Electrothermal motion in an aqueous solution appears when an electric field is coupled with thermally-induced gradients of conductivity and permittivity in the fluid. The temperature field can be produced by external sources, such as strong illumination, or caused by the applied electric field through Joule heating. Electrothermal flow in microsystems is usually important at frequencies around 1 MHz and voltages around. 10 V. In this work, we consider first the two-dimensional problem of an aqueous solution placed on top of two co-planar electrodes that are subjected to an ac potenfial difference when there is either a vertical or horizontal temperature gradient. Secondly, we study the three-dimensional problem of an aqueous solution lying on four co-planar electrodes which produce a rotating field. This electric field when combined with a vertical temperature gradient rotates the liquid. The resulting electric field an liquid motion in these problems are characterised using self-similar solutions. Finally, these analytical solutions are compared with numerical and experimental results.

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