Interfacial dynamics of a composite spherical particle between microstructured and viscous fluids

This study presents a semi-analytical solution, developed using a collocation-based approach, to investigate the flow field induced by the perpendicular motion of a composite spherical particle toward a planar interface separating two immiscible, semi-infinite fluid layers. One fluid exhibits microstructured (micropolar) behavior described by Eringen's theory, while the other behaves as a conventional viscous Newtonian fluid. The composite particle is modeled as a rigid, impermeable spherical core enveloped by a porous Brinkman shell and is assumed to reside in the Newtonian region. The analysis is conducted under low-Reynolds-number and negligible-capillarity conditions, ensuring that interfacial deformation remains minimal. Owing to the linearity of the governing equations, the flow fields in both fluid domains are constructed by superposing fundamental solutions formulated in cylindrical and spherical coordinates. The normalized drag force acting on the composite particle is evaluated over a range of dimensionless parameters, showing excellent numerical convergence and agreement with established limiting cases. Quantitatively, the drag force was found to increase by up to 150%–300% as the particle approaches the interface (from a/z0=0.1 to 0.9), while variations in the porous-layer permeability produced drag reductions of up to 40%–55% for highly permeable shells (α≤0.1). Micropolar effects further modified the drag by 10%–20% depending on the spin-coupling parameter and viscosity ratios. The findings provide valuable insights for the design of advanced microfluidic systems, such as lab-on-a-chip platforms, where the interactions of functionalized or composite microparticles with complex or soft interfaces critically influence particle transport, separation, and sensing performance.