Multiscale modeling of magnetorheological suspensions

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 [24], [27] 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.

Homogenization of Non-dilute Suspension of Viscous Fluid with Magnetic Particles

“…In the framework of a homogenization method, the studies most directly related to this current contribution are [18,17,22]. More specifically, in [18], the behavior of non-dilute suspensions of rigid particles in a Newtonian fluid was studied in the case where the magnetic field was neglected, assuming a locally periodic array of particles.…”

Physical Mechanisms of Magnetic Field Effects on the Dielectric Function of Hybrid Magnetorheological Suspensions

“…These materials, together with magnetorheological suspensions (MRSs) and magnetorheological elastomers (MREs), belong to the class of active magnetic materials. Since the matrix is a liquid for MRSs [ 1 , 2 , 3 , 4 , 5 , 6 ] and silicone rubber for MREs, embedded with ferri-/ferromagnetic microparticles in both cases [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ], the matrix for hMRSs is a fabric of polymeric fibers doped with MRSs [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. The term “hybrid” refers to magnetically active materials made up of a fabric of polymeric fibers doped with MRSs [ 21 , 22 , 23 , 24 , 25 ].…”

“…When applying a magnetic field, the magnetizable phase from MRSs, MREs, and hMRSs orients along the magnetic field in aggregates with chain or column shapes. The strength of the chains depends on the magnetic properties of the magnetizable phase and the intensity of the external magnetic field [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ].…”

“…The chain formation when applying a magnetic field and its unraveling when the magnetic field is cancelled depend on the viscoelastic properties of the matrix where the magnetizable phase is dispersed, and the result is a delay in the settlement of physical properties [ 1 , 2 , 3 , 4 , 5 , 6 ]. For MRSs, this delay depends on the quantity of the magnetizable phase, the viscosity of the liquid matrix, and the additives used [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ].…”

“…The chain formation when applying a magnetic field and its unraveling when the magnetic field is cancelled depend on the viscoelastic properties of the matrix where the magnetizable phase is dispersed, and the result is a delay in the settlement of physical properties [ 1 , 2 , 3 , 4 , 5 , 6 ]. For MRSs, this delay depends on the quantity of the magnetizable phase, the viscosity of the liquid matrix, and the additives used [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ]. For MREs, the delay in stabilization of the response function to magnetic excitation depends on the type of silicone rubber and the polymerization speed of the mixture in the presence or absence of the external magnetic field [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ].…”