Grigor Nika (Weierstrass Institute for Applied Analysis and Stochastic, Berlin, Germany) Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids

In this talk we develop a multiscale approach to describe the behavior of a periodic suspension of rigid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. By upscaling the quasi-static Maxwell equations coupled with the Stokes' equations we are able to capture the magnetorheological effect. The model we obtain generalizes the one introduced by Neuringer and Rosensweig (1964) for quasistatic phenomena. To be more precise, I will discuss existence of weak solutions using Shinbrot’s fixed point theorem, the nonlinear dependence of the effective coefficients on the volume fraction when chain structures are present, and the usefulness of the model by computing velocity profiles for some simple flows.