On the shearing flow of foams and concentrated emulsions

Abstract

Shearing flow of an idealized, two-dimensional foam with monodisperse, spatially periodic cell structure is examined. Viscous effects are modelled by the film withdrawal mechanism of Mysels, Shinoda & Frankel. The primary flow occurs where thin films with inextensible interfaces are withdrawn from or recede into quasi-static Plateau borders, film junctions that contain most of the liquid. The viscous flow induces an excess tension that varies between films and alters the foam structure. The instantaneous structure and macroscopic stress for a foam of arbitrary orientation are determined for simple shearing and planar extensional flow. As the foam flows, the Plateau borders coalesce and separate, which leads to switching of bubble neighbours. The quasi-steady asymptotic analysis of the flow is valid for small capillary numbers Ca based on the macroscopic deformation rate. This requires the foam to be wet, i.e. the liquid volume fraction must be large enough that structure varies continuously with strain. The viscous contribution to the instantaneous stress is ; by contrast, the first normal stress difference is O(1). Even though wet foams are elastic for small but finite deformations, the time-averaged shear stress does not evidence a yield stress.