Section: New Results

Complex fluids

Participants : David Benoit, Sébastien Boyaval, Claude Le Bris, Tony Lelièvre.

In [41] , Claude Le Bris and Tony Lelièvre review the state-of-the-art of numerical and mathematical results on micro-macro models for viscoelastic fluids.

Following previous works, in [32] , Claude Le Bris and Tony Lelièvre together with Lingbing He analyze the longtime behaviour of nematic polymeric fluids (liquid crystals). The longtime asymptotic for such models is much richer than for flexible polymers, that were considered in a previous analysis. Indeed, for these models, periodic in time behaviours are observed.

In his PhD under the supervision of Claude Le Bris and Tony Lelièvre, David Benoît studies models of aging fluids developed at the ESPCI (Ecole supérieure de physique et de chimie industrielles) and designed to take into account phenomena such as shear thinning, aging and shear banding in falling sphere experiments. The work consists in studying on the one hand the mathematical well-posedness of some macroscopic models, see [51] and, on the other hand, in trying to understand the link between such macroscopic models and microscopic models which have been proposed to describe such fluids.

Related to the mathematical modelling of free-surface complex flows under gravity, a new reduced model for thin layers of a viscoelastic upper-convected Maxwell fluid was derived by S. Boyaval in collaboration with François Bouchut, and possibly discontinuous solutions were numerically simulated with a new finite-volume scheme of relaxation type that satisfies a discrete counterpart of the natural dissipation [20] . This work is being pursued for other models.

Finally, in [31] , Alexandre Ern (CERMICS), Rémi Joubaud (CERMICS) and Tony Lelièvre analyze a model describing equilibrium binary electrolytes surrounded by charged solid walls. This work is done in collaboration with physicists from the group PECSA at Université Pierre et Marie Curie. Applications include the modelization of clays for the burying of nuclear waste.