An elasto-visco-plastic model for immortal foams or emulsions

TL;DR

This paper introduces a minimal tensorial rheological model for immortal foams and emulsions, capturing their elastic deformation and plastic flow behavior without aging effects, extending the classical Bingham model.

Contribution

It develops a fully tensorial, rheological model for soft, complex fluids like foams and emulsions that accounts for elastic and plastic deformation behaviors, a novel approach compared to scalar models.

Findings

Model describes elastic deformation before plastic flow

Captures finite yield threshold in complex fluids

Equivalent to scalar Bingham model in tensor form

Abstract

A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.