Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Wednesday, July 14, 19:30 ~ 20:00 UTC-3

Homogenization of non-dilute suspension of a viscous fluid with magnetic particles

Thuyen Dang

University of Houston, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

This talk presents a rigorous homogenization result of a particulate flow consisting of a non-dilute suspension of a viscous Newtonian fluid with magnetizable particles. The fluid is assumed to be described by the Stokes flow, while the particles are either paramagnetic or diamagnetic, for which the magnetization field is a linear function of the magnetic field. The coefficients of the corresponding partial differential equations are locally periodic. A one-way coupling between the fluid domain and the particles is also assumed. The homogenized or effective response of such a suspension is derived, and the mathematical justification of the obtained asymptotics is carried out. The two-scale convergence method is adopted for the latter. As a consequence, the presented result provides a justification for the formal asymptotic analysis of Levy and Sanchez-Palencia for particulate steady-state Stokes flows.

Joint work with Yuliya Gorb (National Science Foundation, USA) and Silvia Jimenez Bolanos (Colgate University, USA).

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