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Mathematics > Analysis of PDEs

arXiv:1804.02066 (math)
[Submitted on 5 Apr 2018 (v1), last revised 17 Jun 2019 (this version, v2)]

Title:Multiscale modeling of magnetorheological suspensions

Authors:Grigor Nika, Bogdan Vernescu
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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.
Comments: 25 pages
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.02066 [math.AP]
  (or arXiv:1804.02066v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.02066
Related DOI: https://doi.org/10.1007/s00033-019-1238-4

Submission history

From: Grigor Nika [view email]
[v1] Thu, 5 Apr 2018 21:37:47 UTC (2,251 KB)
[v2] Mon, 17 Jun 2019 14:36:41 UTC (5,109 KB)
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