An elastic, plastic, viscous model for slow shear of a liquid foam
Laboratoire de Spectrométrie Physique, UMR5588 CNRS-Université Grenoble I, B.P. 87, F-38402, St Martin d'Hères Cedex, France
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Accepted: 12 June 2007
Published online: 13 August 2007
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.
PACS: 83.60.Df Nonlinear viscoelasticity – / 83.60.La Viscoplasticity; yield stress – / 83.80.Iz Emulsions and foams –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2007