Mixing and dispersion phenomena caused by the carrier fluid in an electrophoretic cell is the main subject of this study. In particular, the effects of Joule heating on temperature and velocity profiles for Eyring-model fluids (EMF) are studied. The heat transfer is sequentially coupled with momentum transfer to derive an analytical expression for both the temperature and the velocity profiles. These results are then used to show the hydrodynamic behavior of the fluid in a batch electrophoretic cell. Furthermore, the results obtained are useful to compare with the fluid behavior of other carriers of different rheology, such as Newtonian fluids, power-law fluids, and viscoelastic fluids that obey the CEF model. The results show that EMF are potentially good carriers for relatively high Joule heat generation and therefore good candidates to control mixing inside the electrophoretic cell.