Analytical study of effective Navier-slip and Stokes–Brinkman coupling for a dual-scale flow in a narrow channel over/inside unidirectional fibrous porous media

We present analytic solutions for transverse flows of a Newtonian fluid within a narrow gap channel over/inside unidirectional fibrous porous media, considering microfluidic applications such as the interfacial slip over a lubrication-infused surface (LIS) and rheometry with corrugated surfaces. Based on the lubrication theory, the effective slip length and Navier-slip boundary condition were derived to allow the flow rate over a fluid/porous interface to be reproduced, and these were validated for a narrow gap of up to 1.5 times of the fiber radius. To model the dual-scale flow in both a fluid channel and porous media, the effective viscosity and stress jump coefficient in the Stokes–Brinkman model with continuous and jump stress conditions, respectively, were also derived analytically by matching the slip velocity and velocity gradient (or stress) at the interface. We show that the effective slip length, effective viscosity, and stress jump coefficient can be written as closed-form solutions as a function of the dimensionless void length and channel height for various porous architectures such as quadrilateral (Quad), compressed hexagonal (Hex1), and equilateral hexagonal (Hex2) fibrous porous architectures. The usefulness of the analytical results was validated with comparative numerical simulations.