An elastic, plastic, viscous model for slow shear of a liquid foam

TL;DR

This paper introduces a scalar model capturing elastic, plastic, and viscous behaviors of amorphous materials like foams, applicable to slow shear flows, and aligns well with experimental observations.

Contribution

It presents a novel scalar model that unifies elastic, plastic, and viscous responses in slow shear flows of amorphous materials.

Findings

Model predictions match experimental storage and loss moduli.

Explains non-linear large amplitude trends in shear response.

Applicable to transient and steady flow regimes at large elastic deformations.

Abstract

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called "quasi-static") limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.