An Analytical Investigation for Combined Pressure-Driven and Electroosmotic Flow Without the Debye–Huckel Approximation

Abstract

In the present work, an analytical solution is presented for a combined pressure-driven electroosmotic flow of a Newtonian liquid within a microchannel between two parallel plates. The electroosmotic flow is considered to be induced by an externally applied electrostatic potential field and a pressure gradient. The no-slip boundary conditions are considered. The electric potential distribution is represented by the Poisson–Boltzmann equation. The Debye–Huckel linear approximation is ignored in the present work to minimize error in results. The reduced form of the Navier–Stokes and the energy equations are considered, respectively, to determine velocity and temperature distributions. Homotopy perturbation method (HPM) is adopted as an analytical tool to solve the nonlinear Poisson–Boltzmann equation for electrical potential distribution without the Debye–Huckel linear approximation. The Navier–Stokes and the energy equations subjected to respective boundary conditions are solved analytically. An expression of CfRe product is obtained solving the Navier–Stokes equation. The results obtained are validated with existing literature and show good agreement. The zeta potential is varied for a particular electrokinetic length, and proposed results are presented graphically. Finally, the Nusselt number is presented varying electrokinetic length for different values of zeta potential. The results demonstrate the influence of the zeta potential on the potential, velocity, temperature distributions, and Nusselt number.