Rheology of foams: II. Effects of polydispersity and liquid viscosity for foams having gas fraction approaching unity

Abstract

A constitutive model for foams developed previously is extended here to study the influence of polydispersity on small deformations and the coupled effects of viscous and interfacial forces present in the foam films on both small and large deformations. A formalism for describing cell motion at large strains is also presented. To investigate the effects of polydispersity, the cell deformation and stress—strain behavior for a foam with a bimodal cell size distribution are calculated. The yield stress, critical (yield) strain and the stress—strain relation are found to be independent of the size distribution about a constant mean cell size and are coincident with that of foam consisting of monodisperse, regular hexagonal cells. The introduction of liquid viscosity into the model produces strong deviations from previous results in both the stress field and in the cell deformation for modified capillary numbers ▪ larger than 0.01. Further, these viscous effects are dependent on initial cell orientation. Although the magnitude of the viscous stress is not large, it affects the total stress by changing the cell structure. For smaller Ca′, however, viscosity has a minimal effect on the foam rheology. For large deformations, initial cell orientation and viscosity strongly affect the time periodicity of the system. For certain orientations, the cell structure and stresses showed aperiodic behavior regardless of the magnitude of the ratio of the viscous to the interfacial forces ( Ca′), whereas for other initial orientations they were periodic. For large Ca′ the cells become highly elongated indicating the possibility of cell rupture.