Numerical Simulation of the Interplay of Electrical Double Layers, Electrode Reactions, and Pressure-Driven Flows in Microchannels

We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. The mathematical model for the numerical treatment relies on a first–principle description of the EDL and the electrical forces caused by the electrical field between internal electrodes. Hence, the so–called Debye–Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the Navier–Stokes equations for the flow field, species transport equations, based on the Nernst–Planck equation, and a model for the electrode reactions, based on the Butler–Volmer equation. The simulations are time–dependent and two–dimensional (plane) in nature and employ a finite–volume method. It is discussed, e.g., how the thickness of the EDL expands at the stagnation point of a forced flow, as the velocity (or Reynolds number) is increased. Furthermore, the effect of electrode reactions on the ionic strength and, hence, on the EDL and the electroosmotic flow, are discussed.