Eur. Phys. J. E (2008) 25: 225-251
https://doi.org/10.1140/epje/i2007-10284-2

Regular Article

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

¹ 351 Cours de la Libération, Université Bordeaux 1, INRIA Futurs projet MC2 et IMB, F-33405, Talence cedex, France
² Centre de recherche Paul-Pascal-CNRS, UPR 8641, Université de Bordeaux 1, 115 Av. Schweitzer, F-33600, Pessac, France
³ Department of Endocrinology, Institute of Functional Genomics, CNRS, UMR 5203, INSERM U661, Universities of Montpellier 1 and 2, 141 Rue de la Cardonille, F-34094, Montpellier Cedex 05, France

^* e-mail: francois.molino@igf.cnrs.fr

Received: 2 November 2007
Accepted: 31 January 2008
Published online: 24 March 2008

Abstract

A variety of complex fluids consists 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.