Modeling of Electroosmotic Flow and Capillary Electrophoresis with the Joule Heating Effect:  The Nernst−Planck Equation versus the Boltzmann Distribution

Joule heating is present in electrokinetic transport phenomena, which are widely used in microfluidic systems. In this paper, a rigorous mathematical model is developed to describe the Joule heating and its effects on electroosmotic flow and mass species transport in microchannels. The proposed model includes the Poisson equation, the modified Navier−Stokes equation, and the conjugate energy equation (for the liquid solution and the capillary wall). Specifically, the ionic concentration distributions are modeled using (i) the general Nernst−Planck equation and (ii) the simple Boltzmann distribution. The relevant governing equations are coupled through the temperature-dependent solution dielectric constant, viscosity, and thermal conductivity, and, hence, they are numerically solved using a finite-volume-based CFD technique. The applicability of the Nernst−Planck equation and the Boltzmann distribution in the electroosmotic flow with Joule heating has been discussed. The results of the time and spatial development for both the electroosmotic flow field and the Joule heating induced temperature field are presented. It is found that the presence of the Joule heating can result in significantly different electroosmotic flow and mass species transport characteristics.