Stokes flow past circular cylinders in an out‐phase slip patterned microchannel using boundary element method

Abstract The objective of the present study is to investigate a steady, pressure‐driven two‐dimensional viscous incompressible creeping flow characterized by low Reynold's limit around circular cylinders of equal diameter inside a microchannel exhibiting wall roughness. The wall roughness is modeled using Navier's slip condition on the horizontal surfaces in an alternative manner, which retains a phase difference (i.e., out‐phase arrangement). The governing equations are solved using the stream function‐vorticity variables approach of the boundary element method. We considered the two instances of wall roughness, namely large and fine patterned wall roughness depending on the periodicity of patterning. We studied the streamline and vorticity contour plots, flow profiles, and shear stresses with varying slip lengths and radii of the horizontally aligned configuration of circular cylinders to obtain an in‐depth understanding of flow mechanics. The flow velocity and the shear stress show larger values when fine‐patterned wall roughness is considered. The present framework has immense feasible implications such as optimizing microfluidic devices, enhancing thermal management in electronics, and advancing nanofluidic platforms for various molecular and biomedical applications, including drug delivery systems.