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In confined microfluidic spaces such as microchannels, electroosmosis is a convenient Coulomb-force mechanism used to electrically actuate charged particles and ions presented in the fluid and pump the electrolytic fluid itself through drag forces. The shape and position of electrode pairs, whose induced charges are in contact with the fluid, determine the electric field and hence the resulting fluid-dynamic velocity distribution. In this paper, we address the inverse design of the electrode-pair patterns in such actuation mechanisms. Our approach is to use topology optimization to inversely determine the patterns of an electrode pair. The optimization procedure requires a mathematical description of the desired fluid behaviour, and then drives the patterns of the electrode pairs to achieve the goal performance. We demonstrate the behaviour of the procedure, which couples the Navier-Stokes equations with charge …