RHEOLOGY OF HYDROPHILIC POLYMER SOLUTIONS 151 Thus for the golf ball with a radius of 2.13 cm. and a density of 1.11 we have-- [(4/3•r (2.13) 3 X 1.11) -- (4/3•r (2.13) 3 X 1.00)] X 980 cm./sec. • •r (2.13) • = 306 dynes/cm? These calculated yield values are directly compared with the experimen- tally determined Brookfield yield values in Table 4. TABLE 4--CAt. CULATED YIEt. D VALUE VS. BROOKfIELD YIELD VALUE REQUIRED fOR PERMANENT SUSPENSION Theoretical Approximate Particle Yield Value, Brookfield Suspended Radius Density Dynes/cm? Yield Value R Sand 0.030 2.60 63 107 1.7 Golf ball 2.128 1.11 306 300 1.0 Marble 0.800 2.55 1622 900 0.6 It will be noted that the deviation of the Brookfield yield value from the theoretical yield value varies, depending on the magnitude of the yield value, as expressed by the ratio of the two values, R. We believe this vari- ability to be inherent in the use of the Brookfield instrument based on the fact that a change in spindle r.p.m. is not directly proportional to a change in true shear rate in inverse seconds. In any given system, an empirical cor- rection could be made. However, even without correction, the degree of agreement shown in Table 4 over a wide variation in yield value must be considered adequate for most product development work. This has been demonstrated by the effective ranking.of a wide variety of materials with regard to suspending ability in Tables 2 and 3. In these tables it was shown that gum tragacanth and carboxy vinyl poly- mer "solutions" are the best candidates for consideration in development of permanent suspension. The theology of gum tragacanth was shown to be dependent on the age of the solution and the amount of shear applied in solution make-up (3). Over 2 per cent of gum tragacanth was required to affect permanent suspension of silica sand under the best conditions. The production grade of carboxy vinyl polymer is shown to be effective in main- taining permanent suspension of silica sand at 0.18 per cent concentration and an experimental carboxy vinyl polymer is effective at 0.10 per cent. This highly efficient development of yield value at low polymer concentra- tion in water "solutions" is shown in Fig. 6. As a point of reference the theoretical yield values for silica sand, golf balls, and marbles have been indicated on this graph. /Ipplication to Product Development Problems The mechanism involved in permanent suspension has been demonstrated

152 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS --i •--)AARBLES i ! ..... OOLF BALLS ..... SANE) GRAINS T• •0 ,g, •'4#• ',954 Figure &--Yield value vs. Carbopol-934 concentration. by the use of a simplified system wherein the suspended particles have little influence on the total system. This simplified system can be used directly as the model for creation of new cosmetic and pharmaceutical products based on suspension of relatively large particles. In addition it can be useful in the more common case of a fine particle size suspension. However, as the particle size is decreased or the per cent solids increased, particle interaction increases as well as the possibility of polymer- particle interaction. Particle interaction such as agglomeration results in an increased settling force per unit area and thus increases the minimum yield value requirement. Decreased particle size being associated with large increases in surface area causes an increased tendency toward poly- mer adsorption. This increases the polymer requirement as a result of a lowered polymer concentration in the water phase. In some cases a spe- cific polymer "solution" cannot be used at all due to polymer-particle interaction to an extent resulting in extreme flocculation.