70 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Dashpot L Spring Figure 10. Schematic representation of the Voigt model. G"(co) = Goco•' (14) Tan 0 = coy (15) where •' and G o are the time constant of the Voigt element and the shear rigidity of the spring, respectively. In Figure 11, we have plotted the value of •', the relaxation time of the Voigt element that served as our theological model for the foam. The results suggest that a single Voigt element is insufficient to explain the rheology of the foams in the frequency domain we investigated. The curve in Figure 11 suggests that at least two relaxation mechanisms take place--one with a long relaxation time and another with a time constant in the vicinity of 5-8 sec. The physicochemical processes that are responsible for either of these processes are unclear at the moment. DISCUSSION AND CONCLUSIONS The method that we describe in the present paper provides a simple way for characterizing shaving foams in terms of well-defined rheological quantities: the elastic and loss moduli of foams. These quantities, in turn, can be used for a number of applications. Empirical relationships can be established between the various moduli and the consumer acceptability of shaving foams and, thus, quantitative standards for shaving foam products can be established in terms of exact physical quantities. The rheological properties of foams are amenable to interpretation in terms of structural characteristics of foams (e.g., bubble size distribution, interfacial tension of the surfactant solutions, etc.) (13) and can, therefore, serve as valuable tools to the formulation chemist for optimizing product properties. Finally, various physical quantities that are measurable by our technique can be related to the perceptual attributes of foams and, therefore, in

SHAVING FOAM VISCOELASTIC PROPERTIES 71 E 3O .-- .-- I I Ii I I I I I I i .02 .04 .06 .08 .10 .12 .14 ,16 .18 .20 Frequency, Cycles/Second Figure l l. Plot of relaxation time vs w, the angular frequency. m, Flavor variant no. 1 [], Flavor variant no. 2. principle, exact relationships can be established between the physicochernical composi- tion and structure of shaving foams and their consumer acceptability. We are pursuing active research along all these lines and we hope to report the results of our investigations in subsequent publications. REFERENCES (1) J. J. Bikermann, Foams, (Springer-Verlag, New York, 1973). (2) P. Sherman, Emulsion Science, (Academic Press, London, 1968). (3) P. A. Sanders, Stiffness measurement of aerosol foams, Aerosol Age, p. 33 (1963). (4) J. G. Cottie, "Experimental methods for the study of fire fighting foams," in Foams, ed. R.J. Akers, (Academic Press, New York, 1980). (5) A. F. Sharovarnikov and E. V. Kokorev, Study of the viscoelasticity of high ratio foams, Koll Zhur., 43,883 (1981). (6) H. Komatsu, H. Yamado, and S. Fukashima, Rheological properties of soap foam I. Apparatus for viscoelastic measurement on foam.,J. Sac. Cosmetic Chem., 29, 237 (1978). (7) H. Yamada, H. Komatsu, and M. Tamaka, Influence of bubble size on the theological properties of soap foams,J. Sac. Cosmetic Chemists, 33, 131 (1982). (8) J. D. Ferry, The Viscoelastic Properties of Polymers, (John Wiley, New York, 1980). (9) K. Lawackek, Z. Vet. Deutscher Ing., 43,677 (1919). (10) T. L. Smith, J. D. Ferry, and F. W. Schremp, Measurement of mechanical properties of polymer solutions by electromagnetic transducers,J. Appl. Physics, 20, 144 (1949). (11) J.j. Bikermann, Penetrometer for viscous liquids,J. Colloid Science, 3, 75 (1948). (12) W. H. Hayt,Jr. andJ. E. Kemmerly, Engineering Circuit Analysis, (McGraw-Hill, New York, 1978), p. 267. (13) H. M. Princen, Rheology of foams and highly concentrated emulsion,J. Colloid & Interface Science, 91, 160 (1983).