Two-dimensional foam rheology with viscous drag

Abstract

We formulate and apply a continuum model that incorporates elasticity, yield stress, plasticity, and viscous drag. It is motivated by the two-dimensional foam rheology experiments of Debregeas et al. [Phys. Rev. Lett. 87, 178305 (2001)] and Wang et al. [Phys. Rev. E 73, 031401 (2006)], and is successful in exhibiting their principal features, which are an exponentially decaying velocity profile and strain localization. Transient effects are also identified.