Modulating solute transport in magnetohydrodynamic pulsatile electroosmotic micro-channel flow: Role of symmetric and asymmetric wall zeta potentials

Abstract

This study provides a critical understanding of controlling solute distribution in microfluidic systems by examining the effects of symmetric and asymmetric zeta potentials under magnetohydrodynamic (MHD) pulsatile electroosmotic flow. These findings are vital for enhancing the efficiency of microfluidic devices used in lab-on-a-chip applications. The aim of this study is to explore the modulation of solute transport in MHD pulsatile electroosmotic microchannel flow, focusing on both symmetric and asymmetric wall zeta potentials. Using the Debye–Hückel approximation, the Poisson–Boltzmann equation is obtained. Subsequently, the convection–diffusion equation is solved using the velocity profile, with Aris's method of moments to derive the moment equations. These equations are then solved using a finite difference scheme. The mean concentration is calculated employing Hermite polynomials. We examined the effects of key parameters such as the electroosmotic parameter (κ), the Hartmann number (Ha), and zeta potentials on the dispersion coefficient (DT), mean concentration distribution (Cm), skewness, and kurtosis. We consider three situations: symmetric (ζ1=ζ2), partially asymmetric (ζ1=1.0,ζ2=0.0), and fully asymmetric (ζ1=1.0,ζ2=−1.0) zeta potentials. Our results reveal that asymmetric zeta potentials lead to faster dispersion, with DT decreasing with increasing κ for symmetric potentials and increasing for asymmetric ones. As the Hartmann number increases, dispersion decreases for both symmetric and asymmetric zeta potentials while the peak of mean concentration rises. The mean concentration profile exhibits Gaussian behavior at both small and large times, with anomalous behavior in the intermediate region. For symmetric zeta potentials, Gaussianity is observed at t = 0.001 in the diffusive regime and at t = 10.0 in Taylor's regime, while for asymmetric potentials, Gaussianity occurs at t = 0.03 and t = 3.0, indicating that large-time Gaussian behavior is approximately 3.33 times faster and dispersion becomes transient for asymmetric potentials.