AEROSOL FOAMS 3 5 5 l0 2 .... • ' ' ' I .... I ' ' ' I .... I 10 0 - 10 4 _ 10 -2 ! ! ! i I 10 type • : M-type 0: L-type 10 ø 10 cationic cellulose concentration (%) Figure 4. Relationship between apparent viscosity (qq,) and cationic cellulose concentration. aerosol foams. The experimental conditions were fixed at a maximum shear rate of 320 -1 sec , using a sweep time of 600 sec for the concentrates. A maximum shear rate of 280 -1 sec , using a sweep time of 200 sec, was used for the aerosol foams. Shear rate (d•//dt), shear stress ('r), and apparent viscosity (q]) were calculated on the basis of the Couette equation (22) for the concentric-cylinder setup and the Markovitz equation (23) for the cone-plate setup. RESULTS AND DISCUSSIONS GAS VOLUME FRACTION OF AEROSOL FOAM The relation between the gas volume fraction of the aerosol foams, 4), and the cationic cellulose concentration is shown in Figure 2. The gas volume fraction (4)) increases with the cationic cellulose concentration and becomes saturated near 0.96, regardless of the molecular weight. The critical concentration above which 4) levels off, on the other hand, increases with decreasing molecular weight. BUBBLE SIZE AND COALESCENCE RATE OF AEROSOL FOAM The change in the average bubble size (DN) of the aerosol foams during aging is shown

356 JOURNAL OF COSMETIC SCIENCE 10 -2 10 -3 10 -4 10 -2 I I I A - H-Type ß ' M-Type 0 ' L-Type I I I 10 4 10 ø 10 apparent viscosity (cp) Figure 5. Relationship between apparent rate constant of coalescence (k) and apparent viscosity (qqc). in Figure 3 for the M-type cellulose. D N at all cationic cellulose concentrations shows a rapid increase followed by a more gradual increase. The initial increase may be attributed to the volume expansion of evaporating the liquefied propellant. The average bubble size in the second stage increases linearly (Figure 3). It seems to be related to the first order kinetics of coalescence, expressed by equation 3: lnD t = In D O + k' t (Eq. 3) where Dt is an average bubble size, D o is the average bubble size at t = 0, and k is the apparent rate constant of coalescence. Values of D O and k are summarized in Table I. For a given molecular weight, D O remains constant regardless of concentration, while D O decreases with increasing molecular weight. The apparent rate constant k defined in equation 3 decreases with increasing concentration of cationic cellulose. RHEOLO•ICAL PROPERTIES OF THE CONCENTRATE AND FOAM Apparent viscosity of the concentrate. Figure 4 shows the relation between the cationic cellulose concentration and the apparent viscosity of the concentrate, Xlc, at 320 sec -•' , Xlc increases with polymer concentration and molecular weight.