Impact of anisotropic porosity on electroosmotic flow of micropolar fluid in wavy channel

Abstract

The influence of weak anisotropy on electroosmotic flow of micropolar fluids in geometrically non-uniform microchannels is explored through a comprehensive theoretical framework. Using a rigorous mathematical framework, a comprehensive model is developed that couples the Poisson–Boltzmann equation governing the electric double layer dynamics and the Brinkman equation with the micro rotational term. To tackle this difficulty, the perturbation technique is employed to resolve the coupled equations with appropriate boundary conditions, where the channel’s aspect ratio ($\delta \ll 1$) is taken as the perturbation parameter. A comprehensive analysis is conducted to examine the effects of critical parameters such as the Debye–Hückel parameter, anisotropic ratio, fluctuation parameter, micro-scale parameter ($m$), and coupling parameter ($N$) on various flow characteristics. The findings indicate that a stronger micropolar effect leads to a decrease in linear velocity near the wavy wall, while a contrasting increase in linear velocity is observed at greater distances from the wall. The velocity profiles computed numerically using the finite difference method show negligible difference between solutions from linearized Poisson–Boltzmann equations (Debye–Hückel approximation) and non-linear Poisson–Boltzmann equations for weak anisotropy. These findings have significant implications for optimizing microfluidic devices in biomedical applications, chemical separation processes, and micro-scale heat exchangers where precise flow control is paramount.