Analytical solutions of fluid flow and heat transfer in parallel-plate micro-channels at high zeta-potentials

Abstract

This paper investigates the effect of the EDL at the solid–liquid interface on the liquid flow and heat transfer through a micro-channel formed by two parallel plates. The complete Poisson–Boltzmann equation (without the frequently used linear approximation) was solved analytically in order to determine the EDL field near the solid–liquid interface. The momentum equation was solved analytically taking into consideration the electrical body force resulting from the EDL field and the energy equation was solved analytically taking viscous dissipation into consideration. Effects of the channel size and the strength of the zeta-potential on the electrostatic potential, the streaming potential, the velocity profile, the temperature profile, the volume flow rate, the apparent viscosity, the friction factor, and Nusselt number are presented and discussed. Results of the present analysis, which are based on the complete Poisson–Boltzmann equation, are compared with a simplified analysis that used a linear approximation of the Poisson–Boltzmann equation.