Surface roughness impact on bioinspired rhythmic contractile microfluidic membrane pumping mechanism: A computational analysis

A significant challenge in microfluidic applications lies in understanding the interplay between surface characteristics and fluid dynamics. Our investigation presents a theoretical analysis of rough surface effects in a bio-inspired micropumping system. The mathematical model considers a non-uniform channel configuration, where fluid transport occurs via a specially formulated rough membrane undergoing synchronized expansion-contraction cycles. Traditional pumping analyses have primarily focused on smooth surfaces, leaving a critical knowledge gap in surface-roughness effects on fluid behavior. By examining the temporal evolution of wall profiles and membrane kinematics, we provide comprehensive insight into the system's dynamic response. Mathematical tractability is achieved through lubrication theory approximations, yielding closed-form analytical solutions. The model demonstrates an excellent correlation with the existing literature when tested under zero-roughness conditions. We present quantitative relationships between key system parameters, the surface roughness parameter, the membrane shape parameter, and their effects on pressure distributions, velocity distributions, volumetric flow rates, skin friction, and streamline patterns. These mathematical formulations offer valuable design guidelines for developing next-generation microfluidic devices in biomedical applications.