JOURNAL OF CHEMICAL EDUCATION
1205
JULY-AuG., 1929
RHEOLOGY. 11. THE NATURE OF PLASTIC FLOW AND ITS RELATION TO FLUID FLOW EUGENE C. 81NGHAM. LArAVETTE COLLEGE,EASTON, PENNSYLVANIA It is difficult for one to imagine himself back in history a mere hundred years when the science of electricity was still non-existent and Dr. G. S. Ohm was attempting to overcome the vagueness in the conceptions in regard to the intensity and capacity factors of electricity, clear now to every school boy. Unfortunately, the properties of flow are still vague although Robert Hooke announced his law of elastic deformation twohundred and fifty years ago and Newton gave the fundamental law of fluid flow, later demonstrated by Poiseuille, some two hundred years ago. Thus, the terms consistency, plasticity, tackiness, shortness, hardness, etc., no one understands. There are no properties of colloids which are so characteristic as the properties of flow. It was the prophetic insight of Thomas Graham which caused him to speak of "the viscometer as a colloidoscope." The term "prophetic" is used advisedly because, in the time of Thomas Graham, the viscometer as a colloidoscope was not very satisfactory, yet one can now see clearly enough to go beyond Graham and declare that the plastometer is a colloidometer. The plastometer is more than a detector of the presence of colloids, it promises to give the most valuable control of colloidal properties. The term plastometer instead of viscometer is preferred because colloids are plastic, not viscous, and obey the laws of plastic flow but not the laws of viscous flow; and the attempt to ignore this difference has repeatedly led to misfortune. For example, paint and plaster and clay flow easily under brush, trowel, or shaping tool, hut there is nothing in the laws of viscous flow which permits these materials to remain in position in opposition to gravity after the original deformation of the craftsman. On the contrary, the laws of viscous flow if applied to paint, clay, butter, and plaster would expect them to flow continually under any shearing stress just as pitch does. We therefore conclude that it is the plastometer which is the colloidoscope and to the understanding of the laws of plastic flow we may safely look for the quantitative measurement of colloidal properties. We have seen* that the simple law of viscous flow of Newton is 0
=
qFr... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
The simplest assumption which we can make to account for the phenomena of plastic flow would seem to be that a certain definite shearing stress is required before the material begins to yield and then the flow is proportional to the excess of shearing stress, or, v = p(F-f)r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(2) .
See Part I, THISJOURNAL, 6 , 1113 (June,1929).
VOL.fi, NOS.7 AND 8 RHEOLOGY. 11. PLASTIC AND FLUID FLOW
1207
when p is called the mobility and f the yield value. The mobility becomes the fluidity as the yield value vanishes. It is the existence of this definite yield value that makes the distinction between a solid and a liquid. This is a pure assumption and must he tested out for all sorts of materials and conditions of flow. And just as equation (1) is subject to various correc-
tion terms, which are not entirely understood even yet, so equation (2) is subject to corrections for various factors such as seepage and slippage. But it has been found to hold within certain limits for many types of suspensions. Where there is a structure of filaments which break down under shear, as in the cases of nitrocellulose solutions and the other polar colloids, theequation doesnot hold,for the material behaves as if it had a higher mobility and higher yieldvalue, the higher the shearing stress. In order to secure greater clarity of I1 exposition, let us first confine our attention to the one type of plastic 2 flow (2). The typical fluids OB or OC are represented by Figure 5, the fluidity being measured by the tangent of the angle. A typical plastic o f FIGURE A 5 F D curve BCA is also linear but the velocity of flow u vanishes a t the finite shearing stress, OA = f. The mobility is measured by the tangent of the angle BAD. There are now four types of plastic substances which need recognition. Perhaps they will be found to fall under the following classification: Short-The yield value is large and the mobility high. Tough-The yield value is large but the mobility is low.
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Tacky-The yield value is small but the mobility is high. Long-The yield value is small and the mobility is low. Butter, paint, starch, paste, printer's ink, and clay slip are excellent examples of short materials. If forced out of an orifice, short materials often collect in irregular masses, the yield value preventing the formation of a round drop. However, as the weight increases, it suddenly overcomes the yield value and since the mobility is high the mass quickly "necks off and the mass drops off. Metals like case iron also exhibit shortness, which is a broader term than brittleness. The condition is quite otherwise with molasses candy, gluten, or mixtures of linseed oil and rosin. When the material flows out from an orifice, it tends to form a round drop because the yield value is low, but when it falls due to gravity the necking-off process is very slow because the mobility is low. Hence, the material is stringy or ropy or simply "long." Many sorts of materials, such as glue, dough, paint, and even printer's ink, sometimes show noticeable and even troublesome length. The third class of materials approaches the properties of rather fluid liquids while still being plastic on account of having a small yield value. A hot glue applied to a piece of board is at first thin and runny, i. e., it has very high mobility and very little yield value; as the temperature is lowered or the water is absorbed, or both, the glue develops tack, i. e., it seems sticky because the yield value increases and the mobility falls; with continuance of the same process on touching the glue with the finger or another piece of board no adhesion takes place because the high yield value and low mobility do not permit good contact to be made, but by means of pressure, heat, or long-continued contact adhesion may still result. Thus stickmess is not an absolute term but a relative one. Every one knows that pitch does not normally stick to the hands at ordinary temperature, yet if the hands are once wet with pitch, they will stick to pitch very readily. I t is said that "glue cannot be made to stick to tin." This is hardly true. Tin is covered by a layer of grease, and when glue dries on grease-covered tin, the grease flows under the stresses created and the glue flakes off, but if the tin is cleaned well enough, the glue will stick. I t is well known that glue will stick so firmly to clean glass that on drying it will pull a layer of the glass off resulting in a beautiful frosted effect and this process is used industrially. "Wet" paint or glue is tacky. Finally, we find that there are substances which resist deformations whether long-continued but feeble or short and of great magnitude. Such materials are tough. We have tough metals, tough films of gelatin, rubber, and threads of silk. The above terms have been found necessary in industry but they have not been recognized until now in science. There is no obvious reason why they should not be-made 'respectable 'by being dressed up in the
VOL.6, Nos. 7 AND 8 RHBOLODY. 11. PLASTIC AND FLUID FLOW
1209
clothes of exact definitions which alone will make them respectable. Since there is a continual tendency in literature to debase our verbal coinage, it would be a pleasure to see many of these old Anglo-Saxon words obtaining the dignity of some of their Latin cousins. The list of these words connected with flow might be greatly extended and they are being defined as a part of the official work of the American Society for Testing Materials, for in industry these terms need exact definition and measurement. When "plastics" are made by pressure on a hot plastic material, it is necessary to have a nice adjustment of properties. The material must be soft enough to take shape readily, but it must not be Shearing Stress tacky enough to stick to the mold, F ~ o m 6 it must have yield value enough to maintain its shape after removal from the mold, and after cooling it should be hard and tough. Here is a good opportunity for the adjustment of the factors which make up plasticity. Printer's ink is another case. If the ink is too long, i t will cause the paper to stick to the type and the attempt to remove it may result in pulling off the surface of the paper, or the ink may even pull out in little strings which fall over and blur the half-tones. By adding vaseline to printer's ink i t is made shorter. If the ink is too short, not enough ink will be deposited on the paper. C A few years ago a belting concern 5 was having trouble because the belts 3 4 and became stuck to the pulleys so stiffin warm as to actually weather
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crack! and break in very cold weather. This required a study of Shearing Stress the change of yield value and moFrourn 7 bility with the temperature. It was found that the mobility bad too high a temperature coefficient and the trouble was easily remedied. I n another case tests on paints were being made on a test fence,
using a panel for each sample. Made up to the same "apparent" viscosity, some of the paints remained on the panels as they should, but other paints ran off the fence. No one understood the trouble although the manufacturers of the latter type of paints claimed that their paints were not given a fair chance. It is clear - F from later work that the proper A E G basis of test would have been tomake H them up to have the same yield value. In the starch industry, things had a way of going wrong in the plant and the laboratory personnel could not tell when or why by means of their viscosity pipets. Finally, the knowledge came that they were not D measuring the significant factor and FIG- 8 the problem was solved through the measurement of plasticity. The manufacturers of linoleum have had a similar experience. There are industries such as the nitrocellulose industry which are completely dependent upon the measurement of flow, but which have not yet found any particular advantages in using methods for the separation of the variables that go to make up plasticity. To be sure the problem is more complicated than is the problem of the non-polar colloid of the paint type, for the flow curve is not ,. - .O O L linear but increases rapidly with the shearing stress (Figure 6) as if the structure were being broken down. However, .$a i t appears that even this type a of flow is dependent upon two El00 variables only. Thus by plot-? ting the apparent fluidity , against the shearing stress one d obtains the curve (Figure 7). 8 According to Van Rossen oo 5 10 15 the measurement of plasticity Seconds x 10' is becoming a regular routine FIGURE 9 of the rubber industry but the deformation of rubber is quite largely elastic in character. This deformation has, in the past, been confused with the plastic deformation so that there was no way to measure accurately either the elasticity or the factors which go to make up the plasticity. The most promising
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suggestion depends upon the fact that elastic deformation is nearly instantaneous whereas plastic or viscous deformations are a function of the time. The celebrated law of elasticity of that eccentric English scientist, Robert Hooke, is ut tensio sic vis,which may be rendered, "as the tension, so the stretch" or in mathematical language: s = eFr
We may point out the relation to the law of viscous flow where s is a distance and V is a velocity.
v = 9Fr.. . . . . . . . . . . . . . (3) In other words, if an elastic body ABCD (Figure 8) is subjected to a shearing force, it is deformed a t once let us say, to DE elastically. '1000 If it is a typical plastic solid, it then remains steady until the shearing stress overcomes the yield value, and even then it does not yield suddenly. The yielding is continuous and proportional to the time that the shearing stress acts. From the data obtained for ammonium oleate (Figure 9) one can see that it is possible to determine the deformation which would have O0 50 100 taken place instantaneously by Elastic deformation extrapolating back to zero FIGUFS10 time. The values obtained for the elastic deformation may then be plotted against the shearing stress (Figure 10) to show that Hooke's law does indeed apply to this class of materials to which it has not customarily been applied. The problem is not quite as simple as here presented, but the casual student of the subject need not be burdened with the details of measurement. For example, in Figure 9, it is observed that some of the curves are not quite linear near the origin due probably to inertia effects which are to be allowed for. It has proved disturbing to all earlier investigators that Ilooke's law never holds quite exactly, which signifies that there is a little flow even below the yield value. This may be due to a variety of causes, among which are seepage and slippage. There is also an apparent
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stiffening of plastic materials in flow called by Weber "the 14 elastic after-effect." It is due to strains set up in the ma12 terials which tend to make 2 the materials slowly "creep x 10 back" after a shearing stress Y is removed, unless this adjust8 ment is hastened by "anneal0 ing." The heat of the anneal+0. ing process lowers the yield 4 E 4 value so that the strains can relieve themselves. 2 If one measures the rate of deformation (Figure 8) in exOo 200 400 600 800 1000 1100 cess of the elastic deformation, S h e a r r u Stress for several shearing stresses, FIGURE 11 one obtains data for the determination of the plasticity. In Figure 11 it appears that the plastic flow would take place a t shearing stresses above 200 dynes per cm.l and using this the mobility of a 43% solution has been found to be 0.055. It will produce a vast simplification if all of the complex phenomena of flow can be reduced to a few fundamental properties of elasticity, yield value, mobility, and cohesion (or adhesion). Hardness, strength, solubility, and melting point of colloids a t first thought do not appear to be dependent upon plasticity measurements, but a closer study will reveal the fact that they are dependent upon plasticity and problems connected with these properties are awaiting investigations in the field of rheology. In hardness tests indentations of specimens take place and the amount of indentation depends upon the time ., required. Hardness tests, as now made, are faulty since ; they only a simple constant whereas plasticity is . give . ","..made up of two variables, both of which arepresumably In fact, we have already proved that length important. FIGURE12 and shortness, etc., can only be gaged after one has a Very slowflow of knowledge of both of these variables. In regard to jelly behave measurements of tensile or compressive strength, the a viscous same thing may be said; viz., that the pulling apart of the specimen involves flow and the resistance to flow will largely depend upon the time taken to produce the flow.
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When a substance like nitrocotton is placed in a series of liquids, in some i t swells and becomes dispersed in a colloidal solution. There is no limit of solubility in general which can be sharply determined as in aqueous salt solutions, but there are obvious differences in the flow, and there is sound reason for supposing that the solutions which are much more mobile show better dispersion. In a similar fashion colloidal substances like butter, gelatin, glass, etc., have so-called melting-points or softening temperatures. The tem-
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FIGURE 13 Plastic flow of suspensions of zinc oxide and lamp black at low shearing stress (a), high shearing stress (c), and intermediate ( b ) . The black line in each case shows where the separation between the two colors was originally.
peratures are not true melting points and cannot be sharply determined. The plasticity, however, is real and can he sharply determined. In the case of butter, for example, there is a temperature a t which the yield value disappears, i. e., where it becomes a true liquid. This may be taken as the analog of the melting point. It is in reality the temperatnre of complete melting. There is, also, a temperatnre of complete solidification and therefore a solidification interval between these two temperatures. A great disadvantage of the ordinary melting-point determination of very
viscous materials is the uncertainty due to the slow diffusion in such a viscous medium, and it is needless perhaps to point out that in order for a crystal to either form or dissolve, a process of diffusion must take place. This difficulty can be completely overcome in plasticity measurements because no change of temperature takes place during the measurements which may therefore be continued as long as necessary. In conclusion it may be instructive to demonstrate to the reader the different types of flow by showing first how a viscous liquid flows through a small tube so that after a time a plane surface AB becomes chanced to a paraboloid of revolution as shown in Figure 12. In plastic flow of a suspension such as zinc oxide or lamp-black in oil, the pattern of flow varies remarkably with the shearing stress as shown in Figure 13, ( a ) , ( b ) , and ( c ) . The only difference among the three is that the flow in ( a ) is conducted a t a very low shearing stress while (c) is at a high stress and ( b ) is intermediate. Since the material is not transparent the extruded material had (hi been cut in two in the middle before photographing. Since Illustrating how in polar colloids a low shearing stress (a) produces telescopic flow throughout flow takes place only when whereas a high shearing stress ( b ) causes the material to rpsemble in its flow the suspension undet the shearing stress exceeds the vield value and the shearhigh shearing stress. ing stress is greatest at the wall of the tube, the flow in (a) seems to be complete "slippage" whereas a t the highest shearing stress ( c ) the shearing of the material appears to take place throughout. I n the intermediate case, the central portion of the material is shoved out as a solid plug. For these demonstrations the author is indebted to Mr. Baxter Lowe of Lafayette College. But one must he careful not to draw too broad generalizations from the above because there are various types of plastic flow. For example, collodion made up of nitrocellulose, camphor, and dibutyl phthalate to a stiff paste flows in quite a diierent fashion, apparently in a manner diametrically opposite to that of the paint paste. This is shown in Figure 14 ( a ) and ( b ) ; as before the shearing stress is low in ( a ) and higher in (b). This behavior is readily explicable.
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