Stationary Couette flows of elastoviscoplastic fluids are non-unique
Résumé
The Herschel-Bulkley rheological fluid model includes viscosity and plasticity. In this classical model, under the yield stress the material is strictly rigid. Complementing this model by including an elastic behavior under the yield stress leads to a description of elastoviscoplastic (EVP) materials such as suspensions or liquid foams. We include this modification in a completely tensorial description of Couette shear flows. Both the parameters of the model, at the scale of a representative volume element, and the predictions (velocity, strain and stress fields), can be readily compared with experiments. We perform a detailed study of the effect of the main parameters, especially the yield strain. We discuss the role of flow lines curvature in the apparition of localisation; we determine the value of the localisation length and provide its approximate analytical expression. We then show that, in our tensorial EVP model of Couette shear flows, normal stresses strongly influence velocity profiles, which can be smooth or non-smooth according to the stress initial conditions. This feature can explain several open debates regarding experimental measurements on Couette flows for various EVP materials such as suspensions or liquid foams, including the non-reproducibility that has been reported in flows of foams. We then discuss the suitability of Couette flows to measure rheological properties of EVP materials.
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