| There is a need for non-mechanical micropumps without moving parts for miniature diagnostic kits, implantable drug delivery devices, micro-fuel cells and other micro-fluidic applications. I report the theory behind a new high-frequency (>1 MHz) AC pump design based on Faradaic reactions. Analysis of this system is complicated by the existence of multiple spatial and time scales. We use matched asymptotics to drive an effective boundary conditions for the electrical potential and slip velocity, thus removing the double layer from the problem and reducing the computational and analytical efforts. Both effective boundary conditions are complex after Fourier transform due to the double layer charging dynamics. We use these effective conditions to solve the outer potential, which is a complex harmonic function obeying the Laplace equation, for a unique orthogonal electrode design. A conformal map is used to map the domain into a half plane and the equation is converted into boundary integral equation using the appropriate Green.s functions. The integral equation can be solved explicitly at low frequencies by a perturbation ansatz that expands about the equilibrium limit. We are able to estimate the field distribution and the stream function of the time-averaged electro-osmotic flow for our pump. The flow rate is shown to be at least one order of magnitude higher than the previous AC pumps and the flow field is confirmed with experimental imaging of micro-fabricated pumps. Our particular approach, integrating asymptotics and numerics, can be applied to other electrokinetic phenomena like electroporation, dielectrophoresis, electro-rotation and electro-osmosis. |