Slip-Driven Interaction of Dual Spheres in Couple Stress Fluids Within a Permeable Medium

This study investigates the consistent and uniform movement of two spherical particles within an infinite porous medium saturated with a couple stress fluid, with a particular focus on the effects of surface slippage. The research reveals that surface slippage significantly reduces the drag force experienced by the particles, thereby influencing their hydrodynamic interactions. Conversely, increases in permeability and particle size similarity tend to enhance both the drag force and the inter-particle interaction forces, affecting the overall dynamics of particle motion. The analysis is conducted within the low-Reynolds-number regime, characteristic of laminar flow dominated by viscous forces, and employs boundary collocation methodologies to derive semi-analytical solutions to the governing differential equations. This approach enables a detailed characterization of the flow behavior and inter-particle forces in intricate fluid environments, including those with porous matrices and complex rheological properties. The findings from this investigation are consistent with prior numerical analyses, notably those conducted by Alotaibi and El-Sapa (2025), and corroborate earlier studies by Shehadeh and Ashmawy (2019), which examined cases of no slippage and permeability effects. Additionally, the results align with earlier research by Shreen et al. (2018) concerning viscous fluids, thereby reinforcing the validity of the conclusions. Overall, the study enhances the understanding of particle-fluid interactions in porous, couple stress-rich media, providing valuable insights into the roles of surface slippage, permeability, and particle size in determining hydrodynamic forces.