Multiscale modeling of magnetorheological suspensions
- Nika, Grigor
- Vernescu, Bogdan
2010 Mathematics Subject Classification
- 35M10 35M12 35M30 76D07 76T20
- Magnetorheological fluids, homogenizatio, chain structures, poiseuille, couette
We develop a multiscale approach to describe the behavior of a suspension of solid 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 & Rosensweig for quasistatic phenomena. We derive the macroscopic constitutive properties explicitly in terms of the solutions of local problems. The effective coefficients have a nonlinear dependence on the volume fraction when chain structures are present. The velocity profiles computed for some simple flows, exhibit an apparent yield stress and the flowprofile resembles a Bingham fluid flow.