In general, the modeling of electroosmotic flows can be approached in two fundamentally–different ways. (i) The thickness of electrical double layer (EDL) is ignored and the effect of the electrical forces within the EDL is imaged into a modified kinematic boundary condition, the so-called Helmholtz–Smoluchowski slip condition. This approach is numerically simple and inexpensive, but implies several restrictions. (ii) The EDL is fully resolved, using a first–principle approach based on differential conservation equations for mass, momentum, and charge. This approach is enormously elaborate and numerically expensive, but appears to be applicable for a much wider range of problems. As an example, the treatment of internal electrodes, adjacent to insulating walls at defined zeta potential, appears difficult with the simple approach (i), since any non–continuous potential distribution at the wall leads to a singularity of the electrical field strength. To avoid these difficulties, we develop a hybrid model which, on the one hand, electrically resolves the EDL to reveal a perfectly-continuous potential distribution in the complete microchannel. On the other hand, the flow equations are solved in the fluid bulk only, not comprising the EDL. Hence, the effect of the EDL is still incorporated by means of modified kinematic boundary conditions. The advantage of this hybrid model is, firstly, to avoid artificial singularities of the electrical field strength, where regions of different surface charge meet. These singularities are clearly artificial, since they result from neglecting the extend of the EDL. Secondly, the hybrid model, at each time step, needs to solve only once for the potential distribution, which makes it numerically inexpensive and simple. Hence, systematic parameter studies are within reach. We apply the hybrid model to investigate the influence of internal electrodes onto the flow field, driven by electroosmosis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances (if compared to external electrodes), they can be operated at lower voltages and still ensure strong electrical field strength. Systematic studies on the effect of different electrode positions and voltages are presented, leading to optimized settings for specific tasks as pumping or mixing. Further, a comparison to first-principle simulations using the approach (ii) is presented for selected cases. This demonstrates that the hybrid model perfectly captures the dominant physics.
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A Hybrid Model for the Simulation of Electroosmotic Flows in Microchannels, Induced by Internal Electrodes
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Stieglitz, I, & Ehrhard, P. "A Hybrid Model for the Simulation of Electroosmotic Flows in Microchannels, Induced by Internal Electrodes." Proceedings of the ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels collocated with 3rd Joint US-European Fluids Engineering Summer Meeting. ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels: Parts A and B. Montreal, Quebec, Canada. August 1–5, 2010. pp. 289-295. ASME. https://doi.org/10.1115/FEDSM-ICNMM2010-30750
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