Particle-particle interactions in axisymmetric MHD viscous flow

A. Sellier¹ - S. H. Aydin²

¹ LadHyX, Ecole polytechnique, 91128 Palaiseau Cédex, France
² Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey

Abstract
This work investigates axisymmetric interactions between two solid insulating spheres translating, in an unbounded conducting Newtonian liquid, parallel with both their line of centers and a prescribed steady and uniform ambient magnetic field with a magnitude B > 0. The employed procedure extends for this cluster the boundary formulation proposed and successfully worked out by the authors for a single sphere [1]. The resulting coupled boundary-integral equations which govern the traction arising at each sphere boundary are numerically inverted for two equal spheres and the liquid velocity and pressure fields are then subsequently computed in the entire liquid domain from the relevant integral representations of those quantities. For the addressed two-sphere cluster, the particle-particle interactions are found to deeply depend upon the spheres' spacing and on the flow Hartmann number Ha=aB/√{μ/σ}, where a denotes each sphere radius and μ and σ > 0 designate the liquid uniform viscosity and conductivity, respectively. Tables 1, Figs 7, Refs 9.