Magneto-slip interaction in the migration of two rigid spheres in infinite couple stress fluid

This study investigates the motion of two rigid spheres, arranged linearly, immersed in an incompressible couple stress fluid subjected to a magnetic field. The spheres, possessing unique forms, traverse the axis linking their centers at varying velocities. The analysis begins with an incompressible analytical examination of a couple stress fluid around an axially symmetric particle. A general solution for the flow of couple stress fluid around the two moving spheres is then developed using the superposition principle. The boundary collocation method is implemented to the surfaces of the two spheres to satisfy the boundary conditions. Numerical estimations of the dimensionless drag forces exerted on the spheres are provided in tables and graphs. The results demonstrate that a reduction in the Hartmann number or an elevation in couple stress viscosity results in an augmentation of the dimensionless drag force on each sphere. Also, the slippage parameter is more significant on the hydrodynamic drag force. Additionally, the results are compared with earlier studies on specific scenarios, including the movement of a single rigid sphere across an infinite magnetic media, the flow of viscous fluids, and the behavior of Couple stress fluid without magnetohydrodynamics (MHD) within two concentric spheres (Madasu et al., 2019) and with magnetic field as Kashyap et al. (2019). Also, the results agree with the most recent work, the migration of two hard spheres that translate within an infinite couple stress fluid influenced by the magnetic field (El-Sapa and Alotaibi, 2024).