Rheology of foams and highly concentrated emulsions

Expressions are derived for certain rheological properties, such as the stress vs strain relationship, yield stress, and shear modulus, of monodisperse foams and highly concentrated emulsions for the model of infinitely long cylindrical drops (or bubbles). The variables considered are the volume fraction of the dispersed phase, the drop radius, the interfacial tension, the thickness of the films separating adjacent drops, and the films' associated contact angle. Both the yield stress and the shear modulus are proportional to the interfacial tension and inversely proportional to the drop radius. The yield stress increases sharply with increasing volume fraction, while the shear modulus varies as its square root. The effect of a finite contact angle, θ, is to decrease the shear modulus and, in most cases, to increase the yield stress. Finally, the effect of a finite film thickness is to always increase both the yield stress and the shear modulus. The implications of these results to real emulsions and foams are discussed.