Théorique, numérique
In this project, we proposed to study the flow of yield stress materials, fluids that require a minimal amount of stress to flow, in porous media. Although yield stress fluids are encountered in many applications, the characterisation of flow in disordered systems remains a challenging and controversial task. The main difficulty arises from the strong interplay between the nonlinear rheology and the disorder of the system. In particular, close to the critical pressure, the flow correlation exhibits a fat tail distribution reminiscent of critical systems in disordered media. We will mainly focus on the influence of the structural heterogeneities on the flow-pressure relationship. These problems will be investigated using different approaches: numerical simulations, statistical physics and asymptotic expansions.