Comprehensive model of electrokinetic flow and migration in microchannels with conductivity gradients

A comprehensive model of electrokinetic flow and transport of electrolytes in microchannels with conductivity gradients is developed. The electrical potential is modeled by a combination of an electrostatic and an electrodynamic approach. The fluid dynamics are described by the Navier–Stokes equations, extended by an electrical force term. The chemistry of the system is represented by source terms in the mass transport equations, derived from an equilibrium approach. Moreover, the interaction between ionic species concentration and physicochemical properties of the microchannel substrate (i.e. zeta-potential) is taken into consideration by an empirical approach. Approximate analytical solutions for all variables are found which are valid within the electrical double layer. By using the method of matched asymptotic expansions, these solutions provide boundary conditions for the numerical simulation of the bulk liquid. The models are implemented in a Finite-Element-Code. As an example, simulations of an electrophoretic injection/separation process in a micro-electrophoresis device are performed. The results of the simulations show the strong coupling between the involved physicochemical phenomena. Simulations with a constant and a concentration-depend zeta-potential clarify the importance of a proper modeling of the physicochemical substrate characteristics.