I N S T R U M E N T S FOR TH E D E T E R M I N A T I O N OF RHEOLOGICAL P A R A M E T E R S OF LIQUID BODIES 1

R. N. Weltmann 2

Received February 17, 1950

The laboratory investigator who needs to determine the flow character- istics of a var ie ty of substances such as asphalt, printing ink, and blood finds in his s tudy of the l i terature of instrumentat ion references to many devices. He is soon confronted with the question whether he should use as simple an ins t rument as the Ford cup or as eomplieatect an equipment as a rotat ional viscometer with an automatic recorder and a pressurizing chamber. This investigator will soon realize tha t not any one device will suffice to obtain the required information for the wide range of consisten- cies found in different materials. In addition, he will recognize tha t the term consistency not only relates to the internal friction Of a material as expressed by the coefficient of viscosity for Newtonian liquids but includes also such factors as the yield value, the thixotropie breakdown, pseudo- plasticity, and dilataney.

Even the more experienced worker in the field of rheology might be surprised to learn tha t viscosities of apparent ly Newtonian materials can vary in magnitude from 1 to 1012 and possibly more. Yield values of plastic materials also cover a very wide range, but no data are presently available to permit making a more specific statement. The breakdown curves of thixotropic materials have only been investigated over a restricted range of rates of shear due to a lack of suitable measuring devices. The s tudy of dilataney is still in an embryonic state, since few instruments are strong enough to allow measurements at even conventional rates of shear, be- cause of the rapid increase in dilatant consistency. Pseudoplastie materials, on the other hand, have been studied extensively. These materials seem to compound the widest scale of consistencies and thus a var ie ty of in- s t ruments and methods for evaluating the flow proper t ies of these materials has been proposed. But still there is need for instruments which will provide information on both ends of the consistency scale.

When an a t t empt is made to classify the available devices for rheolog- ical ins t rumenta t ion (16), it becomes apparent tha t they can be divided

Presented at the Annual Meeting of the Society of Rheology, New York, N. Y., November 4-5, 1949.

2 Consultant in rheology to the Research Laboratories, Interchemieal Corporation, New York, N. Y., and ~ member of the staff of NACA, Lewis Flight Propulsion Research Laboratory, Cleveland, Ohio.

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into three classes. To the first class belong all the instruments which express in some arbitrary terms the consistency of the material when this material is subjected to any given set of flow conditions. Values obtained from instruments of this group are frequently calibrated in terms of a- standard material of known consistency. Such measurements, although meaningful only for Newtonian materials, can be used to compare different factory batches of the same non-Newtonian formulation. When more than one set of flow conditions can be produced by the same instrument, it is possible to evaluate the plastic viscosity of true plastic materials, but only if the data obtained from the various flow conditions yield a large straight portion when properly plotted.

Devices like the Gardner bubble tubes (5), extrusion type viscometers, Stokes' type viscometers (19), and others fall into this classification. The same is true for rotational viscometers employing a rotor and stator of such a design that a mathematical interpretation of the model of flow has not been achieved.

The extrusion type viscometers include the commonly used Ford cup, the Saybold viscometer, which is most frequently employed in the oil industry, and others. The best known Stokes' type viscometer is the Hoeppler (10) of which many varieties are used in industry, particularly in the textile field. A typical rotational viscometer of this group employs a paddle as rotor. Any experimenter can add many more constructional arrangements to the already existing substantial variety of devices. In each special case consideration will have to be given to the required con- sistency:range. Physical properties, for example, transparency,opaqueness, degree of evapbration, test temperature requirements, and others, are decisive factors for the design.

The second group of devices differs from the first one in so far as it is possible to represent the flow conditions mathematically. Whenever the picture of the model of flow is available, the instrument can be applied to the rigid investigation of Newtonian materials. On the other hand, these devices are not applicable to the study of non-Newtonian materials since the rate of shear to which the material is subjected varies to such an ex- tent that the non-Newtonian parameters cannot be properly correlated. Some devices of the first group might be transferred into the second group by a change in design, such as to produce flow conditions which are sus- ceptible to calculations. The most prominent instruments of the second group are the parallel-plate and capillary-tube viscometers, which are widely used in industry.

In 1874, Stefan (18) proposed a model of flow for a parallel-plate viscometer, in which the material under test is located between two approaching and separating plates. The instrument can only be used for obtaining viscosities of Newtonian and of true plastic/naterials where the

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rate of shear-shearing force relationship is linear at least over an extended range. Furthermore, the rates of shear which can be applied to the test material are extremely low.

The parallel-plate viscometer has lately found much use in the investi- gation of materials with high solid content. Dienes and Klemm (4) measured viscosities of high polymers ranging from 104 to 109 poises on a specially designed parallel-plate viscometer. Williams' (27) viscometer is reported to measure rubber viscosities in the order of 106 poises. Resin solutions up to 10 s poises were measured on H. Green's (6) Tackmeter. All three parallel-plate viscometers measured the high consistency mater- ial at such low rates of shear that the materials seemed to behave like Newtonian liquids. Hence, the viscosities referred to are apparently the intrinsic viscosities of those materials.

In the year 1842, Poiseuille (14) established the model of flow in capillary tubes. From his equation it becomes apparent that the rate of shear ,at the center of the capillary is zero, hence also the shearing force, and that both increase towards the walls of the capillary. This means that the rate of shear of the material when sheared in a capillary varies considerably over the cross section even in the smallest capillaries. Such a variation does not matter when dealing with Newtonian liquids where the viscosity is proportional to the rate of shear, but it interferes when meas- uring a true plastic material which is characterized by its yield value (1). The yield value is the shearing force per unit area which will just cause flow. Since the shearing force is zero at the center of any capillary, the required yield-value-force can never be reached in the center layer but only at layers closer to the wall. Therefore, a true plastic will never start flowing in the last minute center layer of the capillary. This will result in a nonlinear flow curve which resembles flow curves characteristic of pseudo- plastic materials.

The instruments of the third group are so designed that they not only permit making consistency measurements under controllable flow condi- tions but they also make possible the establishment of an accurate rela- tionship between the shearing force and the rate of shear. This means that the material under test must be subiected to essentially only one rate of shear at any one instant.

In these instruments the substance to be measured is always placed between two members, one of which moves relative to the other one at various known speeds. Furthermore, provisions must be made to establish the forces which are associated with such relative motion. It is, of course, immaterial whether the magnitude of motion is changed and the forces are determined, or whether the forces are changed and the motion is measured.

The rotational viscometer of proper design (3) and the band viscometer are the most prominent representatives of this group. The investigator

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who is ignorant of the type of material he is dealing with should always use these viscometers to determine whether non-Newtonian parameters (25) need consideration. This is especially important in the study of thixo- tropic materials (8), where, in addition, the viscometer has to be cap- able of subjecting the test sample to increasing and decreasing rates of shear (9).

At first glance the band viscometer, as suggested by Wachholz and Asbeck (23), seems to be the ideal instrument, since it is designed in accord- ance with Newton's model of flow. In Newton's model of flow the material is located between two parallel plates which move with respect to each other. The force causing this relative motion is proportional to the rate of shear between the plates. The proportionality constant is the Newtonian viscosity. This equation has been extended by Bingham (1)to true plastic materials by subtracting the yield value force from the shearing force. This model of flow is ideal since the rate of shear and velocity gradient fn the material are constant over the complete separation 0f the plates. In Wachholz and Asbeck's band viscometer an endless band moves for a portion of its length in the center between two parallel stationary plates with the test material between the plates and the band. Such a structure represents in essence the relative motion of two plane-parallel plates. Therefore, it seems to lend itself to a rather simple mathematical inter- pretation. However, its disadvantages are many. Most of the difficulties are caused by end effects. To minimize the end effect, the tape has to have a small width and depth compared with those of the container, and the tape should be wide in relation to its thickness. The tape has to enter and leave the trough containing the test material, hence end effects are intro- duced also at those locations. To make them negligibly small compared to the shearing effect, the tape passing through the trough has to be made rather long. This, however, makes it mechanically difficult to maintain the tape parallel to the stationary plates and well-centered over its entire length, especially at. high shearing stresses and for heavy consistency materials. In the Wachholz and Asbeck instrument the order of magnitude of the rates of shear reaches about 1000 sec. -1 for viscosities of only a couple of poises and decreases linearly with an increase in viscosity of the material to be tested. Band viscometers, however, show interesting possi- bilities for the measurement of non-Newtonian materials. It is entirely conceivable that an improved band viscometer can be designed which is well suited to measurements of higher consistency materials permitting at the same time high rates of shear application. For instance, a highly flexible endless ribbon might be used which is maintained straight and parallel to a stationary plate by an appropriate backing support.

For high-speed applications, the rotational viscometer is the only one presently available. However, this viscometer also introduces several

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problems. The rate of shear and velocity gradient vary over the distance between rotor and stator. In a properly designed rotational viscometer t.his variation in rate of shear over the clearance can be reduced by using a very small clearance and by selecting suitable diameters for the starer and rotor. With increasing diameters the difference in rate of shear from one to the other surface of the two members becomes smaller for a constant distance between them. Hence, it would seem that large diameters should be used: That, however, has three severe disadvantages. To obtain the same rate of shear with increasing diameter, a higher torque is required. This might become mechanically difficult, especially for high consistency materials. With larger diameters the inertia of the stationary member is increased which can introduce difficult oscillatory conditions when a spring deflection system is being imployed (26). Finally, the centering of large members is much more critical and becomes mechanically almost impossible for very large diameters. Thus, a compromise diameter has to be chosen.

For Newtonian materials the nonconstant rate of shear across the clearance does not matter. But already for true plastics this varying rate is noticed by the fact that the rate of shear-shearing stress curve is non- linear at low rates of shear, and becomes linear only when the rate of shear at the outer member corresponds to a shearing force which is just higher than the yield-value force. This is in accordance with calculations made by Reiner and Riwlin (15) for the flow of true plastic materials in a rotational viscometer. Their mathematical interpretation of the model of flow makes the rotational viscometer most useful for measuring non-Newtonian materials. By employing their concept of flow, shearing stresses and rates of shear can be calculated and an average rate of shear can be postulated; this will differ only slightly from the rates of shear at any point between the rotor and the stator. The end effects can be extrapolated experimen- tally (11,24) and thus can be included in the calculated solutions for the consistency. Some investigators (13) have used specially designed rotors and stators to eliminate them altogether.

Because the rotational viscometer is susceptible to a mathematical interpretation, the development of such viscometers has lately received considerable impetus. The literature of recent years is full of descriptive material of rotational type viscometers having special design features to meet the conditions for specific studies. However, only a few instruments have been described which will measure materials at the extreme ends of the consistency scale at high enough rates of shear.

The Mooney-Ewart (13) rotational type viscometer although built for relatively low consistency materials--down to the order of 0.01 poise,--can only employ rates of shear up to a maximum of about 100/sec. This is too low for most practical applications.

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The rotational viscometer built at the Interchemical Corporation for a still lower consistency range and employing relatively high rates of shear, up to about 4000/sec. has been briefly described by H. Green (8). With this instrument, materials of non-Newtonian consistencies down to a plastic viscosity of 0.005 poise and a yield value of 5 dynes/cm? can be measured. This is accomplished by using a very lightweight stator assem- bly with a needle shaft. To lighten the weight further, a multiple pointer rather than a dial is carried on the shaft. Flow curves of industrial finishes, paper coatings, gravure inks, and biological samples have been obtained. Without the availability of such an instrument a casual observer could have misinterpreted those materials to be Newtonian liquids, but a flow curve study showed some of them to be thixotropic plastics and others to be pseudoplastics. Such knowledge will frequently explain their peculiar behavior upon application and will make it possible to suggest changes which will overcome difficulties experienced in practice.

For the determination of flow properties of high consistency materials, Traxler et al. (30,21) built a rotational viscometer. This instrument is designed to measure asphalts ranging in viscosity from 103 to 109 poises. The maximum rate of shear which can be applied is only about 10 sec. -1 when testing the lower viscosity materials and becomes accordingly less when measuring the more viscous substances. To obtain a useful portion of the flow curve, as for instance the linear part when dealing with true plastics, high rates of shear are required. This introduces considerable mechanical difficulties when measuring high-consistency materials, since considerable shearing forces have to be generated. Also, when dealing with materials of high solid content, adhesion between the movable members and the test material often becomes a problem. Means must be found to prevent slippage of the material at the interfaces with the movable mem- bers. For this reason grooved members have been suggested in the litera- ture (7,20), but have only been used for asphalts and lower Viscosity materials. The problem of.slippage will probably differ for each material to be tested, depending on its physical nature.

Even with substances of high-solid-pigment content like printing inks, paper coatings, and others but of only medium consistency having plastic viscosities in the order of a couple of hundred poises and yield values in the order of a couple of thousand dynes per square centimeter, no investiga- tions have been made to extend the flow curve into the region of the rate of shear of the operating conditions. Although three rotational viscometers of the MacMichael type (12), designed for materials of just that consist- ency range have recently been described (2,7,17), none of them enables the operator to test these materials a t the extreme high speeds of modern industrial machinery in the application field.

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For rapid measuring procedures and high rate of shear applications, it is desirable that automatic indicating means be provided. This is especi- ally important for thixotropie materials where very rapid indication is required, since the flow conditions change continuously with time. The stator, if made to deflect against a torsional restoring force, requires time to complete its path and to reach its equilibrium position. It has been shown (26) that the time of deflection depends on the instrumental con- stants, the inertia of the stator system, the amount of deflection, the type of torsional restoring force, the applied angular velocity, and the con- sistency of the test material which supplies the damping to the oscillatory system. To get away from the deficiencies of such a mechanical arrange- ment and to obtain a more rapid measurement, a few of the viscometers employ a strain gage as a force indicator which is coupled to a high-speed reading or recording device.

I t would be of still greater advantage if means could be found to substitute the measurements of force and mechanical action by some electric analog such as dielectric constant or magnetic permeability. Research along these lines has been conducted by Voet (22) in correlating the dielectric behavior of substances with consistency measurements. This might eventually lead to a novel, rapid, and high-speed measurement of flow behavior.

For the rheologist who concerns himself with instrumentation prob- lems, there is still a considerable territory of no-man's-land. It is an unavoidable trend that modern electronic practices which heretofore have found little use in rheologieal instrumentation will have to be em- ployed to an ever-ineresing degree, especially if testing at high rates of shear is to be accomplished.

SUMMARY

• Instruments for rheologieal measurements of liquid bodies can be classified into three groups. Devices of the first and second group provide accurate information on Newtonian viscosities. For non-Newtonian materials, instruments of both groups can be employed only when taking data for purposes of comparison. With instruments of the second group, in distinction to those of the first group, a model of flow can be associated. That means that Newtonian and plastic viscosities can be calculated directly without referring to a standard material which is required when using instruments of the first group.

The third group includes instruments with which controllable flow conditions can be established in such a manner that a specific rate of shear can be correlated to a shearing stress. This requires that the material is subjected to essentially one rate of shear at any one instant. Only the third group of instruments can be used for the determination of all param- eters of non-Newtonian materials.

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The meri ts and disadvantages of most f requent ly employed instru- ments of all three classes are briefly discussed. The range of present ly available devices of the third group is not wide enough to permit investi- gation of very low and very high consistency materials. In m a n y instances, Conditions as they exist in the practical use of industrial materials cannot be simulated. Suggestions are made with regard to the design of improved measuring equipment .

REFERENCES

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414-28, 1926. 6. GREEN, H., Ind. Eng. Chem., Anal. Ed. 13, 632 (1941). 7. GREEN, H., Ind. Eng. Chem., Anal. Ed. 14, 576 (1942). 8. GREEN, H., Industrial Rheology and Reologieal Structures, p. 197. John Wiley and

Sons, New York, N. Y., 1949. 9. GREEN, H., AND WELTMANN, R. N., Colloid Chemistry, Chap. 6, p. 328. Edited by

J. ALEXANDER, Reinhold Publishing Co., 1946. 10. HOEPPLER, F., Chem. Ztg. 57, 62-3 (1933). 11. LINDSLEY, C. H., AND FISCHER, E. K., J, Applied Phys. 18, 988 (1947). 12. MAcMIcHAEL, R. F., J. Ind. Eng. Chem. 7, 961 (1915). 13. MOONE:G M., AND EWART, R., J. Applied Phys. 5, 350 (1934). 14. POISEUILLE, J. L. M., Compt. rend. 15, 1167 (1842). 15. REINER, M., AND RIWLIN~ R., Kolloid Z. 43, 1, (1927). 16. SCOTT BLAIR, G. W., A Survey of General and Applied Rheology, p. 89. Pitman

Publishing Co., 1944. 17. SMIT~, J. W., AND APPLEGATE , P. D., Paper Trade J. 126, 23, 60-66 (1948). 18. STEFAN, M. J., Sitzber. Akad. Wiss. Wien, Math.-naturw. Klasse Abt. II , 69, 713

(1874). 19. STOXES, G., Trans. Cambridge Phil. Soc. II , 8-9 (1851). 20. TRAXLEn, R. N., ROMBERG, J. W., AND SCHWEYER, H. E., Ind. Eng. Chem., Anal.

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