Thermal effects on electro-osmotic pumping of liquids in microchannels

Abstract

In this paper we present a mathematical model predicting combined electro-osmotic- and pressure-driven flow behavior in a straight microchannel for the case when the system is under a non-isothermal condition. The distribution of the charge density is governed by a nonlinear, two-dimensional Poisson–Boltzmann equation, and a body force caused by the interaction between the charge density and the applied electrical potential field is included in the full Navier–Stokes equations. Under non-isothermal conditions, arising from heat sources (Joule heating) within the system and/or a temperature difference between the system and the ambient, the equation of energy conservation describing temperature distribution has to be considered as well. The governing equations, interlinked via temperature, are solved numerically using a finite difference method. The numerical results indicate that for a given cross-sectional mean velocity, there exists an optimal dimensionless parameter (κh), which is the inverse Debye length multiplied by the channel size, which gives the highest hydraulic head generated by the electro-osmotic force. It has also been demonstrated that the pumping performance predicted by the isothermal model deviates substantially from that predicted by the non-isothermal model when Joule heating is significant.