Slow Translation of a Soft Sphere in an Unbounded Micropolar Fluid with Interfacial Stress Jump

This study presents a theoretical analysis of the slow translation of a soft sphere through an unbounded micropolar fluid under steady, low Reynolds number conditions, accounting for the influence of interfacial stress jump. The soft sphere is modeled as a rigid solid core surrounded by a permeable porous gel layer, allowing fluid penetration and momentum exchange across the interface. This core–shell configuration captures the essential structural characteristics of coated or gel-like particles encountered in biological and engineering systems. Closed-form expressions for the velocity components, microrotation, stresses, and couple stresses are derived both within the porous micropolar gel layer surrounding the particle and in the exterior micropolar fluid. The flow inside the permeable coating is described using the general Brinkman solution in spherical coordinates, while the governing micropolar fluid equations are applied in the outer region. Appropriate boundary conditions are imposed at the solid core surface and at the permeable soft-sphere interface to ensure continuity of velocity and microrotation, together with the prescribed stress jump. The normalized drag force acting on the particle is obtained as a function of the particle-to-core radius ratio, permeability, stress-jump parameter, and micropolarity parameter. The results indicate that the hydrodynamic drag decreases as the porous layer becomes thicker and remains finite, approaching unity even when the soft sphere behaves as a solid particle or as a porous sphere translating through an infinite micropolar medium, with other parameters held fixed. Overall, the analysis elucidates the coupled roles of micropolar effects, interfacial stress jump, and porous-layer structure in governing the hydrodynamic resistance experienced by soft particles.