Stabilized Formulation for Electrophoretic Transport Problems

Electrophoresis consist in the relative motion of charged particles with respect to the surrounding liquid when an external electric field is applied. The magnitude of this relative velocity depends on the local magnitude of the electric field and the so-called electrophoretic mobility. Electrophoretic mobility represents the relationship between electric and hydrodynamic transport properties of the moving molecules. On the other side, the magnitude of the electric field depends on the electric conductivity of the solution and the electric potential differences applied at the inlets and outlets of fluid channels. This electric conductivity depends on the local concentration of ions, that also move due to the electrophoretic transport, which generates a strong coupling between mass transport and electric fields. Solving electrophoretic transport problems numerically, and its coupling with fluid and electric problems, generates oscillations or instabilities in solutions that are directly related to the high values of the local Péclet number and the non null divergence of the migrative field. In order to surmount these difficulties a novel scheme of stabilization for this particular application is proposed. This stabilization technique is based on SUPG and shock capturing methods particularly adapted for this situation. In order to demonstrate stabilization capability of the proposed formulation, some test are performed for 1D and 2D electrophoretic separations of molecules of biological interest.