Electromagnetohydrodynamic flow within a fluid-saturated anisotropic porous microtube with rough surface

We investigated electromagnetohydrodynamic (EMHD) flow in a fluid-saturated anisotropic porous microtube with rough walls, which is relevant for microfluidics. Analytical solutions for the linearized Poisson–Boltzmann and Navier–Stokes equations are obtained using boundary perturbation techniques based on the roughness amplitude of the microtube in the low Reynolds number regime. The analysis reveals that the EMHD flow rate is influenced by a second-order term associated with surface roughness on the mean flow rate [Lei et al. “Electro-osmotic flow through a bumpy microtube: Boundary perturbation and detection of roughness,” Phys. Fluids 31, 012001 (2019)]. In this framework, this component of the roughness effect represents a pure enhancement of the flow and is influenced by the applied magnetic field strength, the permeability characteristics of the porous medium, and the angle of anisotropy. This component shows minimal variation at zero anisotropic angle and low permeability but increases with high permeability and Darcy number under weak magnetic fields. The maximum flow rate occurs in an isotropic porous medium. The surface roughness alters the boundary layer near the wall of the microtube, leading to a thinner boundary layer and an increased flow rate. The increased anisotropic permeability creates uneven resistance, forming smaller eddies and boluses. The radial pressure gradient decreases as a result of the increased flow resistance imposed by the porous medium in the radial direction. This study highlights that surface roughness enhances the friction factor ratio between a rough microtube and a smooth microtube due to increased surface area and irregularities, leading to greater friction resistance.