Analysis of electroosmotic flow in a symmetric wavy channel containing anisotropic porous material with varying zeta potential

The present study examines an asymptotic analysis of electroosmotic flow phenomena bounded by the symmetrical wavy channel containing an anisotropic porous material under the variable pressure gradient and zeta potential. The incorporation of anisotropic porous material introduces additional complexities to the flow behavior. Electric potential is regulated by the non-linear Poisson–Boltzmann equation, which is linearized by the Debye–Hückel linearization process, and flow velocity inside the porous channel is governed by the Brinkman equation. The aspect ratio of the channel is considered to be significantly small, i.e., (δ2≪1). Obtaining analytical solutions to these non-linear coupled equations is a formidable challenge. To address this challenge, the equations are tackled by employing an asymptotic series expansion with respect to a small parameter, specifically the ratio of the channel thickness, where δ2≪1. The graphical analysis based on the derived expressions for flow quantities—such as fluid velocity, flow rate, flow resistance, wall shear stress, and pressure gradient along the wall—demonstrates the considerable impact of various governing parameters. These parameters, including the Debye–Hückel parameter, anisotropic ratio, slip length, and fluctuation amplitude, play a crucial role in influencing the behavior of these flow characteristics, highlighting their importance in determining the system's overall flow dynamics. The results demonstrate that an increment in the anisotropic ratio corresponds to an enhancement in fluid velocity and augmented flow rate. This relationship stems from the observed phenomenon wherein an enhancement in the anisotropic ratio leads to an augmentation in the permeability along the x-direction, thereby leading to an elevation in velocity and subsequently enhancing the flow rate. The study also examines the impact of flow reversal at the crests of the wavy channel resulting from the anisotropic ratio. The findings from our study have confirmed the axial fluid velocity in a purely pressure-driven flow system, where electroosmotic effects are not present. These results enhance our understanding of how anisotropic permeability affects fluid flow in microfluidic systems, especially when electrokinetic forces are at play.