RHEOLOGICAL REVIEW FOR COSMETIC CHEMISTS 309 to be preferred by rheologists. The other two were suggested by Houwink in addition to the Bingham concept (2). The valuefL, a lower yield value, is fixed at the beginning of shear, andf•f, a maximum yield value, is fixed at the beginning of laminar flow. While fL is sometimes employed as a "practical yield value,"fu is not often encountered, and the usual practice today is to use the extrapolated intercept according to Bingham. The nature of plastic flow is important and interesting because so many practical applications of pigmented industrial products have this charac- teristic. It has been the sub•iect of considerable argument, but the general explanation which seems to be supported by microscopic evidence is as follows. The particles suspended in the system tend to aggregate through the action of van der Waals forces and form a network of floccules, which in turn are broken down through shearing. During shear both breaking down and reformation are taking place, and a steady state can be achieved if the shear rate is held constant. A type of equilibrium will be reached at each rate of shear. This view is supported by the fact that a plastic body will come down the curve in a straight line if shear is started at the maximum rate and decreased rapidly. Many examples of pigment suspension exhibiting plastic flow have been studied. The yield value, which is obviously quite important in a tube of paste or cream, or in a paint, for example, can be varied in a given sys- tem by a number of factors. The addition of surface active agents will lower yield values, as a rule, by improving the wetting of the particles. Agents which defiocculate particles give lower yield values flocculating agents raise yield values. Materials which increase interfacial tension will raise the yield value and vice versa. The yield value usually goes up with increasing ratio of pigment to vehicle and with the specific surface of the pig- ment. As we will see later, large changes in these factors will often alter the type of flow property completely. The property known as thixo/ropy is often associated with plastic flow, and in some respects would appear to be a sort ofsubspecies with closely re- lated character. Suspensions are termed thixotropic when they have the property of becoming fluid on agitation and of setting to a gel when undis- turbed. We are all familiar with the classic case of bentonire gels in water as an example of thixotropic behavior. But we should consider the ques- tion of what the basic differences are from plastic flow which was shown in Fig. 2. When the yield point has been exceeded, a plastic body shows de- formation which is roughly proportional to the applied force, and many suspensions of this type will liquefy when shaken or stirred vigorously. The similarity between plastic and thixotropic flow has been a source of confusion, and has led to a great deal of controversy, because the time fac- tor and measurement conditions are vital in determining which theological definition should be applied. In thixotropic flow, there is a finite and char-

310 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS acteristic recovery time in the rebuilding of floccule networks, whereas re- building occurs immediately in plastic flow. This can be shown readily by examining the cup-and-bob viscometer curves as shown in Fig. 3. The upcurve is run, using increasing rates of shear, and immediately afterward, the down curve is run over the same distance. Since further breaking down of networks is not taking place, the downcurve of thixotropic bodies does not coincide with the upcurve. In plastic bodies the two curves will coincide, except at the lower end near the yield point. This is the "hysteresis loop" method, advocated by many eminent rheologists, and calculations of a coefficient of thixotropic breakdown have been made in which the area of the loop is measured. There is little question but that the approach is the most suitable one for any reasonable development of quantitative data. Those who object to it cite the arbitrary elements involved in the measure- ment, since the area of the loop is sharply influenced by the time taken in recording the upcurve, and the slope of the downcurve is determined by the Shearing stress Figure &--Model of thixotropic flow. Shearing stress Figure 4.--Model of pseudoplastic flow. top rate of shear chosen for the test condition. Even though this definition of thixotropic behavior may seem narrow because of the empirical nature of the method, there is large-scale agreement that the occurrence of a hys- teresis loop should be the deciding factor. It is understood that certain suspensions would not show a loop under one set of time-stress conditions and would appear to be non-thixotropic but in another measurement taken over an extremely short time period, a loop could be obtained. That illustrates the relative nature of thixotropy and why so much confusion has arisen where different criteria and methods of measurement have been used. In recent years it is unfortunate that the term thixotropy has been applied