WIAS Preprint No. 2598, (2019)

Multiscale modeling of magnetorheological suspensions


  • Nika, Grigor
    ORCID: 0000-0002-4403-6908
  • Vernescu, Bogdan
    ORCID: 0000-0001-6153-6392

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.

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