Electro-hydrodynamics of Stokes flow in wavy microchannel under inclined magnetic field

This study investigates the hydrodynamics of two-dimensional, steady electroosmotic Stokes flow through a symmetric wavy microchannel subjected to a constant wall zeta potential and an externally applied inclined magnetic field. The novelty of the present work lies in the development of a perturbation-based analytical electrohydrodynamic model for this configuration, yielding closed-form analytical expressions for the streamline pattern, velocity components, wall shear stress, and pressure gradient. The electric double layer (EDL) potential distribution is described using the Poisson–Boltzmann equation under the Debye–Hückel approximation. Assuming a small channel aspect ratio and a negligible magnetic Reynolds number, the governing equations are solved analytically using the perturbation method. The influences of the Hartmann number ( H a ), Helmholtz–Smoluchowski velocity ( U H S ), inverse Debye length ( κ ), and inclination angle of the applied magnetic field ( θ ) on the streamline pattern, velocity distribution, wall shear stress, and pressure gradient are systematically examined. The results reveal that increasing the Hartmann number strengthens the Lorentz force, leading to lower axial velocity together with higher wall shear stress and pressure gradient. Increasing the Helmholtz–Smoluchowski velocity enhances the electroosmotic driving force, whereas sufficiently large negative values induce local flow reversal and recirculating vortices near the channel crest. Furthermore, increasing the inverse Debye length confines the electroosmotic body force closer to the channel walls, resulting in lower axial velocity, higher wall shear stress, and reduced pressure gradient. In contrast, increasing the inclination angle weakens the opposing Lorentz-force-induced resistance, producing higher centerline velocity together with lower wall shear stress and pressure gradient. The proposed model has potential applications in lab-on-a-chip systems, electroosmotic micropumps, electrokinetic separation devices, and microfluidic sample handling platforms.