Finite Element Bounds to the Mass Flow Rate for Electro-Osmotic Flows in Two Space Dimensions

The micro pumping technology is one of the major and growing research fields in microfluidics. The use an electric voltage to induce electro-kinetic fluid flow is an efficient and reliable mechanism for micro pumping systems. The prediction of quantities such as the mass flow rate or the mean species concentration for this type of flow, termed the Electro-Osmotic flow, plays a crucial role in the design and control process of the entire microfluidic system. To this end, numerical techniques are efficient to evaluate these quantities but accuracy depends on the mesh utilizes. The a posteriori finite element output bound method is used to calculate these quantities while offering information regarding accuracy. The bound method applied here-in is based on the flux-free approach and provides relevant, inexpensive, and asymptotic lower and upper bounds to the mass flow rate of an Electro-Osmotic flow in a cross-intersection of a two-dimensional microchannel. To obtain shaper bounds, the flux-free approach is further enhanced by an adaptive mesh refinement strategy. This work focuses on the development of the numerical procedure for Electro-Osmotic flows and reports performance of the method in terms of numerical accuracy and computational cost.