66 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS (7) co = (8) where v, G' and G" are the frequency of the plunger oscillations, the storage and the loss moduli of the fluid, respectively. The cross-head (plunger) moves at a constant velocity reversing its direction every half period. The explicit functional form for this type of movement is given by (12) L(t) = Lo • sin - cot -- - sin - cot + -- sin - cot -- -- sin - cot + ß ß ß (9) 2 9 2 25 2 49 2 From equation (5) the in and out of phase components of the force are given by: f'= bvBL(t)cosO (10) f"= bvBL(t)sinO (11) The value of f' at any given point of the cross-head period can be directly obtained by recording of the force as a function of time. To obtain the value of 0, the phase angle, we adapted the following procedure. As mentioned before, our experimental set-up measures the force by a sensing device that is independent of the plunger movement. Since the chart is synchronized with the plunger movement, the time course of the force reflects the time lag between the force and the displacement. The plunger position at any given time can be described by equation (9) and the time course of the force by: f'(t) = vbB 3 [sin (• t -- 0) -- & sin (3-f t -- 0) + -- = vbB • cos t9 sin -- t -- - sin -- 2 9 3co 1 5co ) t q---sin--t .... 2 25 2 02) (co • 3co • 5co )] +sin0 cos -- t - - cos -- t + -- cos -- t .... 2 9 2 25 2 Since the value of t = t' when f'(t) = 0 can be determined from the position of the cross-head, we can calculate the value of t9, the phase angle. Having determined the phase angle, the values of G" and G' can be calculated from equations (6), (7) and (10). DYNAMIC MEASUREMENTS We measured the dynamic viscoelastic properties of aerosol shaving foams. A typical curve showing the force as a function of time is shown in Figure 5. Within experimental error, both the amplitude and the period remained constant over ten periods, indicating that no irreversible structural changes occurred in the foams during this time period.

SHAVING FOAM VISCOELASTIC PROPERTIES 67 40 3• 2• 1C -21 30 60 Time, Seconds 9O Figure 5. Typical curves representing force as function of time in an oscillatory mode of plunger operation. From these experimental curves, we calculated the values of r/', r/", G" and G' by the procedures outlined above. Figures 6-9 represent G" and G' and r/' and r/" as functions of v, within the frequency range v -- 0.021 tO v' = 0.208 cycle/sec. This domain embraces the time scale of the rate of foam distribution over the face during the shaving process. The data of Figures 6-9, which were obtained on two flavor variants of the same aerosol shaving foam product, indicate that the storage (elastic) modulus of the foams investigated is virtually independent of frequency. The loss (viscous) modulus, on the other hand, displays considerable frequency dependence. Characterization of foams by measuring their viscosity at a given frequency (shear rate), therefore, does not appear to be a sufficient procedure. Our results also indicate that minor compositional changes in the formulae, as indicated by a mere change of the flavor component in an otherwise identical product, can bring about alterations in the rheological properties of the shaving foams. These changes, though small, are measurable by our technique. The storage modulus appears affected more strongly by a flavor change than is the loss modulus (Figures 6 and 7). The data given in Figures 8 and 9 suggest that differences in the product might show up in different frequency or shear rate domains. Rheological behavior of fluids generally can be represented by models composed of