Electroosmotic Pumping in Rectangular Microchannels: a Numerical Treatment by the Finite Element Method ∗†

In this work, the analysis of electroosmotic pumping mechanisms in microchan-nels is performed through the solution of Poisson-Boltzmann and Navier Stokes equations by the Finite Element Method. This approach is combined with a Newton-Raphson iterative scheme, allowing a full treatment of the non-linear Poisson-Boltzmann source term which is normally approximated by linearizations in other methods. The computer simulation of fluid flow in microchannels has received an increasing attention recently, due mainly to emerging applications of deep technological signifi-cance. We could mention for instance the microchips and laser diode arrays cooling, as well as flow injection mechanisms in biological micro-reactors. Since the use of me-chanical fluid propulsion in such devices would impose severe practical limitations (like the difficulty to produce components of microscale pumps), surface electric charge ef-fects may be used to induce fluid flows through microchannel devices free from moving parts [2]. It is a well known fact that ion adsorption, ion dissolution or ionization may transfer electric charges to a surface brought into contact with a polar fluid. Through the so called Electric Double Layer (EDL) effect [1], this induced surface charge af-fects the ion distribution of the fluid, in such a way that these ions may pull the fluid molecules under the action of an external electric field, applied along the length of the fluid microchannel(the fluid flow direction). In a few words, this is the electroosmotic pumping mechanism. The EDL theory relates the surface electrostatic potential ψ and the charges within the fluid at the surface neighborhood by means of the Poisson equation ∂2ψ ∂y