Stokes Flow Inside Topographically Patterned Microchannel Using Boundary Element Method

Abstract

Abstarct This study focuses on the investigation of two-dimensional steady Stokes flow inside topographically patterned microchannel. Boundary element method (BEM) is used to solve the Stokes equation and obtain the streamline profiles. The velocity field and pressure gradients are obtained by taking the appropriate spatial derivatives of the stream function and vorticity variables. We restrict ourselves to rectangular stepped geometries and study the effect of variation of step width, step height and step frequency. Interestingly, ‘crown-shaped’ patterns in the horizontal velocity profiles are formed when a sudden contraction is met in the flow region. Pressure gradients, together with the velocity and streamline profiles are analyzed to gain a wholesome understanding of the flow physics.