Temperature gradient focusing is a recently developed technique for spatially focusing and separating ionic analytes in microchannels. The temperature gradient required for temperature gradient focusing can be generated either by an imposed temperature gradient or by Joule heating resulted from an applied electric field that also drives buffer flow. In this study, a numerical model describing the Joule heating induced temperature development and temperature gradient focusing is developed. The model consists of a set of governing equations including the Poisson-Boltzmann equation, the Laplace equation, the Navier-Stokes equations, the energy equations and the mass transport equation. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity and electric conductivity are temperature-dependent, these governing equations are coupled, and therefore the coupled governing equations are solved numerically by using a CFD based numerical method. The numerical simulations agree well with the experimental results, suggesting that the valid mathematical model presented in this study.

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