60 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS rheological properties of shaving foams is that of Sanders. Unlike Sanders' technique, which only yields empirical, comparative data, our method can also be used for measuring the fundamental viscoelastic qualities of foams. THE PHYSICAL CONSISTENCY OF FOAMS Viscoelastic materials combine the features of solids with those of liquids. Ideal solids are pure elastic bodies, i.e., their deformation is governed by Hooke's Law: the stress is proportional to the imposed strain. Ideal viscous liquids obey Newton's Law of Flow: the shear stress is proportional to the rate of shear. In practice, most materials display non-ideal flow and combine the properties of liquids with those of solids: they are viscoelastic. Aerosol foams are viscoelastic materials par excellence. At small strains, foams behave as elastic bodies, i.e., they return spontaneously to their original undeformed shape as soon as the deforming external force is removed. On the other hand, should the strain exceed a critical value, the foam will start to flow and spread. In fact, the utility of shaving foams is closely linked to this dual behavior. Shaving foams are expected to spread over the face once spread out, they are supposed to retain their shape without running or dripping to form a continuous barrier capable of retaining water in the beard hair fibers for the duration of the shaving process. Accordingly, the performance of shaving foam depends, to a considerable extent, on the viscoelastic properties of the foam. Four physical quantities are required for characterizing the rheology of viscoelastic materials (2,8): the static elastic modulus the yield point, i.e., the level of shear rate at which point the body transforms from elastic solid to viscous liquid behavior and the dynamic storage (elastic) and loss (viscous) moduli. The value of static elastic modulus may depend on the magnitude of the applied strain. The dynamic storage and loss moduli generally vary with the rate of straining. Ideally, the experimental methods used for the complete characterizing of foam rheology should be capable of measuring all four of the above-mentioned key viscoelastic parameters. THE ANNULAR PUMPING METHOD FOR MEASURING THE RHEOLOGY OF FOAMS We selected a method that uses the annular pumping principle (8). The foam is contained in a cylindrical vessel into which a cylindrical plunger penetrates at a given speed (Figure 1). Both the displacement of the plunger and the force acting on it are measured as a function of time by suitable transducers. For our measurements, we used an Instron © Tester working in a compression mode. A cylindrical glass plunger (2.77 cm diameter and an 11 cm length) was attached to the cross head of the Instron © and was driven at constant speed. A glass cup containing the foam was placed under the plunger and as the plunger penetrated into the foam, the force acting in the axial direction was measured and recorded as a function of time. We carried out two series of experiments using two different size cups with diameters of 7 cm and 9 cm. The height of the cups was 5 cm. The cups were filled with shaving foams by attaching to the outlet of the aerosol valve flexible tubing and squirting the foam through the tubing carefully into the cup, filling it gradually from the bottom towards

SHAVING FOAM VISCOELASTIC PROPERTIES 61 I Cross Head .... Glass Plunger Foam Load Cell Figure 1. Schematic representation of the experimental arrangement. the top. Great care was taken not to leave any air pockets in the foam. The surface of the foam was then smoothed over with a laboratory spatula to give a surface flush with the edges of the container. The measurements were carried out immediately after filling the cup. All the experiments were performed at constant humidity (65% RH) and constant temperature (21øC). Our experimental arrangement enabled us to measure the plunger displacement and the induced force as functions of time independently from each other. The magnitude of the force in phase with the displacement was measured as a function of time and the phase angle between the force and the displacement could be, therefore, calculated by simple procedures (see below). The theory of the method was first formulated by Lawackek (9) and further developed by Smith et al (10) and Bikermann (11). The technique can be used in three different modes of operation: a) the measurement of strain-stress curves under quasi-static conditions b) the determination of the viscous drag at constant rate of plunger movement using a single penetration stroke and c) the measurement of the dynamic viscoelastic properties using an oscillatory plunger movement. MEASUREMENT OF THE ELASTICITY OF FOAMS At low strain levels, aerosol foams retain their shape and appear to behave as elastic bodies. To test this assumption, we first immersed a plunger into the foam to a depth of 0.787 cm and then measured the force displacement curves using an additional penetration depth of 0.0254 cm and a very slow cross-head speed (0.254 cm/minute). Typical strain stress curves, obtained with repeated cycles of penetrations, are reproduced in Figure 2. Some moderate alteration in the successive force-penetration curves is seen in a decrease in maximum force and an increasing pull on the plunger on reversal of its direction. There is also some curvature at the final portions of each penetration, indicative of departure from Hookean behavior at the later stage of deformation. Nonetheless, the slopes of the initial compression stage of these curves