RHEOLOGICAL EVALUATION OF SEMISOLIDS 647 The theological properties of many cosmetic products are time-de- pendent. When such materials are sheared at a constant rate, the shear stress varies with the time, i.e., 7 o = f(t). If one measures the shear stress as the shear rate is first increased and then decreased in a uniform manner, a hysteresis loop is generated. The rheograms for two time- dependent systems, one thixotropic and the other antithixotropic, are shown in Fig. 2. Thixotropy--exemplified by gels prepared with the montmorillonite clays such as bentonite--is defined as a reversible, iso- thermal, gel-sol transformation. Antithixotropy--exemplified by milk of magnesia (5) and by concentrated dispersions of calcium carbonate in mineral oil or isopropyl myristate (6)--is a much rarer phenomenon than thixotropy and involves the gain in consistency during shear followed by a loss in consistency upon standing. Antithixotropy should not be confused with another time-dependent phenomenon known as rheopexy, which is simply the acceleration of thixotropic recovery by gentle, regular movement (7). For time-dependent systems, the rheogram obtained will depend upon the duration of shear at each of the successive shear rates or shear stresses. A comparison between two samples will not be possible unless the mea- surements are carefully made at each level of shear for the same period o• time. It may well be worthwhile to follow the advice of Umst•itter (8) who recommended the use of a three-dimensional plot of the rheolog- ical data for time-dependent systems. Such a plot of the r-D-t data is illustrated in Fig. 3. Figure 3. Three-dimensional representation of rheological data for time-dependent systems according to Umst/itter (8)

648 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Product Behavior during Continuous Shear Ordinarily, the interrelationship between ß and D is depicted in terms of a multipoint rheogram. Continuous shear measurements, however, involve the continuous monitoring of ß and are most suited for time- dependent systems. Two variations are usually employed. One varia- tion involves automatically programming a suitable rheometer, such as the Ferranti-Shirley, so that shear increases and then decreases at a uni- form rate (9). As the sweep time for the ascending portion of the rheo- gram is increased, the area of the hysteresis loop for thixotropic systems decreases, ostensibly due to greater structural breakdown. This is de- picted for white petrolatum in Fig. 4. Unfortunately, the change in area and shape of the thixotropic hysteresis loops depends upon the sweep time and the maximum shear rate attained (9, 10). Other problems encountered with continuous shear methods include slippage, thermal effects at high shear, evaporation effects, sample fracture, and particulate migration (in viscoelastic systems) (10). Another approach to continu- ous shear evaluation is to continuously shear a sample at a constant shear rate. Shear stress in the system will decrease as the system continues to be sheared until some equilibrium value is reached, i.e., when the rate of structural breakdown is equaled by the rate of structural reformation. The equilibrium value is a function of the shear rate and decreases as the shear rate increases. This is shown schematically in Fig. 5. io $E'C SWEEP TIME Figure 4. Effect of sweep time on the area and shape of hysteresis loops for white pet- rolatum [after Davis et al. (10)] OlO z TIME Figure 5. Shear stress in a time-dependent system as a function of the shear rate and the time of shear