensitive systems like
he203 could be safely manipulated. Measurements were made in the
following way: The thixotropic system, contained in a stopp-bottle was
vigorously shaken during a standard period of 15 seconds. Immediately
after shaking had been stopped the cuvet(s) was (were) filled to the brim
and allowed to stand for a specified time. This time will be referred to
as the time of restquot; (R). In order to avoid evaporation during times of
rest the cuvets were kept in glass tubes which just fitted around the cuvets

^ Freundlich and Rawitzer, KoIIoidchem. Beihefte. 25, 231 (1927).
Wolarowitsch and Borinowitch, Kolloid-Z. 77, 93, (1936).

and which were closed with a cork on each end. As soon as the time of
rest had passed the cuvet was placed in the apparatus, the cover adjusted,
a certain weight placed on the scale and the time needed to cover a certain
distance was determined. This gave us one point of the speed/weight curve.
In order to determine other points of the speed/weight curve with the same
time of rest the cuvet had to be emptied and the process was started all over
again, only a larger weight now being placed on the scale. A minor modifica-
tion of this method was applied at small values of the speed. At small speeds
namely, a smaller portion of the system sufficed for the determination of
the speed since a run of a few em's was sufficient for the car to reach a
constant speed. Thus a portion of 5—10 cm being sufficient, up to 4
determinations could be made in a cuvet of 45 cm length.

The minimum time of rest after which determinations could be made
turned out to be 60 seconds, this being the minimum time required for
adjusting the apparatus.

In the first place betonite and Fe203 will be dealt with, since they
number among the best known and most characteristic representatives of
thixotropic substances. A bentonite suspension 6,2 % by weight was made
by adding 300 c.c. of water to 20 g of bentonite. (Bentonite A).

The substance immediately swells and after 24 hours standing at room
temperature a macro-homogeneous system is obtained. The thixotropic
Fe203 systems were made by mixing equal volumes of KCl solutions of
various concentrations and Fe203 sol (Merck) stock solution.

The concentrations will be expressed in final concentrations of electro-
lyte in the system (i.e. half the concentration of added electrolyte solution).
After mixing, the systems were left undisturbed for various times. Since
time influences thixotropic Fe203 systems in the long run the date of
preparing of the systems will be mentioned in each case.

In figure 23 the results are shown for a 6,2 % bentonite solution after
various times of rest. The numerical data are recorded in table VII.

The curves representing these data appear to be practically straight lines,
which, upon extrapolation intersect the abscissa, i.e. a distinct Bingham
yield value is present in these systems. This yield value appears to increase
with increasing time of rest as may be seen from Table VIII. The data
of col. Ill which have been obtained by abstracting 600 mg from the values
of col. II have been plotted in Fig. 24.

Speed/weight curves of 6,2 % dispersion of bentonite
as function of the quot;time of restquot;.

the solution then the solidification process during the first minute after
shaking is stopped will probably take place according to the dotted part
of the curve.

The yield value/time curve does give us a complete picture of the solidi-
fication of the system: according to it there is a quick rise in consistency
of the system immediately after shaking has ceased, followed by a slight
increase during the first 10—15 minutes; no further increase in consistency
is observed. Of course the question may arise whether it is allowable to
extrapolate the speed/weight curves as has been done in Fig. 23. On
page 6 this question has been dealt with and an explanation given of
why it is difficult to obtain values at small rates of shear. There is, however
a way to check the physical meaning of the extrapolated Bingham yield
values. If namely a weight is applied smaller than the extrapolated yield
value no motion whatever of the car should be observed. This turned out
to be the case indeed; even when the sphere was moved artifically it came
to an immediate stop after release of this extra force.

The yield value of a bentonite suspension naturally depends of the
concentration of the solid phase. Determinations were made of the final
consistency of suspensions of various concentrations the results of which

are shown in Fig. 25. The curves represent speed/weight relations after
times of rest of 16, 28 and 17 hours respectively i for systems containing
5 %, 7 % and 8 % of bentonite by weight. According to these curves the
yield value increases on increasing the concentration. There is no indication,
however, that the mechanism of the process of solidification would be sub-
stantially influenced by an increase in concentration of the solid phase.

In Fig. 26 the results for an Fe20.3 solution with 150 mmol KCl are
reproduced. Curves for times of rest of 4, 18, 27V2 and 118 hours are
shown. The first thing which strikes us is the fact that the solidification
process apparently proceeds much slower than in the case of bentonite;
after 4 hours the system has hardly developed any yield value and after
271/2 hours the process has by no means reached its final state. The yield
1 this implies that the equilibrium condition has definitely been reached.

value-time curve which is shown in Fig. 27 has a shape which is definitely
different from that of bentonite. (compare Fig. 24).

On close inspection of Fig. 26 another problem arises.- it appears namely
that the shape of the curves changes with increasing time of rest; during
the first period after shaking the curves are more or less straight lines
while after 118 hours a very distinctly curved part has developed. According
to our conception of pag. 9 this means an increase of bonds of different
strength. However, a curve like the one for R = 118 h brings us in con-

of a thixotropic system. Should it be the lower yield value, the Bingham
yield value or the maximum yield value? In order to find an answer to
this question one more observation should be taken into consideration;
it is this: on close inspection of cuvets with Fe203 systems, after the
sphere has passed through them at a varying speed the following pheno-
menon is observed: if the sphere has travelled at low speed (± 1 cm/sec.)
a broad track is left behind it. Cracks are present in the system and the
whole content of the cuvet has been broken unto big lumps of system.
When, however, the sphere has moved at relatively great speed (up from
15 cm/sec.) the only traces left by the sphere are just a faint line indicating
where the system has been broken up by the thin metal rod to which the
sphere is fixed. Neither cracks nor big lumps of system are present in
the track behind the sphere.

So what apparently happens is this: when moving under the action
of a small weight the sphere has to overcome the forces which keep the
system together. The system will yield to the force exerted by the sphere
at those places where its cohesive forces are smallest. This may be at any
distance from the sphere. By this breaking-down process lumps are formed
in a more or less haphazard way. When on the other hand a big weight
is placed on the scale the sphere will be able to overcome even the strongest

siderable difficulty as to the question which yield value should be taken
as the correct criterion for the characterisation of the increase in consistency

cohesive forces present in the system. Consequently the shearing will take
place immediately at the surface of the sphere, the system even at short
distances from the sphere remaining practically undisturbed. In the latter
case no lumps of system will be formed, the only portion of the system
which is disturbed being the volume of the sphere multiplied by the
distance over which it has moved. This means that the process of shearing
is essentially different at various rates of shear. Apparently the speed at
small weights is mainly determined by the weakest of the cohesive forces
while at higher rates of shear it is rather the frictional forces between the
structural elements which determines the speed/force relation, i.e. a real
quot;viscosityquot;.

The consequence of this state of affairs would be that we can not
definitely state whether thixotropic systems should be characterised by
the change of either one of the yield values as a function of time but that
the change of each yield value as a function of time may give us informa-
tion about a different aspect of the properties of the system under obser-
vation. It is obvious that for comparing various systems the same yield
value should be taken in each case.

In the following, however, we shall meet with systems which lend them-
selves easily for comparison since they possess only one yield value.
Before dealing with that subject, however, let us return to the question
we have raised at the beginning of this section, i.e. the question by what
kind of a D/t curve thixotropic systems are characterised in our apparatus.
The first thing which is learnt from Fig. 26 is the fact that not one, but
several curves all represent the same system; so if we want to express
the behaviour in curves it will be the shift of the D/r curve as a function
of time that may give us information about the system. Leaving out of
account for a moment the question which yield value should be taken as
a representative point for each D/t curve in order to be able to condense
the sheaf of D/t curves of one system to one yield value/time curve, we
must notice the fact that an appreciable difference does exist between
the bentonite and the Fe203 systems. The former show a rapid increase
in consistency during the first 10—15 minutes but after that remain
practically unaltered, while the latter very slowly develop their consistency,
a process which has not yet reached its final state after as much as 118
hours.

Even though we do not exactly know the details of the solidification
process we must accept the conclusion that this difference in behaviour

between bentonite and Fe203 must of more than a quantitative nature
only. When the rate of solidification varies in such an appreciable way
as in this case it seems appropriate to distinguish between the bentonite
type of thixotropy and the Fe203 type of thixotropy. Other investigators
have come to a similar conclusion on account of experiments with thixo-
tropic systems. Pryce Jones^ mentions in his paper that there are certain
systems which solidify rather slowly, while others exhibit a very rapid
rise in consistency. The latter systems he calls quot;false bodyquot;, this being
a term taken from the painters terminology Even though at this moment
it is not possible to trace out exactly the region where false body thixotropy
stops and ordinary thixotropy — like Fe203 — starts, since no sharp
limit separates the two phenomena, this distinction will turn out to be
justified by strong evidence that causes of a different order of magnitude
are responsible for both of the two types of thixotropy. It may be well,
at this stage, to remember which definition was originally given of quot;thixo-
tropyquot; i.e. which were the properties, for the designation of which the word
quot;thixotropyquot; was originally coined. According to Freundlich, those
systems are called thixotropic which are capable of an isothermal reversible
sol-gel transformation. This means that, in order to obtain the epithet
quot;thixotropicquot; two properties are required; first: the capacity of being
liquified upon shaking, second: the capacity of spontaneously developing
a certain amount of consistency in course of time. In a false body system,
in which the final consistency is reached almost immediately after shaking
has ceased, i.e. after the particles have come to rest from the externally
imparted motion, the first required property is definitely present, the
second however, is absent for there is no gradual increase in consistency,
no gel-building mechanism like in a quot;realquot; thixotropic system such as the
Fe203 sol. It just happens that the false body system has a certain con-
sistency of its own, which, owing to the proportion of solid particles and
liquid medium can be easily disturbed.

Now even in a bentonite system a short time up to ±10 min. is required
for reaching the final consistency; in the extreme case of a false body
system it should take practically no time after shaking has ceased to reach
the final condition.

It happened that we were fortunate in tracing a system which exhibits
this false body thixotropy in a very striking way, while simultaneously
gt; I.e. page 39.

2 For a description of the behaviour of false body paints c.f. D. L. Gamble, l.c. page 73.

being of an extraordinary simple nature. Quite incidentally we became
interested in the behaviour of quartz samples mixed not with water, but
with organic liquids. The original idea was an attempt to eliminate the
interfering tendency of the quartz-water suspensions to settle rapidly which
we intended to circumvent by the application of a medium of the same
density as quartz; to our surprise, however, a suspension of quartz in tetra-
bromoethane exhibited a behaviour entirely different from that of quartz
in water. The system showed a rather paste-like behaviour and even at
low concentrations of quartz the system tenaciously stuck to the walls
of the testtube. Upon systematic investigation we found that the very
quartz particles which used to supply us with such good dilatant systems
when mixed with water, showed an entirely different behaviour when
dispersed in any non-polar liquid. Let us take the system quartz-CCU
as an example to demonstrate the essential features of this peculiar be-
haviour. Suppose a few grams of quartz to be introduced into a testtube,
CCI4 to be added and the system to be well mixed by vigorous shaking;
then the system will turn out to be a perfectly fluid mixture during the
shaking but immediately after shaking has ceased the system sticks to the
walls of the tube upon turning it upside down. The following table may
give a complete picture of this test; Carbontetrachloride has been sub-
stitued by cyclohexane which behaves in the same way in this respect.
The data between brackets are the number of cc's of liquid after reduction
to 10 cc of quartz powder.

Behaviour of quartz on addition of cyclohexane. 10 gr. quartz; average particle size 5—10^.
10 cc (26 cc): Paste-like system, non-fluid.
14 cc (37 cc): Slightly thinner though not fluid.
16 cc (42 cc): „ „ nearly fluid.

20 cc (53 cc): relatively thin system, fluid upon shaking; immediately „solidquot; after
shaking has ceased.

22 cc (58 cc): Thin system, srill sufficiently consistent to stick to tube upon turning
upside down.

24 cc (64 cc): Thin system, still sufficiently consistent to stick to tube upon turning
upside down.

26 cc (69 cc): Thin system; approaches limit of capacity to stick to walls of the tube

32 cc (85 cc): Too diluted to stick to the walls of the tube; resembles collection of
flocks dispersed in liquid; shows obvious syneresis upon standing within
few minutes.

This experiment has been repeated with the same quartz in several other
organic liquids and completely the same result has been obtained with:
carbontetrachloride, cyclohexane, benzene, ethylether, bromophorme and
tetrabromoethane. With nitrobenzene only 12 cc were sufficient to give
a perfectly fluid mixture with 10 g of quartz.

Rice starch behaves in the same way and quantitavely the results fall
in the same order of magnitude as may be seen from the following table:

Behaviour of rice starch on addition of cyclohexane.
3g rice starch, average diameter of the grains 5—10 ju- Numbers between brackets are
quantities of liquid after reduction to 10 cc of rice starch.

Still sufficiently consistent to stick to walls of the tube upon turning
upside down.

8nbsp;cc (42 cc): Still sufficiently consistent to stick to walls of the tube upon turning

9nbsp;cc (48 cc): Approaches limit of consistency.
10 cc (53 cc): Limit of consistency just passed.

Apparently an obvious correlation exists between the dielectric constant
of the liquid and the behaviour of the dispersion of quartz particles in the
liquid. The higher the dielectric constant the higher we must make the
concentration of quartz particles in order to reach a similar consistency
of the system, i.e. the higher the diel. const, the more the system approaches
the condition of dilatancy and consequently, the further it is removed from
the thixotropic condition. With ethyl alcohol for instance the quartz be-
haves almost similarly to water.

The reason why this behaviour of quartz with organic liquids like CCU
is so striking is twofold: first because it represents such a remarkable
example of the false body type of thixotropy; second because it drew our
attention to the dominating influence which must be attributed to the
interrelation of solid particle and dispersing liquid since the very same
quartz particles behave so differently according to the nature of the
liquid in which they are dispersed. The latter point will be considered in
detail in § 17 while we deal with the former point below.

striking example of a false body system it seemed natural to check its
rheological behaviour in our apparatus. Actually this experiment was carried
out with a suspension of rice starch, since we had at our disposal a large
quantity of the latter and only small portions of quartz powder. The
behaviour of rice starch is entirely analogous to that of quartz when
suspended in various media. In Table XI the data are recorded while
curve b Fig. 28 represents these data.

Speed/weight relation for system consisting of 100 g rice starch and 170 cc of CCk
Conc. by volume 27 %.

To make comparison easier the speed/weight relation for CCU was also
determined the result of which is shown in curve a Fig. 28. From curve b
we learn two things: first that the system rice starch — CCI4 is represented
by one curve only. Whether a determination is made after a time of rest
of 1, 10 or 60 minutes does not make any difference; the properties of
the system do not alter with time; second: the curve is practically a straight
line and a very obvious Bingham yield value is present, which amounts to
just over 2,0 g; in accordance with this no movement of the sphere took
place at a weight of 1,4, 1,9, and 2,4 g. This curve closely resembles the
diagramatic one of Fig. 2, curve d. Obviously this system provides a
striking example of the false body type of thixotropy; in systems like
these the value of the yield value is determined only by the concentration
of the solid phase. Increase of the concentration increases the yield value;
this means that on increasing the concentration of the solid phase the D/t
curve shifts to the right; up to quite considerable concentrations the
direction of the curve will remain practically unaltered. Not until higher
concentrations (roughly ± 15—20 %) are reached the system will remain
perfectly capable of being liquified by shaking.

Now how can we understand the reason why quartz behaves so dif-
ferently in CCI4 compared with its behaviour in water? The question will
be approached in chapter VI; before doing so, however it is appropriate

§ 16 - CORRELATION OF THIXOTROPY WITH OTHER PROPERTIES
OF THE SYSTEMS UNDER OBSERVATION

Sofar we have only dealt with the rheological behaviour of thixotropic
systems. In order to understand the reason why these systems show this
particular behaviour, however, due attention should be paid to the pro-
perties of these systems as a whole, in order to get as complete a picture
as possible of the conditions which influence thixotropy.

Careful observation of various thixotropic systems by numerous authors
has resulted in tracing those properties which seem to be connected some-
how with the thixotropic conditions of such systems. Freundlichi
starting from the assumption that dilatancy and thixotropy are the opposite
of each other came to the following rough classification of various suspensions:

This hypothetical correlation was checked with some 30 different mine-
rals and generally speaking found to be satisfactory, though owing to the
too qualitative criteria for each of the phenoma, the properties often
appeared to overlap each other. Broadly speaking, however, this correlation
holds.

The idea of linking the properties of a system with the condition of
packing of the particles is frequently met with in the literature concerning
the behaviour of plastic substances.

Several authors propagate the opinion that the relation between solid
matter and liquid vehicle should be the only dominant influence governing

However valuable this point of view may be, the conclusion seems
inevitable that it is not the quantitative relation of solid and liquid matter
only which determines the properties of a suspension, but that there must
be another factor which may in even greater degree contribute to the
final behaviour of the system as a whole. We will not go into a detailed
consideration of the theories concerning the condition of packing but rather
deal with those phenomelogical observations which may supply us with
facts that are characteristic for the behaviour of suspensions in general.
From the table on the preceding page we see that the volume of sedimen-
tation is among these physical criteria that lend themselves for quantitative
observation.

The volume of sedimentation as well as the speed sedimentation
are both magnitudes which in many cases are easily accessible to
quantitative measurement. It seemed appropriate to observe in this respect
the behaviour of quartz in water and compare it with the behaviour of
quartz in CCI4 to find out if an equally dissimilar influence might be
established as we have found in the rheological behaviour of these systems.
To that purpose 40 g of quartz, 1—5 a«, were dispersed in 25 cc of water
resp. CCI4, in ground-stoppered measuring cylinders and allowed to settle
after having been vigorously shaken. The results are summarised in
table XII.

If a system is made up representing the conditions of the sediment of
column VI what are its properties? A 54 % suspension of quartz in water

is a hard dry clod, refusing even to be stirred with a spatula, owing to its
consistency. When contained in a testtube the mass will naturally not flow
down, but stick to the top when turned upside down. Upon dilution with
water dilatancy appears at 45—40 % of solid, and at concentrations below
40 % the systems behaves perfectly fluid.

In addition there is one more feature of the quartz sediment which is
very characteristic: when the cylinder which contains the settled quartz
powder on the bottom of it is laid down horizontally the sediment will
quot;flowquot; as if it were a heavy liquid, and slowly spread itself out in a
horizontal layer in the lower portion of the cylinder; obviously any such
tendency would be prohibited if the sediment exhibited a yield value,
however small. Apparently this fact is in perfect agreement with the
rheological features of the quartz suspensions. For similar observations as
those just mentioned c.f. von Buzagh^.

When CCI4 is added to quartz, quite a different behaviour is
observed. A mixture containing 7 % by volume of quartz particles 1 —4 ^
in CCI4 will be just macro-homogeneous, i.e. the quartz will be homo-
geneously dispersed in the hquid phase. The system consists of flocks of
particles loosely touching each other and enmeshing a large quantity of
liquid in its interstices. The whole system, being so quot;porouslyquot; built up
will easily flow when softly shaken. When the tube containing the system
is laid down horizontally the mass will, however, hardly move; it remains
in its original condition but does not acquire a horizontal level however
long it is left in this position. The properties of this system do not essentially
alter upon either increase or decrease of the concentration of the solid
phase; in the former case the system gradually becomes more consistent,
in the latter case it shows an increasing layer of clear liquid on top of the
quickly settling flocks of sohd particles.

The conclusion these experiments lead to is this that while the quartz
particles may be dispersed in water at liberty they do not exhibit the
slightest tendency to being capable of dispersion in an apolar vehicle; this
behaviour causes immediate formation of flocks in any such liquid, which
will settle quickly while giving rise to a large total volume of sediment plus
liquid enmeshed in it.

§ 17 - GENERAL CONCLUSIONS CONCERNING PROPERTIES AND
BEHAVIOUR OF SUSPENSIONS
In the preceding pages we have been dealing with the results of the
observations on dilatant and thixotropic systems, in connection with flow
as well as their behaviour in general. In the following lines we will try to
deduce from these observations a picture which may make clear how to
understand these phenomena. Already we have pointed out that the be-
haviour of the systems under discussion must be looked upon from the
point of view of the relation between particles and the surrounding liquid
medium. This relation may give rise to the particle behaving as a quot;stablequot;
individual unit with no attraction for its fellow particles or an quot;instablequot;
individual with the tendency to aggregate with neighbouring particles as
soon as possible. From this point of view we are able to understand the
rheological properties as well as the behaviour in general of these systems.

Since we are going to make frequent use of the words quot;stablequot; and
quot;stabilityquot; in the following pages, it may be well to emphasise that what
we are referring to is a quot;stability of the particlesquot;, definitely to be distin-
guished from the stability of the system as a whole. In colloid-chemical
terminology the word quot;stablequot; originally used to be applied to indicate
the capacity af a system to maintan macro-homogeneity for a prolongued
period (of the order of a number of days or weeks at least). When we
think of a hydrophobic sol, for instance, the condition of quot;stabilityquot; of the
system owes its existence to a certain condition at the phase-boundary
particle-dispersion medium; only when the resultant of the mutually attrac-
ting and repelling forces suffices to prevent the particles from aggregating,
then the system as a whole will remain macro-homogeneous. Suppose,

however, that it were possible to make a system in which, while everything
remained the same as in the sol mentioned above, the particles grew larger
and larger then a moment would arise at which the energy content of the
particles, due to the Brownian motion might no longer be able to compensate
their tendency of settling due to the force of gravity, even though the
condition at the phase-boundary particle-dispersion liquid were still the
same as before. In that case we would have in front of us a system which,
though as a whole it did no longer deserve the qualification quot;stablequot;, were
still composed of quot;stable particlesquot;.

In the following pages we shall see that this case is actually present in
certain quartz suspensions and for that reason we shall use the qualifications
quot;stablequot; and quot;stabilityquot; irrespective of the fact whether the system as a
whole happens to be macro-homogeneous or not

According to the introductory lines of this section we were about to deal
with the rheological behaviour of suspensions from the point of view of the
degree of stability of the particles in their surrounding dispersion medium.

This issue comes down to the question: what are the consequences of
the dispersion of solid particles in a liquid as far as the rheological pro-
perties of the vehicle are concerned? According to the experimental
evidence reported in the previous sections we will distinguish between
the two cases just mentioned, of: a - the particles possess a certain stability
in the liquid under discussion, b - the particles are not stable under these
conditions.

In case a the introduction of particles will hardly influence the movement
of the liquid until the concentration of solid particles has become so great
that they mutually touch each other and thus hamper the flow of the
molecules of the liquid.

The particles will behave as a kind of mammoth-molecule amidst the
rheological units of the liquid, but for the rest they will not dominatingly
interfere with the movements of those. Consequently we shall find no
great influence on the viscosity up to quite a considerable concentration.
Neither will the influence show much difference at various rates of shear;
when, however, the rate of shear becomes so large that the big particles
are going to collide then an other factor enters into the system. At this
moment, namely, the movement of the original constituents of the liquid

1 For a concise treatment of the dynamics of hydrophobic suspensions and emulsions c.f.
quot;Hydrophobic Colloidsquot;, being the report of a Symposium on this subject held at Utrecht,
Nov. 1937. Published by D. B. Centen's Uitg. Mij. Amsterdam.

vehicle may be hampered, in consequence of which the whole system
locally acquires a certain degree of consistency. Apparently this is what

A priori it is not quite impossible that at much higher stresses the
congested particles should be forced to be redispersed. In our experi-
ments, however, we have not reached this condition.

Let'us see how far the conditions will be altered when we rob the
particles, which are to be dispersed, of their stability, i.e. case h.

Since the particles tend to aggregate, even in small concentrations they will
form an impediment to the movement of the molecules of the liquid. Since,
upon increase of the rate of shear the influence to redisperse the particles will
equally rise, a relative decrease of the original increase in viscosity of the
system as a whole may be anticipated in this case. This line of argument
will a fortiori hold when the concentration of the solid phase is increased;
so in this case there will be a considerable influence of the solid phase
on the rheology of the liquid, and this influence will decrease with in-
creasing rate of shear.

Now this is exactly what is observed in the flow of systems of the
quartz-CCU type and in those systems in general which are called quot;plasticquot;.
This trend of thought equally explains the properties of these systems in
general. We have found the quartz particles when dispersed in water to
settle slowly and to yield a sediment which quot;flowsquot; upon the application
of however small a shearing stress. Apparently the quartz particles remain
individual beings even in the sediment where they may touch each other
but,, even so, do not cohere. The same quartz particles, dispersed in an
apolar medium, however, lack the quot;stabilised individualityquot;. They con-
stantly tend to join each other and strongly cohere as soon as they have
been able to satisfy this tendency.

By the application of small shearing stresses they do not come off, which
is endorsed by the appearance of a yield value; when, however, the stress
is sufficient to counterbalance the aggregating tendency then the flow of
the system will equal that of the original medium in proportion to the
annihilation of the aggregation of the particles.

Reasoning along this line, we may be able to understand why quartz gives
a small, compact sediment in water and a loose fluffy mass in an apolar
medium. In water the settling quartz particles fall down smoothly and,
owing to their stability they will be able to arrange themselves in the
condition of lowest energy, i.e. take up a position which is as near to that

of dose packing as possible. In CCI4, however, the particles, devoid of
any stabilizing influence, will immediately aggregate at random, fall down
haphazardly and remain in that irregular disarrangement since they lack
sufficient freedom of movement to approach the close packing condition.
Microscopic observation supplies us with more evidence that the stability
of the particles forms the conclusive property of their behaviour; the
quartz particles, when dispersed in water show a lively Brownian motion;
upon dispersion in an apolar liquid, however, not a trace of move-
ment can be discovered since the particles can not be really incorporated
in the liquid. The experiment is most striking when the particles are
watched on a slide when dry, and after addition of a drop of liquid. With
water the system gets into a state of general activity, while addition of
CCI4 does not alter the condition of the particles in any respect. The
outcome of this trend of thought being the paradoxal conclusion
that it is the stable particles which are capable of being wel dispersed
but always retain their tendency to obey the force of gravity and sink
to the bottem of the vessel in course of time, yielding a consistent sedi-
ment. Unstable particles on the other hand resist homogeneous dispersion
since they constantly tend to join at random; therefore they quot;fillquot; a great
volume of the liquid, though in a haphazard way, thus greatly affecting the
consistency of the system as a whole.

Realising these correlations between the stability of a particle and its
influence on the properties of the dispersing liquid, we are immediately
inclined to apply this point of view to such systems as paints in which
similar influences must be of paramount importance. Such systems are
of much interest in connection with the systems under discussion in these
pages because the classic paint industry constantly deals with dispersions
of pigments in a liquid phase, while repeatedly it is noticed that a certain
pigment may be very well suited to be dispersed but will settle in the
container in course of time, while another pigment may require much
more trouble for obtaining a homogeneous mixture but will have far more
influence upon the rheological properties of the dispersing liquid. In § 19
we shall deal shortly with such systems.

It may be well to lay some emphasis on the property of the unstable
particles to arrest a relatively large portion of dispersion-liquid in the
spacious interstices that must necessarily follow the haphazard aggregation
of the original particles.

preceding pages, namely the fact that the quickly aggregating systems
always exhibit the tendency to show syneresis. Apparently the particles,
though mutually cohering, are still aiming at reaching the final state of
minimum energy, supported by the impulses of the liquid-molecules.
Syneresis is a feature which is encountered in practically all thixotropic

So far the characteristic features of thixotropic systems, i.e. the FegOs
type of thixotropy, have been outside our attempts to understand the
phenomena involved. Starting from the assumption that thixotropic systems
belong to those which are composed of dispersions of unstable or partly
destabilised particles, we are faced with the question why the consistency
of these systems depends upon the amount of time elapsed after the dis-
persing influence has ceased to act.

A priori two possibilities seem to come into consideration. First: we
might think of a partly déstabilisation of the particles which has left
them with sufficient repulsive forces to resist immediate aggregation but
which will let them fall as victims to such tendencies in course of time.
Second, we may think of a process in which there is a different influence
exerted by the smaller particles compared with larger ones. It must not be
forgotten that the false body type of systems mainly occur amongst the
coarser suspensions of particles of say 1 — 10/^, while the quot;realquot; thixotropic
systems mainly consist of particles of much smaller size, of the order of
magnitude of 0,1 fi. Since the degree of stability will undoubtedly be a
strong function of the size of the particles this more or less comes to the
same thing as the preceding suggestion. It seems quite possible that the
initial quick rise in consistency of thixotropic systems — as expressed
by the left hand part of the curve of Fig. 27 is due to the aggregation of the
biggest among the particles, while the subsequent slow increase of the right
hand part owes its existence to the smallest of the particles, gradually
settling themselves in the interstices of the big ones. Since a difference in
stability needs not necessarily be accompanied by a difference in size, we
may say in general that it is the divergence of degree of stability of the par-
ticles that induces a system to acquire thixotropic properties, assuming that
the relation solid phase/liquid phase is within the limits for allowing the
system to reach sufficient consistency to exhibit thixotropic behaviour. From
this point of view it becomes understandable why the false body systems
behave in such a one-sided way, showing the transition quot;solid-fluidquot; and vice
versa, but not showing the gradual rise in consistency of the Fe203 type of

system; apparently they are composed of particles so utterly devoid of
the least trace of stability that they must reach their equilibrium position
immediately after shaking of the system has ceased.

Before proceeding to trace out in how far the various phenomena occurring
in practise can be adequately explained from this point of view one point
should be taken into consideration: namely the influence of the viscosity of the
dispersing medium itself. Evidently there must be a difference between a
medium of high viscosity in comparison with a low one. As shown above,
however, the viscosity of the medium should never be considered without
taking into account the specific influences of the medium on the stability of
the particle. It is not so easy experimentally to investigate the influence of a
change of viscosity without altering the system in such a way that the
stability of the particle may be simultaneously affected. Since the viscosity
of a liquid is the outward indication of its interior architecture — un-
fortunately a perfect understanding of this problem in itself is hardly
available at present — differences of this property must per se influence
the stability i.e. the relation between the particle and the surrounding
liquid. So it may seem almost too simphstic to discuss the influence of
an increase in viscosity as if it were a property that can be independently
changed at will.

However, let us try to find out what influence might be expected
from an increase in the viscosity, leaving everything else the same.
Upon dispersion of stable particles in liquids of increasing viscosity
the difference in mobility between the particles and the rheological units
of the liquid will become smaller consequently the influence of the particles
will tend to decrease upon increase in viscosity of the vehicle. In one
respect there will be a difference: as the particles experience a higher
resistance the settling tendency of the particles may be considerably re-
duced. So the result of the dispersion will tend to become of a more
lasting effect in the case of a medium of high as compared with one of
low viscosity. If there is a difference in density between the particles and
the liquid the density of the total system will undergo the influence of
the incorporation of the sohd particles.

The question may arise if in a medium of high viscosity dilatancy can still
occur. A priori there is no obvious reason why, at a sufficiently high con-
centration, the particles should not be forced together by mechanical move-
ment and thus give rise to the local increase in consistency characteristic for
dilatancy. However, the quot;reflowquot; of the system will be slower owing to the

higher viscosity and therefore the behaviour of such a system will offer a less
spectacular alternation of quot;solidquot; and quot;liquidquot; behaviour as compared
with a dispersion in a vehicle of higher mobility. The suggestion has been
launched ^ that an example of such a type of system might be found in
the silica systems described by Bingham^ which show properties very
much resembling those of dilatant systems. In § 19 these systems will be
dealt with shortly.

When unstable particles are dispersed in liquids of increasing viscosity
a more or less similar effect will result as we have anticipated in the case
of stable particles. Since the unstable particles affect the initial mobility of
the liquid vehicle they will enhance the consistency of the system as a
whole, and this effect may be relatively smaller in the case of a high as
compared with a low viscosity of the medium. A higher viscosity of the
medium will hamper the particles in their aggregation-tendency; so the
behaviour of the system will be different in so far that, after it has been
disturbed, it may take some time to reestablish the condition of aggregation
of the particles which existed before the shear took place.

Consequently, an increase of the viscosity apparently tends to induce a
quot;thixotropicquot; factor into a system which only exhibited the false-body
variety of thixotropic behaviour at a low viscosity of the dispersion medium.
Generally speaking, it seems that the influence of suspended particles which
tend to form an additional contribution to the consistency of the dispersing
hquid will be relatively smaller at higher viscosity of this medium (in
comparison with a low viscosity), while the difference in behaviour between
stable and unstable particles tends to be smoothed out at increasing
viscosity.

§ 18 - MEASUREMENTS OF THE RHEOLOGICAL BEHAVIOUR OF QUARTZ
IN ORGANIC LIQUIDS AND SALT SOLUTIONS

In the preceding section we have been dealing with the general aspect
of our experiments and the conclusions they have lead to. Since these
conclusions come down to the conviction that the degree of stability of the
particles is at the root of their rheological behaviour as well as of their
properties in general, it seems logical to check these conclusions by arti-

1 H. Freundlich and H. L. Röder, Trans. Faraday Soc. 34, 308, (1938).
E. C. Bingham amp; J. W. Robertson, Kol!oid-Z. 47, 1 (1929).

ficially inducing déstabilisation or promoting stability and find out if this
results in a corresponding change of the rheological properties of the
systems under observation. Starting from this base, a decrease of the
stability of the particles of a dilatant system should result in an alteration
of the rheological properties in the direction of the false body type of
systems. In order to realise any such investigations two ways are open
from the experimental point of view. We can either investigate the rheo-
logical properties of a quartz suspension in salt solutions of various con-
centrations, or investigate suspensions of quartz in media of varying
dielectric constant since we have found the stability to be a function of
the d.c. of the dispersing liquid. We have made both these types of suspen-
sions, choosing for the former KCl solutions and for the latter mixture
of ethyl alcohol (d.c. 26) and benzene (d.c. 2,3).

Since electrolytes are known to have a destabilizing effect on hydro-
phobic sols a similar action may be anticipated in the case of quartz
suspensions. A qualitative experiment quickly convinced us that this
anticipated effect does exist. Upon addition of a solution of KCl or BaCU
the characteristic dilatant behaviour of the quartz particles entirely dis-
appears. A plastic paste is what results.

Table XIII provides a record of these observations. From it we see that
NaOH up till a concentration of 100 mmol. is of no influence on the
behaviour of quartz, while rice starch remains unaffected by the addition
of KCl solution.

In order to control these results it was decided to make an examination
of the quartz-KCl system in the apparatus.

Let us see what kind of effect destabihsation of the quartz particles ought
to have. In the first place, according to § 17 the concentration at which
the solid particles influence the mobility of the liquid phase should be
lower than in the case of electrolyte-free suspensions. In the second place,
since we have been induced to consider the presence of a yield value a
true criterion for the degree of destabilisation of the particles a yield
value may be expected to be developed by the system.

100 mmol KCl solution. From these curves it may be seen that the mobility
of the system is far less at the same concentration of solid in the case of
KCl solution as compared with water. C.f. Fig. 20.

There is no pronounced indication of the presence of a yield value in
Fig. 29. In addition no vibrating motion of the sphere could be observed
in the quartz-KCl system. From these graphs we see that the typical
quot;dilatantquot; shape of the curves has been considerably reduced and has

degenerated into a weakly concave curvature towards the weight-axis.
Apparently this experiment is just the opposite of the treatment to which
we subjected the quartz before starting the dilatancy experiments, when
we removed any impurities and adsorbed salts which might have been
present in the commercial quartz.

The experiments with suspensions of quartz in alcohol-benzene mixtures
were carried out with the intention of demonstrating the possibility of
gradually changing a false body thixotropic system into a dilatant one, and
of finding out by what changes of the D/t diagram this process might be
accompanied. A similar experiment might have been carried out with
quartz and salt solutions but we preferred the quartz-organic liquid
suspensions because the quartz can be easily recovered by simply
evaporating the organic liquid. In order to eliminate electrolytes from quartz
elaborate extraction and washing would have had to be applied. Benzene
was chosen as a liquid of low dielectric constant since it is easily soluble
in ethyl alcohol.

Some of the curves representing the behaviour of quartz in ethyl-
alcohol (96 %) are shown in Fig. 30. Although the curves are not

as spectacularly representative for a dilatant system as the curves for
quartz-water they show the same characteristic curvature towards the
abscissa. In addition it must be noticed that the concentration of sohd
matter at which these curves have been determined is lower than those
of the quartz suspensions in water.

In Fig. 31 another example of a dispersion of quartz in ethylalcohol is
represented; the same system has been measured with two different

spheres (diam. 4 and 8 mm). From this graph it is obvious that a small
yield value is present in the systems.

dispersed in two different mixtures of ethylalcohol and benzene, (a 50 %
benzene and a 20% benzene solution). Curve I of Fig. 32 very clearly

shows the presence of a yield value in this system since at forces smaller
than those of the extrapolated value for speed = 0 (i.e. 2,1 g) no motion
of the sphere occurs, (c.f. points at 1,4 and 1,9 g. Fig. 32).

The yield value is larger in the 50 % benzene solution than in the 20 %
solution as may be seen from table XIV in which the yield value pro vol.
percent of quartz is recorded.

Generally speaking these curves confirm the anticipated effect of an
increase of the yield value after an increase of the percentage of benzene.

Having adopted the yield value as a criterion for the absence of stability
of the particles this means that the dispersion of a certain substance may
exhibit dilatant and/or falsebody-thixotropic behaviour, depending on the

Numerous curves for various mixtures of alcohol and benzene have been
determined which all show the same shape while the consistency of the
systems increases with increasing content of benzene with the same pro-
portion of solid/liquid phase.

The result may be summed up as follows: 1 - decrease of the stability
of the particles always results in an increase of the yield value. 2 - In-
crease of stability allows the solid phase to be dispersed at a still higher

Starting from a dilatant system the curves representing the various
systems that may result subsequent to a decrease of the stability, are sche-

It certainly would have been desirable to keep the concentration of the
solid phase constant but in that case the systems immediately fall outside
that range of speed-weight relations which could be measured in our
apparatus. A dilatant system for instance at least requires circa 42 % of solid
matter, while thixotropic systems with a content of solid phase of 42 %
are so consistent that their rheological behaviour is of a completely diffe-
rent order of magnitude.

Our investigations of the behaviour of concentrated suspensions as
represented by dispersions of quartz under various conditions drew, in the
course of time, our attention to other members of this class of systems.
Amongst them came paints. Ever since thixotropy has been quot;discoveredquot;
the ordinary paints, consisting of dispersions of pigments in a viscous vehicle
on linseed oil basis, have been recognised as important representatives of
the thixotropic systems. In increasing degree thixotropy has been seen
to be the essential principle which gives these systems the peculiar qualities
which make them suitable in those cases, in which the formation of a film
of narrowly defined physical requirements is aimed at.

Systematic investigations of the thixotropic properties of paints, however,
are so far fairly rare; one of the reasons obviously being that paints are not
particularly convenient systems to deal with in testtubes, nor do they show
the phenomenon in as striking a way as iron hydroxyde sols, bentonite etc.
Thixotropy mainly manifests itself in paints by an increase of viscosity after
the system has been stirred and left to stand.

A systematic investigation has been carried out by P r y c e J o n e s i
by means of his apparatus specially constructed for the purpose. His
measuring technique, which registers the recoil of a cylinder, which has
been given a certain deflection, as a function of the time elapsed after
stirring of the system, reveals the increase of consistency in an obvious
^ I.e. page 39.

way, though a rather complicated mathematical trea.tment would be required
to deduce from his measurements a D/t relation.

From his measurements he draws the conclusion that there are systems
which show a quick increase in consistency upon standing, while others
need more time for quot;settingquot;. So far our observations run closely parallel
with the results of his experiments.

While the number of investigations of paint systems on a basis of
examination of D/t relations is very limited indeed, the amount of ex-
perimental facts offered by the paint industry is almost equally difficult
to handle owing to its huge dimensions. The difficulty is enhanced by the
wild variety of terminology in this field of industry, while the lack of
adequate standards of reference for all those properties which are of
decisive importance for the systems in their practical application, hardly
contribute to a better understanding of those phenomena which are at
the basis of these materials.

When we try from this abundance of observations to deduce a picture,
capable of explaining at least some of the major phenomena involved, we
find that the argument developed in the preceding pages serves us well.

In its most simple form a paint consists of an anorganic pigment dispersed
in a vehicle composed of standoil amp; linseed oil. The standoil forms an
essential part of the vehicle since, by leaving it out, a good dispersion will
never be obtained. Of course, in actual practice numerous substances are
added to the systems to give them all the required properties of a satis-
factory paint, but we will ignore these for a moment and focus our atten-
tion on the fundamental components, pigment, standoil and linseed oil.

Without the standoil the particles may be dispersed in the linseed oil,
with which they form a consistent mass showing a strong tendency to develop
a yield value. However, this system will not be anything like a good paint;
in order to provide the system with qualities that make it applicable as a
coating, standoil has to be added. The standoil exerts on the system what
is known as a quot;dispersingquot; action; in addition it influences the rheological
properties of the system. Obviously the standoil supplies the pigment par-
ticles with a stability sufficient to allow the particles to remain in dispersion
individually. Consequent on this quot;stabilisationquot; of the system its consistency
drops, i.e. the viscosity upon stirring decreases. In course of time, however,
it may rise again. This increase in stability of the particles, on the other
hand, is responsible for the decrease in viscosity which is effected by the
addition of standoil.

A simple experiment, reported by G r e e n i strikingly illustrates this
course of action. When linseed oil is added to lithopone, a consistent mass
is obtained, which does not flow after stirring; on addition of a trace of
poppy oil, however, the mass becomes quite quot;fluidquot; and completely loses
its consistency. Now there is nothing special in the choise of the pigment
in this experiment since it may be carried out just as well with quartz
powder; the poppy oil may be substituted by standoil and in this form the
experiment is still as convincing as before. The addition of the highly
boiled oil in a minute trace in sufficient to quot;individualismequot; the particles.

Essentially the same phenomenon is described by R. V. Williamson^
in a paper in which numerous phenomena occurring in various suspensions
are mentioned ^; he described the behaviour of ZnO dispersed in gasoline,
which at first exhibits false body behaviour, but becomes perfectly fluid
after addition of a few drops of quot;blown linseed oilquot;. quot;The dispersionquot;,
the author adds quot;then remains perfectly fluid after shaking but the pigment
settles rather rapidly to the bottom of the containerquot;, wich, however, is
exactly what we should expect in a case like this.

We found that poppy oil influences a suspension of quartz in CCI4
in the same way; two drops of it to a consistent system of 5 g quartz, of
particle size IV2 /«, in 18 cc CCI4 turned the system into a perfectly
fluid suspension. Apparently the standoil or poppy oil is able to equip the
particle with a factor which stabilises them towards the apolair carbon
hydroxide dispersion-liquid. Here again we see that an increase of the
stability is accompanied by a decrease of the yield value of the system.

The current opinion concerning the rheology of paints has been that the
quot;thixotropicquot; qualities determine the brushing properties of the system.
The decrease of the yield value upon stirring — i.e. brushing — is supposed
to allow the system to flow over the substratum, while the yield value,
developing as soon as the brushing has ceased is supposed to prevent the
quot;saggingquot; of the paint film. However, it will be obvious that the yield value
must not immediately develop, because in that case the brush marks will
have no time to disappear; this means that those systems which have
been indicated as quot;false bodyquot; are not suitable for an ideal paint. Neither
does a system of the FegOs-type represent anything like an ideal paint
since the yield value develops too slowly. Apparently a very special yield

3nbsp;This paper also contains interesting hints at the occurrence of dilatancy.

value/time curve is what is essential for the brushing qualities of a paint.
A systematic investigation of these systems by mkns of an apparatus like
the one we constructed might be able to provide data to check this assump-
tion. In this connection c.f. paper by G a m b 1 e i.

Two more classes of systems which must be described in relation to
dilatancy are the silica systems described by B i n g h a m 2 and in the
second place those systems known as quot;quick sandquot;.

The former has been refered to on page 63 where the suggestion of
Freundlich was reported, according to which these systems should be
representatives of dilatancy in a special way. According to Bingham it
is possible to prepare systems, consisting of a potassium silicate solutioti
plus silicic acid, which behave as a solid piece under quick mechanical
impact, on the other hand continue to flow under however small a

We found that these systems can be easily reproduced by addition ot
hydrochloric acid to a potassium silicate solution and heating the system to
evaporate a surplus of water. The systems are peculiarly brittle. Upon mani-
pulating them with a spatula small pieces will scatter in al directions. Any

Weight	Speed
g	cm/min.
11,0	0,014
21,0	0,016
41,0	0,031
61,0	0,048
81,0	0,069
101,0	0,096

small fragment will, however, immediately start
to quot;flowquot; i.e. round off its angles and tend to
become a sphere. Obviously a yield value is
' not present in these systems. Their resistance
to a quick impact, however, is quite remark-
able. They share their behaviour with pitch
and suchlike bituminous substances. The de-
terminations we made with one of these
systems in our apparatus are represented by
Fig. 35 which shows the data of Table XV.

The perfectly straight course of the curve in this region suggests perfect
quot;Newtonian flowquot;, however paradoxical this may seem at first sight. From
this experiment we must draw the conclusion that, although dilatancy may
occur in systems of more sol than suspension-like character, it is obvious
that the size of the constituting particles will have a dominating influence
upon the intensity of the phenomenon, in such a way that it is doubtful
whether an analogous mechanism is the basis of both forms of appearance.
At first sight this hardly seems probable. It rather seems as if a high

In the second place there are the systems called quot;quick sandquot;, which,
actually were the first to direct attention to dilatancy. In a paper by
Freundlich and Juliusburger^ the authors come to the con-
clusion that quick sand belongs to the thixotropic systems.

Examination of the samples made it clear that in this case we are dealing
with the false body type of thixotropy. Although it may be possible that
quick sands show thixotropic behaviour under certain conditions experi-
mental evidence tends to convince us that the typical quot;quick sand be-
haviourquot;, i.e. the stiffening under sudden impression and the yielding to
prolonged pressure must be due to dilatancy. A dilatant system like quartz-
water or rice starch-water, if in sufficient amount present, will doubtlessly
provide as treacherous a stretch of quot;synthetic beachquot; as the most romantic
novelist's pens aim at convincing us to be the case in reality.

A similar view appears to be supported by R. V. Williams and W.
Heckert^ when they describe the behaviour of potato-starch systems
— which is virtually dilatancy — under the heading: quot;Some properties of
dispersions of the quick sand typequot;. Sofar we have not personally been
able to observe the phenomenon of quick sand in nature.

out those systems in which dilatancy either in one form or another plays a
part in systems of practical importance. There is no doubt that the whole
branch of engeneering and investigation which deals with sand, stones
and water, the constructions of roads, dikes, canals etc. constantly deals
with dilatant systems — without calling them by that name.

In quite a different field of investigation a phenomenon occurs which
definitely reminds us of the behaviour of dilatant systems, though at first
sight there is very little analogy between the systems which show these
phenomena most characteristically. We are referring to the investigations
concerning the behaviour of muscles carried out by J o r d a n i. What he
describes as the quot;snow-plough-effectquot;, representing a periodic increase and
decrease of resistance against deformation of a muscle upon stretching, in
such a way that upon slow deformation the muscle exhibits an elongation
proportional to the force but an alternating extension movement upon
application of higher forces, is completely similar to the phenomenon
exhibited by dilatant systems. Although the linking of these two pheno-
mena may at first sight seem hardly more than quot;just a superficial analogyquot;,
considering the wide difference between a quartz suspension and a muscle
of Metridium Dianthus, there is one factor which points to the possibility
of a somewhat greater similarity between these two classes of systems.
It is reported, namely, that the water content of the muscle may have a
dominating influence upon the behaviour of the muscled Within very
narrow limits of the water content of the muscle the snow-plough-effect
may be exhibited, and disappear upon the slightest transgression of these
limits; which is exactly the same behaviour which we have learnt to con-
sider as characteristic for a dilatant system. In how far this analogy may
endorse the current opinions concerning the structure of tissues may be
left to experts of physiology.

2nbsp;H. J. Jordan, Naturwissenschaften, 25, 17 (1937).
also c.f. Dissertatie P. J. Kipp, Utrecht, 1939.

The literature dealing with thixotropic systems and the measuring
of plastic and consistent systems in general, is of such vast dimensions
that even the faintest approach to anything like a complete survey might
well nigh imply complete quot;drowningquot; of the reader — not to mention
the preceding state of mind of the reviewer. Almost every author who
takes rheology serious will in the course of his paper prove to develop a
terminology of his own, followed by a theory and a mathematical treatment
of his own, in consequence of which the concert of papers inevitably tends
to be of a kaleidoscopic rather than of a coherent character.

When, however, we are going to deal with a few of them in this section,
our choice will be guided by an endeavour to see in how far the previously
developed point of view can be applied to the results of observations of
other investigators, or if it may be of some assistance in explaining hitherto
unsolved inconsistencies.

1 - quot;^Measurement of thixotropy in absolute unitsquot;. G o o d e v e and
Whitfieldi.

The authors give a description of an apparatus for the measuring of
thixotropic systems. The apparatus is a modification of the Couette type
of viscometer. The two cylinder walls of the Couette apparatus have been
replaced by two cone-shaped walls, the outer one of which is rotated by
a motor. By simply raising the inner cone the distance between the cones
can be modified. Thus the idea is to vary the rate of shear by varying
the distance over which shear takes place, while the speed of the outer cone
remains constant and the spring which counterbalances the drag imposed
1 C. F. Goodeve amp; G. W. Whitfield, Trans. Faraday Soc. 34, 511 (1938).

on the inner cone equally remains the same. In this way the inconvenience
is avoided of having to change the torsion wire, which rules out an
ordinary Couette for application to the type of systems under investigation.

A theoretical derivation is given of a magnitude, called the quot;coefficient of
thixotropyquot; which is computed from determinations of the force exerted
on the inner cylinder as a function of the rate of shear. The derivation
starts from the assumption that the viscosity is determined by the equili-
brium between a building-up tendency of the system and a breaking-
down tendency by the rate of shear. From comparison with B i n g h a m's
equation it is learned that the coefficient of thixotropy is similar to the
yield value of Bingham. Measurements of suspensions of carbonblack

in linseed oil are described. Curves of as a function of { i.e. the
reciprocal of the rate of shear are reproduced. A different treatment
is given for quot;highly thixotropicquot; systems. Measurements of these systems
are forecasted.

When we try to estimate the experimental method at its mtrensic
value, we come to the conclusion that there is one condition which
is not fulfilled. The determinations are made in such a way that the readings
were taken after a number of rotations sufficient to guarantee the inner
cone having reached a stationary position. But no account is taken of the
fact that the revolutions preceding this stationary position will have inter-
fered with the condition of the system at the very beginning of the de-
terminations. So what is measured is not the properties of the original system
when undisturbed, but the properties of the partly destroyed system. Now
this will not matter, provided the system is able to restore its initial condition
immediately, if this is the case then the deduction is perfectly acceptab e;
i.e. for a falsebody thixotropic system the method may be succesfully
applied. When however the condition of immediate restoration is not ful-
filled then the evaluations must necessarily lead to erroneous results; i.e.
a system of the FesOs type can not be rightly estimated in this way, owing

In addition, one more objection to the line of approach must be raised.
In deducing the rate of shear it is assumed that the shear really reaches from
the wall of the outer cone (which has a specified speed) to the wall of the
inner cone (which is stationary). This assumption obscures the real diffi-
culty since the real question is what is the distance over which the shear
actually extends. This fact is adequately illustrated in the paper itself by the
references to measurements of quot;highly thixotropicquot; systems. It seems to us

that the primary question to be solved should be the distance over which
shear is propagated when a body — or a wall — moves in an infinite
amount of system.

1 - 7he viscosity of suspensions of rigid particles at different rates of
shear. E. Hatschek amp; Miss Humphrey^-

The purpose of these authors was to determine the influence of the
dispersion of particles on the viscosity of a Newtonian liquid. They
choose dispersions of starch in mixtures of carbontetrachloride and
toluene in order to exclude a difference in specific weight between
dispersed phase and dispersion medium. The conclusion they arrive at
is, that their results do not agree with Einstein's law, but that the visco-
sity is a function of the rate of shear. In the light of our own results wfe
can perfectly understand these conclusions; we can equally realise that
the choise of the system is among the least fitted for checking the law
of Einstein, owing to the aggregation-tendency of the particles in
this particular system. The conclusions of the authors can thus be sum-
marised: 1 - The viscosity of a suspension is a function of the rate of
shear; decrease of the rate of shear results in an increase in the viscosity.
2 - For all rates of shear the increase in viscosity exceeds the increase
in concentration of suspended particles. 3 - The same applies to the
relative viscosity, the difference becomes less the higher the rate of shear.
The experiments lead the authors to the conclusion that there is a strong
mutual influence of the particles. Thus their conclusions are perfectly
consistent with the results of our observations on the same systems.

After an extensive introduction, these authors give a description of the
behaviour of quartz suspensions to which AI2O3 had been added in com-
bination with various amounts of electrolyte. As a result of these experi-
ments, the authors make a distinction between various ranges of thixotropic
gelation. The first range lies at low concentration of electrolyte, 50—
110 mmol NaCl, where quot;hydrophobous flocculationquot; takes place. The
second zone ranges from f 10—200 mmol where a quot;gelatinousquot; flocculation

1nbsp;E. Hatschek amp; Miss E. Humphrey, Proc. Phys. Soc. London, 28, V, 278 (1915).

occurs, with a distinct optimum at 200 mmol. At concentrations exceeding
200 mmol there is a definite tendency to the formation, of irregular flocks
which aggregate and settle at random. In this region syneresis is quite
definitely present.

An explanation of the experiments is proposed by the introduction of
the assumption that suspensoid and hydrophylic components are present,
which are influenced by the addition of electrolytes in a different
way. The total sum of these influences accounts for the behaviour
of the system as a whole. The paper leads to the conclusion that it
cannot be precisely stated whether the different properties of the com-
ponents are due to a difference in chemical composition, or merely to
a difference in size of the particles. Concerning this question, it is not
difficult to mention a great number of papers which all lead to much
this same conclusion. However, it must not be forgotten that it is not
only the size of the particles which is determining for its properties, but
that it is the sum of the variations of properties as function of the size
of the particle that determine its final behaviour. The reason why we
have referred to this paper is that the order of magnitude of the additions
of electrolytes seems to be of more than occasional relevance. We have
observed that with various systems monovalent electrolytes exert their
influence at a concentration of about 100 mmol, while complete floccu-
lation is attained at circa 400 mmol/L. This applies to quartz suspensions,
and to clay suspensions, as well as to certain dyestuff-solutions like benzo-
purpurine. This fact may be understood to be another indication that
there is a collective factor determining the behaviour of all these systems.

In this paper an illuminating description is given concerning the shift of
properties of a system as a function of the size of the constituting particles.
The particles ranged from 14-87 and their thixotropic properties were
investigated by means of mechanically reverted tubes containing the various
fractions. From these experiments it is firmly established that a decrease of
particle size results in an increase of the quot;general activityquot; of the particle.
The systems investigated also very obviously show the presence of rheopexy.

5 - Vber Tiskosität und Plastizität disperser Systeme. N. N. Kula-
koff amp; W ol arowitschi.

A series of highly informing papers has been issued by these authors
under the above heading. Various aspects of plastic systems, mostly
selected from systems of topical interest from the point of view of a Peat-
research Institute are investigated and described. In the paper, mentioned
here, a description is given of the results of various methods of visco-
metry for the examination of peat suspensions. The results dearly demon-
strate that measurements like these are seriously liable to be influenced by
factors that can not be quantitatively appreciated, owing to which rather
divergent results can be attained.

In a paper from the same series a description is given of measurements
of suspensions of printing inks by means of an apparatus of the Searle-
viscometer type. Incidentally the authors mention a system consisting of
naphta soot in hydrocarbon which exhibited a rate of shear/shearing stress
curve concave to the stress axis. Since in the opinion of the authors this be-
haviour was just opposite to the type of curve they were looking for the
system was discarded as quot;inconsistentquot;. It is quite possible, however, that
what appeared to be an unusual behaviour may actually have been a
case of dilatancy. It seems by no means impossible that naphtha soot should
exhibit towards the hydrocarbon dispersion medium a behaviour analogous
to that of quartz towards water. The only detail the authors mention is the
fact that the naphta soot was of very course partide size, which makes
dilatancy even more probable.

An interesting account is given in this paper of a method of measuring
rates of shear by observing the change in resistance brought about in a
nickelwire in consequence of the flowing of the system in which it is
immersed. It does not need to be emphasised that this is a highly inte-
resting measuring method. The results obtained are in dose harmony
with experimental evidence obtained with the more usual devices for
viscometry. This method certainly deserves dose attention for further
devdopment and extension to various dasses of systems.

N. N. Kulakoff und Wolarowitsch. Kolloid-Z. 80, 205 (1937).
2 E. Richardson, Journ. Oil amp; Col. Chem. Assoc. 21, 215 (1938).

In this paper experiments are described which lead to the rather startling
conclusion that a concentrated cane sugar solution exhibits an increase of
viscosity after vigorous stirring. The increase amounts, in the three cases
mentioned in the paper, to 18, 6 and 17% of the viscosity before stirring
took place. After 2 hours standing the effect has disappeared and the
original viscosity is restored. Provided this effect was not caused by the
incorporation of air into the system, it would be a remarkable case and
one might be tempted to assume the presence of some mysterious dilatant
behaviour. Minute crystals might take the place of particles in the system
while the relative high viscosity of the medium might be responsible for
the aggregation, caused by the stirring, to be maintained over the period
of about one hour. The assumption of the presence of crystals is endorsed
by the experimental evidence given in the paper that the viscosity of the
system increases during the first 2 hours immediately after the solution has
been made — at a temp, of 75° —.

Having dealt with the various aspects of dilatant and thixotropic
systems, and having gained from our experiments a certain insight into
the problems that are involved, we should like to conclude our discussion,
with some coordinating remarks aiming at giving a few suggestions con-
cerning the direction in which the investigations might be extended

The measuring technique which we have described is necessarily still
in its infancy, and will need a good deal of development in order to reach
such maturity that it should be possible to deduce perfectly reliable magni-
tudes from the measurements. To reach that goal, first of all the construc-
tion of the quot;carquot; would need general improvement. A new specimen should
be considerably lighter than the one we used. A synthetic plastic
would probably be a suitable material for its construction; in addition
agate cones should be applied for the axle bearings. It might also be useful
to make the apparatus self-registering, the construction of which would
offer no difficulties. The measuring method of thixotropic systems might
be considerably simplified by the application of broad, shallow containers
— in combination with the arrangement of Pict. IV — instead of the glass
cuvets v/e used, which would enable us tOquot; make a number of readings
by slightly displacing the container each time the sphere has travelled
through the system. In this way it will be possible to collect a number of
points of the speed/weight curve at one time of rest — at least a practi-
cally constant time of rest — without having to refill the container after
each determination.

A point which certainly needs closer examination is the question of
how far the shear actually reaches in the system at various speeds. By
making use of a cuvet provided with walls that can be easily shifted, it
should be possible to solve this question quantitatively.

In addition a further investigation of the mathematical evaluation of
the measurements should be made in order to be able, not only to compare
differences brought about in one system in the semi quantitative way in

which we have interpreted our results, but to be also able to compare
systems with consistencies of a completely different order of magnitude.

Further development of the measuring technique therefore seems of
paramount importance since any further progress of our knowledge in
the whole field of rheology virtually depends upon reliable measure-
ments. What is lacking most at the present time is certainly not a collection
of fresh suggestions, but far more a simple method for collecting reliable
data to enable us to check the numerous suggestions, abundantly launched

And, as far as we can see, it should not be impossible to work out
such a'technique on the base of the apparatus described in the preceding
pages, since the size of the container as well as the size of the sphere can
be adapted to any representative of the whole scale of consistencies from
1 poise up to IQio, while both the container and the sphere can be inter-
changed in a few seconds time.

An investigation has been carried out of the properties of dilatant and
thixotropic systems in connection with their rheological behaviour. The
aim of the investigation has been, to establish a relation between the shape
of the rate of shear/shearing stress curve of the systems and their com-
position.

A discussion of the way, in which measurements of these systems should
be carried out is given, and an apparatus is described which allowed the
determination of a magnitude proportional to the rate of shear as a function
of the shearing stress.

It is pointed out that the relation between the particles and the dispersion
medium is of paramount importance for the behaviour of the system as a
whole. Only those systems in which the particles are completely stable
show dilatancy; as soon as the mutual attraction of the particles leads to
aggregation, a system will develop a yield value and thixotropy results.

It appears to be of some practical value to distinguish between two types
of thixotropy: the quot;false bodyquot; type of thixotropy and the quot;Fe203quot; type of
thixotropy, although the difference between these is a gradual rather than an
essential one. The former type is characterised by a momentary increase
in consistency after stirring, while the latter systems solidify gradually.

A consequence of the decisive influence exerted by the dispersing liquid
is, that the same particles which yield a dilatant system when dispersed in
one medium may exhibit thixotropy upon dispersion in another liquid.
Quartz particles turned out to present a striking example; with water a
dilatant system results, while with apolar liquids perfectly quot;false bodyquot;
thixotropic behaviour comes into operation.

A brief survey of the properties of dilatant and thixotropic systems not
directly concerning the flow of these systems is given. Attention is drawn
to the fact that quot;unstablequot; particles, per se, are able to enclose considerable
amounts of liquid.

A treatment in detail of the subjects under discussion may be found in the following
books :

E. Bingham; Fluidity and Plasticity. McGraw-Hill Book Co. 1922.
E. H a t s c h e k; The Viscosity of Liquids. Bell, 1928.

First Report on Viscosity and Plasticity; prepared by the Comittee for the study of
viscosity of the Academy of Sciences at Amsterdam. Noordholl. Uitg. Mij. Amsterdam,
1935.

R. Houwink; Plasticity, Elasticity and the Structure of Matter. Cambridge University
Press, 1937. (German edition, Theodor Steinkopf, Leipzig, 1938).

G. W. Scott Blair; An Introduction to Industrial Rheology. Churchill Ltd. London,

Kulakoff und Wolarowitch; 80.
McMillen, Elliot; 12.
Pryce Jones; 39.
Reed c.f. Haus er;
Reynolds, Osborne-; 29.
Richardson; 80.
Robertson c.f. Bingham;
Röder c.f. Freundlich;
Russell and Rideal; 78.
Verwey and de Boer; 31.
Whitfield c.f. Goodeve;
Williamson; 72.
Williamson and Heckert; 74.
Wolarowitch und Borinowitch; 40.
Wolarowitch c.f. Kulakoff;
Wolff c.f. Droste.

De door Kanamaru c.s. gemeten grootheid „Grenzflachenladungs-
zahlquot; mag niet als maat voor de C-potentiaal der micellen beschouwd
worden.

De door Bergmann op grond zijner experimenten uitgesproken
meening, dat de enzymen de richting in welke een reactie verloopt zouden
kunnen bepalen, is niet juist.

Het is in principe mogelijk de moeilijkheden, die optreden bij de
structuurbepaling op grond van „von Laue-diagrammenquot;, te ondervangen
door de methodiek zoodanig te wijzigen dat de bij iedere reflectie be-
hoorende golflengte berekend kan worden.

De door Neumann c.s. bepaalde waarden van de vormingswarmte
van chroomnitride en mangaannitride zijn te verkiezen boven de door
Satoh berekende waarden.

Het is niet gerechtvaardigd een immobilisatie van dispersiemiddel door
de disperse phase steeds als solvatatie te interpreteeren.

De stabiliseerende werking van organische vloeistoffen electrolyten
op amphotere kolloiden kan als opheffing van een inwendig complex
worden beschouwd.

Jirgenson, Kolloidchem. Beihefte, 44, 285, (1936).
L. Theunissen-Van Zijp, Diss. Leiden 1938.

De bestudeering van het rheologische gedrag van suspensies van an-
organische stoffen in organische vloeistoffen biedt de beste mogelijkheid
tot verdieping van het inzicht in de eigenschappen van organo-solen.

Het is gewenscht dat voor studenten in de Chemie de mogelijkheid ge-
schapen worde om tijdens hun studie met de Industrie in contact te komen.

I Weight: mg	II Run: cm	III Dist.: cm	IV Time: sec.	V Speed: cm/sec.	VI Average Speed: cm/sec.
1100	0-40	40—60	4,18	4,8
	0-30	30-60	5,82	5,15
	0-30	30-20	3,68	5,43
	0-20	20—40	3,55	5,63
	0-20	20-50	5,30	5,66	5,60
	0-20	20-60	7,05	5,67
	0-50	50—60	2,02	4,95
	0-10	10-30	3,84	5,20
	0-10	10-40	5,50	5,45
1200	0—10	10—40	4,20	7,14
	0-10	10-50	5,59	6,79
	0—20	20—40	2,66	7,52
	0-20	20—50	4,05	7,40	7,36
	0-30	30-50	2,80	7,15
	0-30	30—60	4,30	6,98
	0-40	40-60	2,85	7,01
	0—50	50-60	1,55	6,45
1300	0-20	20—50	3,35	8,95
	0-40	40—60	2,35	8,51
	0—20	20-40	2,20	9,09	8,74
	0-30	30—50	2,34	8,50
	0—10	10—30	2.31	8,66
1400	0-20	20-50	2,67	11,2
	0-20	20—60	3,65	10,9
	0—30	30-60	2,65	11,3
	0-10	10-40	2,89	10,4	11,14
	0-10	10-50	3,80	10,5

I Weight: mg	yquot; Run: cm	III Dist.: cm	IV Time: sec.	V Speed: cm/sec.	VI Average Speed: cm/sec.
1400	0—40	40—60	1,87	10,7
	0—30	30-50	1,82	11,0
	0—20	20—50	2,70	11,1
1500	0-20	20-50	2,42	12,4
1500	0—30	30-50	1,61	12,4
	0-40	40—20	1,63	12,3	12,4
	0-10	10—30	1,80	11,1
	0-30	30-60	2,37	12,6
1600	0—20	20-50	2,15	14.0
1600	0—30	30—60	2,01	14,9
	0—30	30-50	1,35	14,8	.14,3
	0—40	40-60	1,44	13,9
	0-20	20—40	1,43	14,0
	0-10	10-40	2,26	13,3
1700	0—20	20-50	1,97	15,2
1700	0-40	40-60	1,26	15,9
	0-20	20-40	1,23	16,3
	0—30	30—60	1,84	16,3	15,9
	0—30	30-60	1,94	15,5
	0-20	20—50	1,98	15,3
	0—10	10—40	2,15	14,0
1800	0-30	30—60	1,76	17,1
1800	0-40	40-60	1,21	16,5
	0-20	20-60	2,39	16,7	16,7
	0-10	10—40	1,90	15,8
	0-20	20-50	1,81	16,6
1900	0—30	30—60	1,49	20,—
1900	0-20	20-60	2,05	19,5
	0-10	10-60	2,34	17,1	19,7
	0—40	40—60	1,02	19,6
	0—20	20-50	1,74	—

Weight: mg	Run: cm		Dist.: cm		Time: sec.	Speed: cm/sec.	Average Speed:
1100	0-	-20	20-	-30	1,42	7,05	^ Q7
	0-	-20	20-	-35	2,25	6,68
1200	0-	-20	20-	-40	2,12	9,45
	0-	-10	10-	-40	3,29	9,15
	0-	-30	30-	-40	1,30	7,70	8,75
	0-	-20	20-	-40	2,23	8,99
	0-	-20	20-	-40	2,37	8,46
1300	0-	-30	30-	-55	3,02	8,30
	0-	-20	20-	-45	2,51	10,0
	0-	-10	10-	-30	1,95	10,3	9,14
	0-	-30	30-	-40	1,09	9,20
	0-	-30	30-	-40	1,13	8,88
	0-	-30	30-	-55	3,07	8,18
1500	0-	-30	30-	-55	1,92	13,0
	0-	-20	20-	-45	1,84	13,6
	0-	-30	30-	-50	1,48	13,5	13,4
	0-	-20	20-	-50	2,20	13,6
	0-	-30	30-	-50	1,52	13,2
1700	0-	-30	30-	-55	1,57	15,9
	0-	-20	30-	-45	1,46	17,1
	0-	-30	30	-45	0,95	15,8	16,2
	0-	-20	20-	-40	1,30	15,4
	0-	-20	20	-45	1,47	17,0
1900	0-	-30	30-	-55	1,37	18,3
	0-	-30	30-	-55	1,36	18,4
	0-	-20	20-	-55	2,15	16,2
	0-	-10	10-	-55	2,49	18,1

Weight:	Run:	Dist.:	Time:	Speed:	Average
mg	cm	cm	sec.	cm/sec.	Speed:
1900	0-20	20-45	1,38	18,1
	0-10	10-45	2,00	17,5	18,5
	0—10	10—55	2,49	18,1
	0—30	30—55	1,24	20,2
	0-30	30-55	1,25	20,0
	0—20	20-55	1,79	19,6
	0—20	20-55	1,84	19,0

Weight mg.	I	B4 II	F.S.	I	Be II	F.S.	I	Bs II	F.S.	I	Bio 11	F.S.
800	3,6	3.4	7,1
900	2,5	2,2	10,6	4,0	4,7	5,7
1100	1,6	1,4	16,6*	2,3	2,2	11,1				6,8	7,4	4,2*
1200	1,3	1.3	19,2	2,1	1,8	12,9				5,3	5,6	5,5*
1300	2,4		20,9	1,8	1,6	14,7	2,3	2,3	10,9	4,5	4,7	6.5*
1400	2,2		22,7	1,5	1,5	16,6	1,8	1,9	13,5	3,1	3,3	7.7
1500	2,0		25,0				2,1	1,9	15,0	2,7	2,8	9,1
1600				2,4		20,8	1,8	1,6	17,6	2,4	2,3	10,6
1700							1,4	1,2	19,2	2,1	2,0	12,2
1900								2,2	22,7	1,7	1.7	15,0
2000								2,1	23,8	1,6	1,4	16,4*

weight	speed
1100 mg 1300 „ 1700 „ 1900 „	6,38 cm/sec. 9,68 „ 15,6 „ 18,1

Diameter sphere (mm)	Speed at 1,0 g cm/sec.	Product speed X radius	Mean value:
B 10	13,6	136
B 8	18,2	146
B 6	20,7	124	130
B 4	28,6	114

200—	100 At	no dilatancy
100—	75	/, u
75—	50	very weekly dilatant
50—	30	ir „ «
30—	15	rather „
15—	10	distinctly „
10—	5	very well „
5—	1,5	highly
lt;	1,5	weakly „

sphere	cone.		weight: (grams)
sphere	cone.	0,700	0,800	0,900	1,13	2,13	3,13	4,13	5,1	6,1	7,1	9,1	11,1	15,1	16,1
B4	44,7			1,2	1,9	2,5	2,4	2,3	2,4		2,5	2,5	2,4	2,6	2.4
84	42,9		3,0	3,1	3,5	4,8	4,8			4,7		5,0	4,5	2,6	4,7
B4	41,6	2,8		8,2	11,7							5,0			4,7
B8	41,6			5,0	7,0	7,7	8,2	8,7		7,7			8,7		8,7
		weight:		0,630 0,680 0,780 0,880 0,980						1,08	1,28
B8	40,6			—	4,3	7.0	8,7	10,7		11,7	15,5

Time of rest: hours	Weight: mg	Time sec.	Speed: cm/sec.
18	1800	2,95	6,8
18	2000	1,80	11,1
23	2000	2,15	9,3
23	2300	1,60	12,5
45	1900	3,80	5,3
45	2300	1,65	12,1

I	II	III
Time of rest	extrap. values acc. to fig. 23	Yield value
1' 10'	1030 rag 1065 „ 1180 „ 1200 „	430 mg 465 „ 580 „ 600 „

Weight	Seconds for 25 cm	Speed, (cm/sec.)
1,4 g	no movement
1,9 „	„
2,4 „	„
2.9 „	2,3	11
3,0 „	1,6	15
3,2 „	1,1	22
3,4 „	1.0	25.

I	II	III	IV	V	VI
Dispersion liquid	aspect of system	height of sediment	time required to reach this final cond.	Habitus of sediment	Concentration of solid phase in sediment
water CCU	bright white bright white	8,5 mm 53 mm	± 6 hours ± 15 min.	hard, compact lose, fluffy	54 % (by volume) 7 % (by volume)

quartz			Rice starch
	on	addition of
mmol.	KCl	NaOH	KCl
0	definitely dilatant	definitely dilatant	definitely dilatant
25	well	tr n	rt n
50	n tr	— —	— —
100	plastic mass; no reflow	ri tt	n It
400	very plastic mass		tf u

vol. % of quartz	% benzene	value of weight at speed = 0 (acc. to extrap. from Fig. 32 amp; 33)	Yield value; (value of prec. col. diminished with 0,6 g)	Yield value pro % of quartz (g)
37,3	20	1,3 g	0,7 g	0,018
38,5	20	1,4 „	0,8 „	0,021
33,6	50	2,1 „	1.5 „	0,045
35,5	50	2,7 „	2,1 „	0,060

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