The role of Joule heating in dispersive mixing effects in electrophoretic cells: hydrodynamic considerations

The analysis described in this contribution is focused on the effect of Joule heating generation on the hydrodynamics of batch electrophoretic cells (i.e., cells that do not display a forced convective term in the motion equation). The hydrodynamics of these cells is controlled by the viscous forces and by the buoyancy force caused by the temperature gradients due to the Joule heating generation. The analysis is based on differential models that lead to analytical and/or asymptotic solutions for the temperature and velocity profiles of the cell. The results are useful in determining the characteristics of the temperature and velocity profiles inside the cell. Furthermore, the results are excellent tools to be used in the analysis of the dispersive-mixing of solute when Joule heating generation must be accounted for. The analysis is performed by identifying two sequentially coupled problems. Thus, the "carrier fluid problem" and the "solute problem" are outlined. The former is associated with all the factors affecting the velocity profile and the latter is related to the convective-diffusion aspects that control the spreading of the solute inside the cell. The analysis of this contribution is centered on the discussion of the "carrier fluid problem" only. For the boundary conditions selected in the contribution, the study leads to the derivation of an analytical temperature and a "universal" velocity profile that feature the Joule heating number. The Grashof number is a scaling factor of the actual velocity profile. Several characteristics of these profiles are studied and some numerical illustrations have been included.