A mathematical perspective on thixotropic yield stress fluids.


Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE

29/05/2012 - 14:00 Mme Yuriko RENARDY (Virginia Tech.) Salle 1 - Tour IRMA

This is joint work with Kara Maki (Rochester Institute of Technology).
We present a mathematical perspective to study the dynamics of constitutive models with non-monotonic curves that naturally explains thixotropic yield stress behavior. To illustrate, a viscoelastic constitutive model, which generates a non-monotone shear stress as a function of shear rate for a steady homogeneous parallel shear flow, is investigated for the dynamics initiated by a step-up or step-down in prescribed shear stress. The stress tensor for the model is a combination of the Partially Extending strand Convection model modified to allow the shear stress to approach a non-negative limit for large shear rates, and a Newtonian solvent contribution. We address the case where the relaxation time is large. In this limit, the first maximum in the non-monotone curve occurs at a small shear rate, characterized by a parameter $?epsilon$, where $?epsilon<<1$. There is no presumption of a yield stress, but nevertheless, we obtain yield stress behavior in this limit. Complex behaviors such as yield stress hysteresis, dependence of yield stress on time scales, thixotropy, apparent unyielding at a small non-negative shear stress, an apparent viscosity which evolves on a slow time scale, and the dependence of viscosity on rest time, are predicted by this model. The direct numerical simulation of the full governing equations is performed in conjunction with a perturbation analysis with multiple time scales. A novel time-periodic fracture-heal solution, with each period composed of a short yielded flow and a long unyielded state is found. Oscillations of this nature have been reported for a soft-glassy material which fractures on a fast time scale and reheals on a slow time scale.

Les deux séminaires sont communs avec LAMA, Université de Savoie, et sont sponsorisés par l'ANR-maniphyc : http://www.lama.univ-savoie.fr/Maniphyc/index.php