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

Abstract

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.

Joule heating in electrokinetic flow

“…Such nonuniform temperature and velocity fields then make the sample front translate faster but more dispersed. The same authors later validated the applicability of PoissonBoltzmann equation in describing the ionic distribution through comparison to the full Nernst-Planck equation [72].…”

Effect of Joule heating on electrokinetic transport

“…Deviation occurs as the channel size-to-Debye length ratio decreases. In that case Boltzmann distribution may not be suitable for nanochannels [3,11]. The EOF field is governed by continuity and modified Navier-Stokes equations…”

“…Numerical solutions are the only way to solve these highly coupled set of equations, Eqs. (2)- (11). Numerical solutions are further complicated by the simultaneous presence of three separate length scales, the channel length in millimeters, the channel cross-sectional dimension in microns and EDL thickness in nanometers.…”

Estimation of Joule heating effect on temperature and pressure distribution in electrokinetic‐driven microchannel flows

“…The specified flow rate and constant wall temperature were assumed in their study. Tang et al [23][24][25] proposed a numerical model for predicting the Joule heating effect on the temperature, velocity, and concentration distributions in microchannels and microtubes. In their model, the coupled Poisson-Boltzmann, Navier-Stokes, and energy equations were solved.…”