Role of Joule heating in dispersive mixing effects in electrophoretic cells: convective-diffusive transport aspects

This contribution addresses the problem of solute dispersion in a free convection electrophoretic cell for the batch mode of operation, caused by the Joule heating generation. The problem is analyzed by using the two-problem approach originally proposed by Bosse and Arce (Electrophoresis 2000, 21, 1018-1025). The approach identifies the carrier fluid problem and the solute problem. This contribution is focused on the latter. The strategy uses a sequential coupling between the energy, momentum and mass conservation equations and, based on geometrical and physical assumptions for the system, leads to the derivation of analytical temperature and velocity profiles inside the cell. These results are subsequently used in the derivation of the effective dispersion coefficient for the cell by using the method of area averaging. The result shows the first design equation that relates the Joule heating effect directly to the solute dispersion in the cell. Some illustrative results are presented and discussed and their implication to the operation and design of the device is addressed. Due to the assumptions made, the equation may be viewed as an upper boundary for applications such as free flow electrophoresis.