Numerical analysis of thermal conductivity effect on thermophoresis of a charged colloidal particle in aqueous media

Abstract

It is well known that colloidal particles dispersed in aqueous media usually are naturally charged and thus an electrical double layer (EDL) is formed near the surface of the charged particles. Here, we report a numerical analysis of the thermal conductivity effect on thermophoresis of a charged colloidal particle in aqueous media. The proposed numerical model includes the coupling energy equation, Nernst-Planck equation, Poisson equation, and Stokes equation. The numerical simulations reveal that the temperature distributes non-linearly around the particle surface due to mismatch of the thermal conductivity of particle and liquid, and such non-linear temperature distribution has a profound effect on the thermophoresis of the charged particle. When the non-linear temperature region is much thinner than the EDL region (or thick EDL cases), the thermodiffusion coefficient of the particle is similar to that of the “normal” particle (namely a particle with an equal thermal conductivity to the liquid), and the thermal conductivity effect on the thermophoresis is negligible. Yet, when the non-linear temperature region is much thicker than the EDL region (or thin EDL cases), the thermal conductivity effect becomes significant, and the particle thermodiffusion coefficient decreases with increasing the thermal conductivity ratio of particle to liquid. Finally, a parameter, the average dimensionless axial temperature gradient along the radial axis (r) in the EDL region, is derived to approximately estimate the thermophoretic behavior of a charged particle with arbitrary thermal conductivity and EDL thickness.