arXiv subjects

Bogdan Vernescu

Publications and source records attributed to Bogdan Vernescu.

4 recordsLinked to original sources

arXiv2019

Multiscale modeling of magnetorheological suspensions

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.

math.AP↗

arXiv2014

Nonlinear Neutral Inclusions: Assemblages of Coated Ellipsoids

The problem of determining nonlinear neutral inclusions in (electrical or thermal)conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well known Hashin coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids.

math.AP↗

arXiv2013

Homogenization for Rigid Suspensions with Random Velocity-Dependent Interfacial Forces

We study suspensions of solid particles in a viscous incompressible fluid in the presence of highly oscillatory velocity-dependent surface forces. The flow at a small Reynolds number is modeled by the Stokes equations coupled with the motion of rigid particles arranged in a periodic array. The objective is to perform homogenization for the given suspension and obtain an equivalent description of a homogeneous (effective) medium, the macroscopic effect of the interfacial forces and the effective viscosity are determined using the analysis on a periodicity cell. In particular, the solutions $\bm{u}^\e_ω$ to a family of problems corresponding to the size of microstructure $\e$ and describing suspensions of rigid particles with random surface forces imposed on the interface, converge $H^1$-- weakly as $\e \to 0$ a.s. to a solution of the so-called homogenized problem with constant coefficients. It is also shown that there is a corrector to a homogenized solution that yields a strong $H^1$-- convergence. The main technical construct is built upon the $Γ$-- convergence theory.

math.AP↗

arXiv2012

Nonlinear Neutral Inclusions: Assemblages of Spheres

If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated spheres and the two-dimensional analogous problem of assemblages of coated disks.

math-ph↗