Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field

In this study, we examine the movement of two hard spheres aligned in a straight line within an incompressible couple stress fluid under the impact of the magnetic field. Both objects have distinct shapes and move along an axis connecting their centers with varying velocities. As a first step, an incompressible analytical analysis is performed on a fluid with couple stress properties around an axially symmetric particle. Using the superposition principle, a general solution is developed for couple stress fluid flows over two moving objects. In order to achieve the boundary conditions, the boundary collocation strategy is applied to the surfaces of the two spheres. A set of tables and graphs illustrates numerical estimates of the dimensionless drag forces acting on two spherical objects. In addition, a drop in Hartmann number or an increase in couple stress viscosity will increase the dimensionless drag force on each spherical particle.