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 Jou le heating generation on the hydrodynamics of batch electrophoretic cells ( i.e., cells that do not display a forced convective term in the motion equa tion). The hydrodynamics of these cells is controlled by the viscous forces and by the buoyancy force caused by the temperature gradients due to the J oule heating generation. The analysis is based on differential models that lead to analytical and/or asymptotic solutions for the temperature and velo city profiles of the cell. The results are useful in determining the charac teristics of the temperature and velocity profiles inside the cell. Further more, the results are excellent tools to be used in the analysis of the dis persive-mixing of solute when Joule heating generation must be accounted fo r. The analysis is performed by identifying two sequentially coupled proble ms. Thus, the "carrier fluid problem" and the "solute problem" are outlined . The former is associated with all the factors affecting the velocity prof ile and the latter is related to the convective-diffusion aspects that cont rol the spreading of the solute inside the cell. The analysis of this contr ibution is centered on the discussion of the "carrier fluid problem" only. For the boundary conditions selected in the contribution, the study leads t o the derivation of an analytical temperature and a "universal" velocity pr ofile that feature the Joule heating number. The Grashof number is a scalin g factor of the actual velocity profile. Several characteristics of these p rofiles are studied and some numerical illustrations have been included.