Consistency of Concentrated Suspensions ~
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The consistency of a dispersed system, in which the concentration of the dispersed phase is so great that the particles are in contact with each other, is influenced by the particle size and particlesize uniformity of the dispersed material. When the phase volume ratio of the system is maintained constant, a decrease in particle-size uniformity is accompanied by a decrease in consistency because particles of various sizes assume a more loosely packed condition than do those of the same size. The fewer points of contact and larger films of continuous phase between the dispersed particles result in a system of lower consistency. The effects of particle size and particlesize distribution are illustrated by data obtained on systems composed of mineral powder dispersed in asphalt and of asphalt dispersed in aqueous soap solutions (bituminous emulsions).
RALPH N. TRAXLER
The Barber Asphalt Company, Maurer, N. J.
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HE control of the consistency of food, pharmaceutical and bituminous emulsions, pastes of all kinds, greases, clay slips, etc., is of great practical importance. Although methods for measuring the flow properties of these suspensions and dispersions have been fairly well established, there is not a very clear understanding of the means by which the consistencies can be controlled and regulated other than by alteration of the phase volumes. This situation probably exists because the properties influencing and governing the consistencies of concentrated dispersed systems have not been completely determined. In dispersed systems two conditions may exist: (a) where the dispersed phase is so large in amount that the particles are in some state of packing, and ( b ) where the quantity is so small that the particles of dispersed phase are not in constant contact with each other. Theories based on the work of Einstein (3) have been used by numerous investigators in studies of the latter class of systems. Lawrence (6) pointed out that Einstein’s equation could not be applied to systems exhibiting anomalous or non-Newtonian flow because the equation postulates no mutual interference of the particles. In the discussion to follow, only systems containing a high concentration of dispersed phase (class ta) will be considered. Phase volume is an important factor in regulating consistency, since the fluidity of an emulsion or suspension can be increased within certain limits by the addition of continuous phase. However, the consistency may be regulated, without changing the phase volume ratio, by alterations of the particle size or size distribution of the dispersed phase. Terry, Gabriel, and Blott ( l a ) patented the production of a fluid “pourable” bituminous emulsion of high bitumen content by the creation of both large and small dispersed particles in the same system. I n their United States patent the low viscosity was ascribed t o the packing effect of the large and small particles. Gabriel (4)discussed the process further, but did not explain the mechanism by which the change in particle-size distribution influences consistency.
interstice decrease until twelve-point contact is attained. The following table is taken from the work of Manegold, Hofmann, and Solf (7) and gives a list of the various packings and the calculated percentages of interstitial space for each packing arrangement for spheres of uniform size. As Smith, Foote, and Busang ( I I ) , and Broch (2) proved, there may be various mixtures of these different packings which give interstitial volumes intermediate to the following: Points of Contact 4 6 S 10 12
Interstitial Space, 66.0 47.6 39.5 30.2 25.9
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Dispersed systems belonging to class a and containing spheres all of the same size must have between 25.9 and 66 per cent by volume of the continuous phase. Starting with a system containing 66 per cent of continuous phase and adding more particles of the same size as those already present. the dispersed particles will rearrange to form a more closely packed state in which the volume of the continuous phase still equals that of the voids (interstices). This equality between the volume of the continuous phase and the volume of the interstitial space in the dispersed phase will be maintained during the addition of more particles of uniform size until the continuous phase becomes 25.9 per cent by volume of the system. Below this percentage of continuous phase, spherical particles can no longer rearrange to form a more closely packed system (unless distortion of the particles occurs), and hence there is no longer a sufficient volume of continuous phase to fill the interstices. During this rearrangement to closer packing of the disperse particles, the consistency of the system steadily becomes greater, because of a con-
Dispersed Particles of the Same Size Consider the particles in a disperse system belonging t o class a to be spheres of the same size. The volume of the continuous phase is equal to the interstitial space of the disperse phase as present in the system. The interstitial space varies with the packing arrangement of the particles, and as a consequence the size of the individual interstice (identical with the dimension of the average film of continuous phase separating the dispersed particles) varies with the degree of packing. The loosest packing is obtained with four points of contact between any particle and those surrounding it. However, such an arrangement has little structural strength and will collapse unless the continuous phase is very viscous. As the number of points of contact increases, the percentage of voids (interstitial space) and the size of the average individual 1011
tinuous decrease in the diinensions of the average interstice. Also, as the number of points of contact incream, the phenomenon of dilatancy ( I , . i , 8, IO) becomes more strongly manifest.
Dispersed Particles of Various Sizes
measurement were applied. Tile syst.erns all possessed structural viscosity or were plastic because the dispersed particles were in a packed condition. However, for similar systems the conditions of test (sample size, shearing stress, etc.) were identical so that a comparison of the results obtained by any particular method is justified.
Consider two similar systems of the same phase volume composition, in which the dispersed particles are in seine state of packing. The first system contains particles of the same size; the second contains particles of various sizes. Particles of various sizes give a more compact mass for any given packing arrangement than do those of uniform size. However, since the volume of the continuous phase is the same in both cases and equals the volume of the voids or interstices associated with the packed dispersed particles, the packing is looser in the system containing particles of various sizes. Consequently, this system is more fluid tlian the one containing particles of the same size hecause there are fewer points of contact between the dispersed particles and because the films of continuous phase separating them are larger. If the packing arrangement did not adjust itself so that the volume of interstitial space was identical with the volume of continuous phase, the excess of the latter would separatc as free liquid. This occasionally happens to some extent in suspensions and eniulsions. Data supporting the concept just described are given here for several different systems. Because of the widely varying consistencies of the difEerent mixtires, various methods of
Commercial date and silica powders were fractionated as described by Traxler, Baum, and Pit.tman (Zq), using a Federal air classifier. The resulting fractions, all containing particles of the same narrow distribution of sizes, and the original nnfractionated powder, possessing a wide size distribution, were compounded with identical amounts (with one exception) by volume of a soft asphaltic bitumen. A parallelplate plastometer of the type and the technic proposed by Peek (.9) were used to measure the consistency, a t 25" C . , of the resulting mortars. Table I gives the composition and apparent yield value in dynes per sq. cm. for each mixture. The silica, and more especially the slate particles, are irregular in shape and consequently will he in a packed state even when the volume of the continuous phase exceeds 66 per cent. Since the various fractions have about the same size distribution, the difference in consistency of the mortars prepared using them are probably dne to particle size. It has been shown (13) that, as the average particle size of the dispemed phase becomes smaller, the rliinensions of the aver-
Mineral Powder Dispersed in Asphalt
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INDUSTRIAL AND ENGINEERING CHEMISTRY
SEPTEMBER, 1936
Further evidence that particle-size distribution is a factor SIZEAND SIZEDISTRIBUTION more important than particle size in regulating the viscosity TABLEI. EFFECTOF PM~TICLF: of a disperse system is found in a study of two bituminous -Black Slate-AsphaltMixtures ,-Silica-Asphalt Mixturesemulsions, D and E. Soap emulsion D , a diluted sample of Size Fraction of Vol. of Apparent yield Vol. of Apparent j i e l d Powder asphalt value (25’ C.) asphalt value (25 C.) which is illustrated in Figure 1D, was prepared by means of % Dyneslsq. cm. Microns % D u n e d s q . cm. a simple propeller type of stirrer. The photomicrograph in66 731,000 57 484,000
