Interaction of Two Rigid Spheres Oscillating in an Infinite Liquid under the Control of a Magnetic Field

Abstract

The transient creeping motion of two rigid spheres oscillating in a boundless viscous fluid beneath the impact of the magnetic field is investigated. There is no slippage associated with a Stokes flow on the two rigid spherical surfaces with different sizes and radii. The solutions can be obtained using the boundary collocation scheme at low Reynolds numbers. The unsteady real and imaginary drag coefficients are estimated on the hard spherical particles. These coefficients are computed in tables for various parameters and illustrated graphically. The frequency parameter and Hartmann number also play a significant role in this study where the drag coefficients decrease or increase by 100 percent after the value of $\kappa =5.0$ . Using available literature data, we tested the accuracy and reliability of our results.