Structure and Coarsening of Foams

Prud hoimne should not be universal, but there should be a variation with the parameter (r/a32) /. However, in the experiments of Otsubo and Prud homme, this quantity was varied by a factor of less than two, and deviations from universal scaling are therefore within the scatter in Fig. 9-26. In the range rjsy = 10 -10° Pa, the data of Otsubo and 

Prud homme are about a factor of three larger than the predictions of Eq. (9-55), if Y( j ) and C ( p) are taken from Eqs. (9-51) and (9-53), respectively. More significantly, the data of Fig. 9-26 show a trend toward a constant Newtonian viscosity plateau at low shear rates, while Eq. (9-55) predicts yield behavior at low shear rates, with a power-law viscosity-shear rate slope of—1. The emulsions of Otsubo and Prud homme are evidently affected to some extent by Brownian motion, which is not accounted for in Eq. (9-55). Further experimental and theoretical work on emulsion rheology will be required to establish general scaling rules for these complex emulsions. 

Foams can be made by releasing a gas within a foamable liquid. For example, the opening and pouring of a bottle of soda releases pressurized CO2 gas, producing foam bubbles. Chemical reactions can also generate bubbles within the liquid. Other methods of foam production are to force both liquid and gas through a packed column (Khan et al. 1988), to spray foamable liquid onto a screen on which a fan is blowing (Aubert et al. 1986), or to use the foam-extrusion process (Han 1981). 

Foams are not stable. They eventually collapse as their liquid films drain and rupture under gravity or as small bubbles are slowly cannibalized by large ones due to diffusion of 

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