652
J. E. ARNOLD AND C . F. GOODEVE
(3) FOOTE, BRADLEY, AND FLEISCHER: J. Phys. Chem. 37, 21 (1933). (4) JACKSON AND DERBY:Am. Chern. J. Z4, 16 (1900). (5) JURGENSEN: J. prakt. Chem. 2, 347 (1870). (6) KREMANN AND BORJANOVICS: Monatsh. 36, 923 (1915). (7)MELLOR: Comprehensive Treatise on Theoretical and Inorganic Chemistry, Voi V, p. 460. Longmans, Green and Company, London (1924). (8) SCHMIDT: Z. anorg. Chern. 9, 432 (1895). (9) WALKERAND DOVER:J. Chem. Soo. 87, 1584 (1905).
T H E COEFFICIENT OF THIXOTRCPY OF SUSPENSIONS OF CARBON BLACK I N MINERAL OIL J. E. ARNOLD AND C. F. GOODEVE The Sir William Ramsuy and Ralph Forster Laboratories of Chemistry, University College, London, England Received February 6, 1039 I. INTRODUCTION
It is well known that certain classes of fluids do not obey the ordinary Newtonian laws of flow in that their viscosity is dependent on the rate of shear. Fluids possessing such non-Newtonian viscosi’y a t constant temperature may be divided into three main classes: ( a ) those showing a reversible decrease of viscosity with increasing rate of shesr, a phenomenon which has been called “thixotropy” by Freundlich (1); (5) those showing a reversible increase of viscosity with increasing rate of shear; and (c) those showing irreversible viscosity changes. Colloidal dispersions commonly show non-Newtonian behavior and especially that of type a. Extreme cases of thixotropy are those in which a more or less rigid gel is made fluid by mechanical agitation and again sets to a gel on standing. Goodeve and Whitfield (4) among others (5, 8, 10) have recently shown that if a thixotropic fluid is subjected to a uniform and steady shear rate, u, the apparent viscosity, q , generally follows the empirical equation
.
where qo and e are constants and FT is the force per unit area. If the apparent viscosity is plotted against the reciprocal rate of shear, l/u, a straight line is obtained, the slope of which, e, is called (4)the “co&cient of thixotropy.’’ As deviations from this equation are sometimes found to occur a t low shear rates, the values of the coefficient are taken from the “limiting slope of the apparent viscosity-reciprocal shear rate curve aa the
THIXOTROPY OF SUSPENSIONS OF CARBON BLACK
653
shear rate approaches a high value.” A critical examination (2) of the application of equation 1 has shgwn that the two terms on the right represent independent parts of the apparent viscosity,-a Newtonian and a thixotropic part. 70 has been called (4)the “residual viscosity.” The object of the present work was to investigate the effect of concentration of dispersed phase, temperature, and degree of dispersion on the coefficient of thixotropy of a simple colloidal suspension (carbon black in non-polar paraffin), using a new form of apparatus. 11. DESCRIPTION OF THE THIXOVISCOMETER
Any type of viscometer in which the sample is subjected to a uniform and continuous shear, the rate of which may be conveniently altered over a wide range, may be used to measure thixotropy. h new type of instrument has been developed fulfilling these requirements and has been called a “thixoviscometer.J’ This has been used for the present work. A subsequent model, differing in some details, has been described in a recent paper (3), to which the reader is referred for a critical examination of the design. The instrument is shown in figure 1. A heavy triangular base X, to which is bolted at right angles a length of T-section casting, Y, forms the framework of the apparatus. A gramophone motor R, of the synchronous type, operating on 50-cycle A.C. mains, is mounted on the casting Y as shown and is capable of being swung out sideways to facilitate the interchange of gear wheels on the motor spindle. The whole motor unit may be locked in position by the thumb screw L. A hollow aluminum cone B, of semi-angle 22.5’, is attached coaxially a t its base to a spindle, which is set in ball bearings mounted in a casting, C, bolted to Y. An accurately cut gear wheel G is placed on the lower end of the spindle and this engages with the gear system operated by the motor. It is thus possible, using a range of different gear wheels and employing either single or double reduction gearing, to rotate the outer cone B a t a large number of different speeds. Suspended coaxially inside the cone B is a solid aluminum conical frustum A of the same angle as B, whose upper and under surfaces are cut away as shown. The dimensions of this frustum are given in figure 2. h thermometer, T, of the Anschutz type is placed inside a hollow brass stem attached coaxially to A, and the whole unit is suspended by a steel wire from the torsion head H so that it hangs inside B. The torsion head may be moved in a horizontal plane in two directions a t right angles by means of the screws SS’ in order that the inner cone A may be adjusted until it hangs coaxially with B, the whole instrument, of course, having first been levelled. A mirror ?If, attached to the thermometer stem and used in conjunction with a lamp and circular scale, is used to measure the deflection of the inner cone resulting from the torque transmitted to it
654
J. E. ARNOLD AND C. F. GOODEVE
when a liquid is placed in the cone B and the motor switched on. The whole of the shaded part of the apparatus, together with the inner cone, can be moved vertically up or down by means of the screw head V, the position being read on the head scale, h, on the tube F. The length of the suspension wire, W, is adjusted so that, when the head scale reading is zero, the inner cone is just in contact with the inner surface of the outer cone B and a light twisting motion of the fingers
U X
n
I
FIG.1. An instrument for the measurement of thixotropy in abeolute units
applied to the upper surface of the inner cone just fails to move it. On raising the inner cone by screwing up through one small scale division, the same finger motion should just cause the inner cone to rotate. This method of setting the zero position has been found very satisfactory. This instrument possesses sundry advantages over that described by Goodeve and Whitfield (4), among which may be mentioned the quantity of material required for a measurement, the greater accuracy due to the
THIXOTROPY O F SUSPENSIONS O F CARBON BLACK
655
optical system, and the larger range of viscosities measurable, as the cone speeds can be varied and t)he suspension wires interchanged. The advantages to be obtained by the use of cones rather than cylinders have been pointed out by one of the present authors (3). 111. CALIBRATION O F THIXOVISCOMETER AND CALCULATION OF SHEAR RATE
The instrument is most conveniently calibrated using a Newtonian oil whose viscosity, q , has been accurately determin,J a t a temperature T'C. in a standard viscometer of the Ostwald type. Deflections, a , are obtained for the complete range of head scale readings, h, a t constant outer cone speed, 52, in R.P.M., the zero position of the inner cone being first adjusted as described and the temperature of the oil being maintained constant a t T'C. throughout. From these data, a value for a factor P (which contains the torsion constant of the wire, the distance between the conical surfaces, and factors relating to the geometry of the suspended frustum) may be deduced from the relation P.ff 9=,
The apparent visbosity, q, of any non-Newtonian fluid is defined as the viscosity of the Newtonian liquid which would, a t the same setting, h, and cone speed, Q,give the same deflection, a. The question now arises-is this apparent viscosity as measured equal to a quantity which may be described as the "elemental" viscosity and defined as the ratio of stress to shear rate for an element of volume? I n other words, is the apparent viscosity a property only of the fluid and independent of the apparatus? The following considerations show that it is. Let us first consider the case of coaxial cylinders. If we take a thin layer of liquid of thickness 6L formed by two planes perpendicular to the axis of the cylinders, the moment, 6M, on any ring of liquid of radius r is given by 6M = A . r . F = 2n-r.6L.r.F (3) where A is the surface areit of the ring and F the force on the ring per unit area of surface. This equation is, of course, independent of the nature of the liquid. A Newtonian viscosity, q N , is defined by the equation
F N = qN.0
(4)
dw The rate of shear, u, can be written T -, where w is the angular velocity dr of the ring of liquid under consideration. Substituting for F in equation 3 we have, for a Newtonian liquid, 6N, 1 -.-. dr = qN.dw (5) 2T.6L 7J
656
J. E. ARNOLD AND C. F. GOODEVE
As 6MN is, in the steady state, the same for a ring of any radius, we may integrate this equation between the limits r = ri, the radius of the inner cylinder, and r = re,that of the outer:
we being
the angular velocity of the outer cylinder. If, on the other hand, we substitute in equation 3 the value of F for a thixotropic fluid, given by equation 1, and integrate the resultant equation between the same limits as above, we obtain
This equation describes the behavior, in a coaxial cylinder type of viscometer, of a liquid obeying equation 1 and is essentially the same &s that derived by Reiner and Riwlin ( 7 ) . We thus have two equations (6 and 7), valid respectively for Newtonian and thixotropic fluids under the same experimental conditions, and it is clear that calibratibn with a Newtonian liquid implies that 6MN = 6MT.We see that, for this to be the case,
Le., a non-Newtonian liquid will give a scale deflection corresponding to a Newtonian viscosity, q , given numerically by equation 8. If we let d be the separation between the cylinders (Le., r. - ri), it may be shown d (e.g., using log. tables) that the logarithmic factor is equal to Ti 3d within a maximum error of 0.1 per cent for the greatest value of d / r i (5/31.6)which was used. Therefore
+
has the dimensions of a reciprocal shear rate, and if The term W.(T( ad) the apparent viscosity, q, is plotted against this term, a straight line should be obtained, the slope of which is 8. Conversely, i f we$& experimentally
+
i s a straight line, we know that the vis+ 3d) cosity of a n element of volume i s given by equation 1. that the plot of q against
we(Ti
We may now proceed to a consideration of the coaxial cone instrument in a similar manner. It should, however, first be pointed out that the flow of the fluid in such an instrument is not only in the form of coaxial
THIXOTROPY O F SUSPENSIONS O F CARBON BLACK
657
conical laminae, but must also have a vertical component arising from the centrifugal force. This component can contribute no rotational force to the suspended inner cone, but may have a slight effect on the thixotropic viscosity. It has been calculated that, for the order of shear rates used and viscosities measured in this work, the magnitude of this component,
k
FIG.2. A section of the inner cone showing its dimensions (all to scale, except that the distance d as shown is relatively four times greater than the largest value used). The actual dimensions were T I = 27.0 mm., rl = 35.4 mm., fl = 22.5”.
even a t the greatest value of d used, is quite negligible compared with the horizontal viscous force. If, as before, we take a thin layer of liquid of thickness 6y (represented in section by the shaded area in figure 2),the moment, 6M, on the surface of the “conical ring” of radius r (represented in section by the short thick line) will be given by (cf. equation 3)
6M = 2ar.6y.r.F
(10)
658
J. E. ARNOLD AND C. F. GOODEVE
(the force F is normal to the plane of the paper). If we now substitute the value of F for a thixotropic.fluid, given by equation 1, we obtain
z being as shown in figure 2. It may be seen from the figure that
r = x cos 6
+ y sin B
(12)
and since y is constant irrespective of the value of x, equation 11 becomes
Integrating with respect to r between limits ri and re (cf. equation 7),
where ri and re are as shown and we is the angular velocity of the outer cone. If we now substitute 6y = 6ri cosec 6, equation 14 may be integrated over the length of the cone to give the total moment,
where TI and r~are the lower and upper radii, respectively, of the suspended frustum. Replacing r. by (ri d’) (where d’ = d cos 6, d being as shown in figure
+
2 and itself = h sin
a) and the logarithmic factor by
dl expanding, d’ ’
Ti
+?
and neglecting terms of order
from which we may at once write down t,he corresponding value of M Nfor a Newtonian liquid; thus,
As before, calibration with a Newtonian liquid implies that MN = MT. Equating 16 and 17 and integrating, gives
THIXOTROPT O F SUSPENSIONS O F CARBON BLACK
659
which may be written
rm,which is a function only of d, is obtained by comparing equations 18 and 19 and, when expanded as far as the first power of d, gives
This equation may be applied to the coaxial cone instrument for any given set of geometrical dimensions. For a coaxial cylinder instrument, p = 0” and 7, = 7%= ~ iwhere , ~iis the radius of the inner cylinder. If these values are substituted in equation 20 (the terms in round brackets must first be factorized in order to avoid indeterminates) rm becomes equal to ( ~ i i d ) , which agrees with the result obtained for cylinders in equation 9.
+
For the present instrument, = 22.5’; r1 = 27.0 mm.; r2 = 35.4 mm. and, substituting these values in equation 20, we find T,,,
= 31.6
+ 0.48d
(21)
The number 31.6 represents a radius of the suspended frustum slightly greater than its mean radius, and if we let r 0 = 31.6 we may rewrite equation 19 as
This final equation corresponds exactly with equation 9, which was deduced for coaxial cylinders. As for the corresponding term in equation 9, the term d w.(ro 0.48d)
+
has the dimensions of a reciprocal shear rate and, if the apparent viscosity of a non-Newtonian fluid obeying equation 1 is plotted against this term, a straight line will be obtained, having a slope 8. Hence the value for the reciprocal shear rate which has been taken throughout this work is given by
(In the above treatment, no account has been taken of the difference between the “end effects” with Newtonian and non-Newtonian fluids. This is small (3) when the separation between the cones is small, &s in the experimental work described below.)
660
J. E. ARNOLD AND C. F. GOODEVE
It is to be concluded from this theoretical treatment that values of the apparent viscosity obtained a t small separations with this instrument describe the ratio of stress to shear rate for an element of volume of a fluid obeying equation 1, as is the case for carbon black suspensions. This is confirmed experimentally by the fact that the values of the apparent viscosity and of the coefficient of thixotropy are independent of the method of altering the shear rate (by altering w or d ; see sections V and VIC). A special test of one of the carbon suspensions in an apparatus having cones of semi-angle 11.5’ gave the same values as for the present apparatus. For convenience, equation 23 may be rewritten
where Q is the speed of the outer cone in revolutions per minute, and Q = f ( d ) = f ( h ) . Values of Q corresponding to each head scale reading, h, are shown in figure 3. IV. PREPARATION OF CARBON BLACK BUSPENSIONS
The carbon bIack used for this work was of the grade used in the manufacture of newspaper printing ink. The suspending medium was “liquid paraffin B.P.”,dlsa=0.88 g.per cc., viscosity (HOC.) =2.5 poises. Measurements of its dielectric constant showed that its molecules were effectively non-polar, and spectroscopic examination showed that only a very small amount of cyclic aromatic hydrocarbon was present. Absence of an iodine value showed that it was completely saturated. I n order to standardize conditions, the carbon black was first heated for 2 hr. in an evacuated flask placed in a water bath, thus removing adsorbed water and gases. It was then weighed with the flask still evacuated and the calculated volume of liquid paraffin to make a suspension of the required concentration (by weight) was introduced into the still evacuated flask. After thoroughly shaking, the mixture was transferred to a single roller mill of the type used by paint manufacturers’ and milled until homogeneous, when it was then ready for use. (See, however, section VI B.) V. EXPERIMENTAL PROCEDURE
The thixoviscometer was first adjusted as described in section I1 and the scale reading when the inner cone was at rest in air noted. The carbon black suspension was then placed in the outer cone and the suspended cone lowered into it until the separation between the cones was as small as practicable. It was then possible to alter the rate of shear either (a) by XSupplied by 8. Smith, Ltd., Manchester, England.
THIXOTROPY OF SUSPENSIONS OF CARBON BLACK
661
rotating the outer cone a t a constant speed and varying the separation between the cones by means of the screw head (method l ) , or ( b ) by keeping the cone separation constant and small and varying the angular velocity of the outer cone by means of the system of gears (method 2). The available range was 0.08 to 8 radians per second. In either case the outer cone was allowed to rotate until a steady deflection was obtained before commencing to take readings. In the case of the more concentrated suspensions, it was found convenient to leave the instrument running overnight in order to attain the initial steady state before commencing to vary the shear rate. The steady state for subsequent readings was attained in a few minutes. Except where stated otherwise, all readings were taken a t 18OC. The apparent viscosities were then calculated using equation 2 and plotted against reciprocal shear rate, calculated’from equation 24. For a given suspension, the slopes of the curves obtained by both of the above methods have been found to agree quite well (see table 1). VI. EXPERIMENTAL RESULTS
A . Preliminary experiments (series A ) Mixtures containing 4,5, 6, 7, and 9 per cent by weight of carbon black were prepared separately, and each was milled to as nearly the same degree as possible by keeping the setting of the mill constant throughout. The results obtained for each of these suspensions show that 0 is a marked function of the concentration of carbon black. The values of 0 and 70 are given in table 1.
B. Effect of milling It is important in standardizing the procedure to study the effect of successive millings on the same suspension, and accordingly a 6 per cent mixture was prepared for this purpose. This mixture is not very homogeneous before milling, since it contains large and irregular aggregates of carbon black. Measurements for such a mixture were not attempted, as it is probable that the non-homogeneity would render them quite irreproducible. The mixture was therefore milled very lightly in the single roller mill until thoroughly mixed, placed in the thixoviscometer, and a series of readings taken. It was then removed, remilled more heavily, and a further series of readings taken. This process was repeated, giving the suspension successively heavier millings, until a t a fourth milling the “shearing plate” was hard down upon the roller. A final fifth milling was then given. The results are shown in figure 3,-the deflection CY being plotted against the head scale reading h. The values of the factor P (equation 2) and Q (equation 24) for each head scale reading are also shown. The
662
J. E. ARNOLD AND C. F. QOODEVE
derived apparent viscosity-reciprocal shear rate curves are shown in figure 4. It is seen from these two figures that the values of the deflection and of the apparent viscosity increase with milling until the third milling, after which they are effectively constant. Also, the coefficient of thixotropy, e, increases to a constant value. This means that it is possible, with a given milling apparatus, to mill a suspension to constant thixotropy. During the course of the millings, horizontal ridges were observed in the issuing mixtures,-a phenomenon well known to the printing ink and I
I
I
30
2.5
2 .o
1 c
-e 0
-
20
d W
1.5
n
5
P
0,
x
*)
1.0 U
io
9 0.5 0
0
0.5
I .o
Head Scdle Reading h-cms.
FIG.3
.2 RcCiDf'OCdl
1.5
.4
Shedr R d l e d
.6
- seconds _- - 1
w('o+ 0 . 4 8 d )
Qn
FIG.4
FIG.3. Observations on a suspension (6 per cent carbon) subjected to successive millings (curves 1 to 5 ) . The apparent viscosity is obtained by multiplying the deflection a by the value of P for the same head scale reading and dividing by the number of revolutions per minute, Q. Likewise, the shear rate corresponding to any head scale reading is the product of Q and 0. FIG.4. Results derived from those shown in figure 3
paint manufacturer. The more thixotropic the mixture, the more pronounced were the ridges. C. Eflect of concentration For experiments subsequent to the preliminary ones the following procedure was adopted: A 7 per cent mixture was prepared in the usual manner and milled to maximum thixotropy. Its carbon black content was checked by analysis (repeated washings with petroleum ether and weighing), and its viscosity measured a t a number of rates of shear, vaned
663
THIXOTROPY OF BUBPENSIONS OF CARBON BLACK
by methods 1 and 2. The required quantity by weight of paraffin was added to reduce the concentration to 6.5 per cent, the mixture milled, its carbon content again checked by analysis, and the measurements re-
I
0
I
I
I
.2 .4 Reciprocal Shear Rate
.6
- seconds
FIQ.5. Results for suspensions of various concentrations TABLE 1 Values of the residual viscosity and Ihe coeficient of thizotropy for series A , B , and C
Method 2
e dynea per
p e r cent by
weight
em.'
9
163 70
7 6.5 6 5 4 0
46 21 18.5 1
_-
?o
poisea
13.7 5.5 4.5 6.5 5.2
e
70
9
cm.2
poisea
dynca per
63 52 45 30.5 21
5.2 5.8 4.1 3.5 3.1
____ __ dyncspcr
-~ 0 = 0; 7 = 2.5
1
Method 1
cm.9
65 52 41
28 18.5
7.0 5.8 5.5 4.9 4.2
62
6.8
45 30.5 21
4.1 3.5 3.0
poises
peated. The mixture was then diluted successively to various lower concentrations, using the same procedure. The results obtained are shown in figure 5 , and the derived values of 70 and e are given in table 1 (series B).
664
J. E. ARNOLD AND C. F. GOODEVE
A new 7 per cent suspension was prepared 3 months later and the series of measurements described above repeated, using the same procedure. A new sample of the liquid paraffin was used. The values of 7 0 and e for this series (C) are also given in table 1. It will be seen from this table that, except for the preliminary series (A), the reproducibility of the measurements is good. (In series A the suspensions were not milled to constant thixotropy and their composition was not so accurately controlled.) This shows that it is possible to make accurate quantitative measurements on colloidal systems, provided that the procedure is standardized.
.. /
O I!
.;
.1
.$
Reciprocal Shear Rete
;.
- 5ecs.
Viu. 6. The effect of temperature
It will be observed from figure 5 that the curves for concentrations less than 4 per cent do not follow equation 1 over an appreciable range of shear rates. No values of 0 or qo have therefore been calculated. These curves are discussed in section VIIF.
D. Effect of temperature In each of the three series of measurements already described, the temperature of the suspensions was maintained constant at 18°C. For the 5 , 7, and 9 per cent suspensions (series A), values of 0 have been obtained at other temperatures in order to see whether the coefficient is
THIXOTROPY OF BUSPENd6NB OF CARBON BLACK
865
altered. The outer cone containing the suspension was heated with a Bunsen burner and allowed to stand until a steady temperature was attained. It was necessary only to obtain four or five points to establish 1 the slope of the 7-- curve; the cone separations could be altered and the corresponding scale deflections noted before any appreciable temperature drop occurred (even when the temperature was considerably in excess of that of the room). The curves in figure 6 show the results obtained. It may be seen from the figure that increase in temperature decreases the apparent viscosity by an amount which is practically independent of rate of shear. The fractional rates of change of the residual viscosity and of the coefficient of thixotropy with temperature are shown in table 2, together with that of the oil medium. It is seen from the table that the temperature coefficient of the residual viscosity is of the same order of magnitude t w that of the oil, whereas for the coefficient of thixotropy the TABLE 2 Temperature coeficients of the residual viscosity and the coeqicient of thizotropy CONCENT%4T3ON
I
p a cent
9 7 5
-0.041 -0.057 -0.11
0
-0.074
-0.0047 -0.0032 -0.02
effect of temperature is many times less. The temperature coefficients, being differences, are subject to a higher limit of error than the individual observations. VII. DISCUSSION
A . The structure of carbon black suspensions It is now generally agreed that the phenomenon of thixotropy involves a breaking down and a subsequent reforming of some type of structure. Opinions differ, however, as to the precise nature of this structure. Some investigators favor a non-contact structure held together by long-range forces of the van der Waals’ type between the colloidal particles. Others postulate the formation of a “scaffolding” structure, in which the particles are actually in contact. In the case of carbon black there is considerable evidence for the second t,ype. Carbon black particles are plate-like with strong valence forces around the edges. Therefore they have the possibility of building up large structures enmeshing considerable quantities
666
J. E. ARNOLD AND C. F. GOODEVE b
of the suspending medium. Such a structure might be likened in this case to a “house of cards.” McDowell and Usher (6) have found that a 1 per cent carbon black suspension in non-conducting organic solvents conducts the electric current when allowed to stand, but ceases to do so on shaking. The phenomenon is apparently indefinitely reversible (the observations of McDowell and Usher have been qualitatively confirmed by the present authors). The conductivity of such suspensions could only be explained by direct contact between the particles, chain-like structures being formed and thus providing a series of continuous paths from one electrode to the other. A structure involving direct contact is shown to be extremely likely by measurements made on the bulk density of the carbon black. When carbon black particles were allowed to settle out of the air, they occupied a volume corresponding to a density of 0.075 g. per cubic centimeter. As ordinarily obtained, carbon black has a concentration two to three times this value. In the dry bulk condition each carbon black particle must be touching other particles a t a number of points. It would seem, therefore, that in liquid suspensions (density about 1) in which the concentration is 7.5 weight per cent or higher, the particles are forced into touching one another a t many points,-there is not room for them to be separated. As the dry particles, even when allowed to settle out of air, are somewhat compressed by gravitational forces, touching of particles is to be expected a t concentrations somewhat lower than 7.5 per cent. B. Efect of milling The particles of carbon black in a non-milled mixture are in the form of large and irregular aggregates of ultimate plate-like particles. These ultimate particles, the size of which varies to some degree with the grade of carbon black, are extremely small, probably smaller than those of any other known pigment. Recent measurements (9) suggest that the value is about 0.06 p , As the force breaking up the aggregates in milling decreases as the square of the diameter, it is unlikely that they are ever resolved to ultimate particles. The fact that the suspensions can be milled to constant thixotropy indicates either that the milling is unable to break down the particles any further, or simply that further breakdown does not alter the values of the apparent viscosity and thixotropy. The increase in viscosity and thixotropy with milling is probably associated with the fact that the actual number of particles able to build up a structure has increased. On a number of occasions suspensions several months old were reexamined, and it was found that the coefficient of thixotropy had decreased by 10 to 20 per cent. Remilling brought the coefficient back to its former value.
THIXOTROPY OF 8USPEN8IONB OF CARBON BLACK
667
C. T h e residual viscosity The residual viscosity is that a t infinite shear rate, Le., when the thixotropic effect is absent. It may be seen from tables 1 and 2 that it is somewhat greater than the viscosity of the medium and its temperature coefficient is of the same order of magnitude. I t is well known from hydrodynamical considerations that independent solid particles increase the viscosity by an amount proportional to their volume concentration. The proportionality const ant increases with the anisometry of the particles. The viscosity is Newtonian, and the particles act through the dispersion medium. The observed values of the residual viscosity and of the temperature coefficients can be completely accounted for by this hydrodynamical mechanism. D . T h e impulse theory of thixotropy It has recently been shown by one of the authors (2) that the resistance to flow of a non-Newtonian fluid can be divided up into two parts, operating by different mechanisms. The first part is “Newtonian,” that is, the force is proportional to the rate of flow, or the viscosity coefficient is constant. The second part is thixotropic, that is, the force is approximately constant, independent of the rate of shear. This thixotropic behavior has been explained by considering the impulses conveyed from a moving layer to a non-moving layer by interference of the colloidal particles. It is seen in section VIIA that the particles of carbon black have a marked tendency to link together. When a shearing force is applied to the system, the link between a fast and a slower moving particle will be stretched and a force will be applied to the latter. When a critical point is reached, the link will break. The slower moving particle will thus have experienced a force for a definite period of time, Le., it will have received an impulse. After the link has broken, the faster moving particle will pass on to form a link with another slower moving particle and the whole process will be repeated. It has been shown that the value of each impulse is inversely proportional to the shear rate, while the number of impulses is proportional to the shear rate. The total force, which is the product of the impulse value and the rate of impulses, is therefore a constant, independent of the shear rate, and the apparent viscosity, which is F / u , decreases with increasing shear rate. The theory gives a quantitative description of the phenomenon of thixotropy and shows the conditions under which it is to be expected.
E . Relation between coefiient of thixotropy and. concentration of carbon black It is possible to deduce from the impulse theory the relation to be expected between the coefficient of thixotropy and the concentration. The rate of formation of links, or the number of impulses per second, given
6G8
J. E. ARNOLD AND
C. F.
GOODEVE
by one particle will be proportional to the concentration of particles in the layer passing over it. The number of particles receiving impulses from the passing layer will also be proportional to the concentration. The total number of impulses per second between the layers is therefore proportional to the square of the concentration. That this is the case for the system carbon black-non-polar paraffin may be seen from figure 7, in which the logarithm of the coefficient of thixotropy taken from table 1 is plotted against the logarithm of the concentration. It is seen that between concentrations of 4 and 7 per cent, inclusive, the coefficient is proportional to the square of the concentration, but rises more rapidly at higher concentrations. The values a t lower concentra-
FIG.7. Showing that the coefficient of thixotropy is proportional to the square of the concentration. (Points for series BIand C in most cases coincide.) tions are rather indefinite, and a t the higher concentrations agreement is not to be expected, in view of the fact that the particles are crowded very closely together. It would appear, therefore, that the impulse theory in its present state of development can explain the relation between 6 and concentration. F. Low concentrations
If the concentration of the suspended particles is low, a continuous structure of links throughout the fluid (in an unsheared state) will not be possible. It is probable that isolated groups or aggregates of linked particles are formed, the size of which is limited by the low thermal diffusion. Shearing slowly will result first of all in these aggregates being orientated in the usual way and very little breaking of links will occur.
THIXOTROPY OF SUSPENSIONS OF CARBON BLACK
669
When the shear rate becomes sufficiently high, however, these links will be broken as before, end a decrease in viscosity will result. Such a suspension will therefore behave very nearly as a Newtonian liquid until high 1 shear rates are attained, when the q-- curve will drop sharply. This is what happens for concentrations of 3 per cent carbon and less, as may be seen from figure 5. Apparently the 4 per cent curve represents a trawition type before normal thixotropy is shown. A slight irregularity appears in all of the curves. At low concentrations we therefore have two characteristic viscosity values for a given suspension,-the residual viscosity and the limiting viscosity a t low shearing stresses. de Waele and Din& (11) have observed similar “high and low shearing stress mobilities” in work with cellulose nitrate sols.
G. The temperature coeficient The low value of the temperature coefficient of thixotropy compared with that of viscosity is to be expected from the ‘[impulse theory.” A process in which the links between particles are broken and reformed by a shearing motion does not depend upon thermal energy and is therefore independent of temperature. I n the full treatment of the theory (2) it is shown that in a case where the heat of formation is not too large compared with k T , the life of the links will be governed by thermal energy; the viscosity is then Newtonian and strongly temperature-dependent. High values of the link energy lead to high viscosities. In colloidal solutions, however, there are generally fewer links per unit volume and a structure by which energy can be concentrated on each link. In these cases links are broken only by the shear; the viscosity is thixotropic and independent of temperature. The results for carbon black suspensions described in section VID indicate that the impulse theory may be applied to this system and that the link energy is great compared with k T . It may be of the order of magnitude of a carbon-carbon bond in graphite. SUMMARY
An instrument for the measurement of anomalous viscosity has been described, together with its calibration and mode of use. An analysis has been made of the flow of thixotropic fluids, and it is shown that true elemental viscosities may be measured in absolute units. Suspensions of carbon black in liquid paraffin have been studied, and it has been found possible to mill them to give constant and reproducible results. It has been found that over the range 4 to 7 per cent carbon black, the value of the coefficient of thixotropy, 0, increases as the square of the concentration.
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V. N . IPATIEFF, B. B. CORBON AND J. D. KURBATOV
Temperature has been shown to have little effect on 0 over a fairly wide range but the normal large effect on the residual viscosity. The results have been interpreted in terms of the “impulse theory” of thixotropy. The authors desire to record their indebtedness to Mr. A. C. Stevenson, of this College, for his valuable advice, and criticism of the mathematical treatment in section 111. REFERENCES
(1) FREUNDLICH, H.:Thirotropy. Hermann et Cie, Paris (1935). (2) GOODEVE, C. F.: Trans. Faraday SOC.86, 342 (1939). (3) GOODEVE, C. F.: J. Sci. Instruments 16, 19 (1939). (4) GOODEVE, C.F., AND WHITFIELD,G. W.: Trans. Faraday SOC.34, 511 (1938). (5) KUHN,W.: 2. physik. Chem. A161, 1 (1932). (6) MCDOWELL, C. M., AND USHER,F. L.: Proc. Roy. SOC.(London) A151, 573 (1931). (7) REINER,M., AND RIWLIN,R.: Kolloid 2.43,1 (1927). (8) Rossr, C.:Gam. chim. ital. 67, 691,751 (1937);68,3 (1938). (9) SWEITZER, C. W.: Official Digest, Federation of Paint and Production Clubs, February, 1935;and Messrs. Binney & Smith & Ashby, Ltd., London. (10) SZEQVARI, A,: 2. physik. Chem. 100, 175 (1924). (11) DE WAELE,A., AND DINNIB,G.: Physics 7, 426 (1936).
MIXED COPPER-CHROMIUM OXIDE HYDROGENATION CATALYSTS V. N. IPATIEFF, B. B. CORSON,
AND
J. D. KURBATOV
Research Laboratories, Universal Oil Produels Company, Riverside, Illinois Received October 3, lQ3Q INTRODUCTION
It has been shown (7) that pure copper does not hydrogenate benzene a t ordinary pressure at 225°C.) but that the presence of certain impurities enables it to do so. It was thirty years ago that the senior author discovered this promoter action in hydrogenation (5, 9). Pure copper is able to hydrogenate benzene only under superatmospheric pressure. This paper describes a series of coprecipitated copper-chromium oxide catalysts whose activities were evaluated by the hydrogenation of benzene and of isopentene at ordinary and superatmospheric pressures. Under the test conditions both of the pure components-copper and chromium oxide-were inactive, but as chromium oxide was added to copper the activity rose abruptly to a maximum at 5 per cent of oxide, and then
