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Frequency-dependent bifurcation in electromechanical microfluidic structures

Dielectric liquids rise up between vertically oriented, parallel electrodes if a voltage is applied. The resulting hydrostatic equilibrium balances the upward-directed ponderomotive force with the downward-directed gravitational force. Coating the electrodes with a dielectric layer makes it possible to achieve a similar, but now frequency-dependent effect with conductive liquids. If the electrodes (either coated or uncoated) are made slightly convergent, with the spacing closer at the top, the electric field coupled hydrostatic equilibrium exhibits a bifurcation. In this paper, a simple theory based on the Maxwell stress tensor and a linear RC circuit model is used to predict the frequency-dependent height-of-rise and the bifurcation phenomena. In the experiments, we used parylene-coated stainless steel electrodes, 24 mm long and 6.5 mm wide, to observe the height-of-rise of DI water and 1 mM KCl solution over the frequency range from 50 Hz to 20 kHz. The frequency-dependent experimental height-of-rise data, including the critical voltage and column height at which bifurcation occurs, are consistent with theoretical predictions. A simple model based on this theory successfully predicts the trapped liquid volume. Bifurcation phenomena have potential implications for the dynamic behavior of microfluidic schemes based on electrowetting and dielectrophoretic liquid actuation.