Multiscale modeling of magnetorheological suspensions

TL;DR

This paper presents a multiscale model for magnetorheological suspensions that captures their complex behavior under magnetic fields, including nonlinear effects and apparent yield stress, by upscaling Maxwell and Stokes equations.

Contribution

It introduces a generalized multiscale approach that explicitly derives macroscopic properties from local problems, extending previous models to include nonlinear volume fraction dependence.

Findings

Effective coefficients depend nonlinearly on volume fraction.

Flow profiles exhibit apparent yield stress similar to Bingham fluids.

Model captures magnetorheological effects and chain structure influences.

Abstract

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 flow profile resembles a Bingham fluid flow.