Drag on a semipermeable spherical particle covered by a couple stress fluid

This paper focuses on the hydrodynamic interaction between a semipermeable spherical particle and a laminar flow of couple stress fluid. The framework of the flow is divided into two regions, in which the non-Newtonian characteristics of the couple stress fluid are governed by classical Stokes equations and the permeable region is governed by Darcy's law. The asymptotic series expansion involves the stream functions in terms of modified Bessel's function and Gagenbauer's polynomials for the inner and outer regions. The graphical analysis demonstrating the superior outcomes of numerous parameters such as the couple stress parameter, the permeability parameter, and the couple stress viscosity ratio on the drag coefficient is conducted, and the outcomes are discussed comprehensively. The present study discovered that the drag of a semipermeable sphere is greater than that of a couple stress fluid sphere. A continuous reduction in the pressure distribution is observed with the rising value of the couple stress parameter. However, an increasing value of the couple stress parameter in the semipermeable medium contributes to increasing the tangential stress with respect to the distance from the surface. The current study's findings could be useful in analyzing significant clinical and industrial applications such as the filtration process for wastewater treatment, the design of the digestive system, fluid-solid disperse systems, and the petroleum industry. However, experimental verification is required for the proposed work.