A simple continuum model for the dynamics of a quasi-two dimensional foam

Nominally two-dimensional foams, created by confining a single layer of bubbles between two plates, or one plate and a liquid surface, or floating on the liquid, have provided convenient model systems for foam research. We show that, in the case of rheology, viscous drag forces due to the confining plates have large effects. They can give rise to shear bands, similar to those observed by Debrégeas et al. [G. Debrégeas, H. Tabuteau, J.-M. di Meglio, Deformation and flow of a two-dimensional foam under continuous shear, Phys. Rev. Lett. 87, (2001) 17–8305]. A continuum equation that incorporates elastic, plastic and viscous drag terms is used to analyse the rheological behaviour. We also discuss the meaning of the term quasistatic in this context.