Hydrostatics and steady dynamics of spatially varying electromechanical flow structures

Abstract

The hydrostatic and steady laminar hydrodynamic equilibria of spatially varying electromechanical flow structures are investigated. Under certain conditions the relationship between the dielectric height of rise and the applied voltage is found to be double valued. It is found that one of the two equilibrium values is always unstable. This gives rise to the experimentally observed spontaneous rise of the fluid to the top of the structure, once a certain critical voltage is reached. Starting above this critical voltage with the structure completely filled and decreasing the applied voltage toward the critical value results in pinch-in failure at an intermediate point along the structure and trapping of dielectric fluid at the top. The simple mathematical model developed predicts all these phenomena, without recourse to tedious point-by-point surface force equilibrium determination. Experiments are reported which verify the results for the hydrostatic case.