Electroosmosis-modulated Darcy–Brinkman flow in sinusoidal microfluidic pipe: an analytical approach

Purpose This investigation is devoted to analyze the electroosmotic flow characteristics in a sinusoidal micropipe through a porous medium. This study aims to investigate the impact of surface waviness on Darcy–Brinkman flow in the presence of electroosmotic force, achieved through the unification of perturbation techniques. Design/methodology/approach Analytical approximate solutions for the governing flow equations are obtained through the utilization of a perturbation method. Findings The analytical study reveals that the periodic roughness on the surface of the micropipe generates periodic disturbances not only in the potential fields but also in the velocity profiles. An increase in the relative waviness of the pipe leads to the generation of corresponding waviness within the boundary layers of the flow. Surface waviness reduces the average velocity by increasing frictional resistance, while higher Darcy numbers and electroosmotic parameters lead to higher velocities by reducing flow resistance and enhancing electrokinetic forces, respectively. In addition, the presence of waviness introduces higher flow resistivity, contributing to an overall increase in the friction factor. Higher permeability in porous media induces boundary-layer reverse flows, resulting in elevated flow resistivity. Originality/value The current findings offer valuable insights for researchers in biomedical engineering and related fields. The author’s discoveries have the potential to drive advancements in microfluidic systems, benefiting various domains. These include optimizing drug delivery in biomedical devices, improving blood filtration applications and enhancing the efficiency of fluid transport in porous media for engineering applications.