Effect of permeability on the interaction between two spheres translating through a couple stress fluid

This article explores the steady and uniform motion of two spherical particles submerged in an infinite fluid with Brinkman-couple stress properties, where the particles are entirely immersed and surface slippage is disregarded. While the particles may vary in size, they are composed of the same material and move along the line that connects their centers, influenced by different velocities or external forces. The analysis is performed under low Reynolds number conditions, which signify laminar flow dominated by viscous forces. Using boundary collocation methods, semi-analytical solutions to the governing differential equations are derived, facilitating a thorough investigation of the system. The study employs normalized drag force to evaluate the effects of particle interactions, presenting calculated values graphically and discussing them with several key factors, such as particle size and separation distance, thereby enhancing the understanding of particle dynamics in complex fluid environments. The analysis of how varying the permeability parameter affects flow patterns around two spheres in a couple of stress fluids is shown.