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On Two Dimensional Electrohydrostatic Stability
C. Sozou and R. C. Hewson-Browne
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 349, No. 1657 (May 4, 1976), pp. 231-243
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/79030
Page Count: 13
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Complex variable techniques are used for the study of the electrohydrostatic stability of two dimensional charged conducting membranes, which are assumed to be fixed along their edges. The formulation of the problem is quite general, but the numerical solution presented refers to the case when the membranes are symmetrical with respect to the plane bisecting their width and carry equal and opposite charges. It is found, as expected, that for a given set of data the equilibrium configuration breaks down if the membranes are sufficiently charged. When the membranes are sufficiently apart the breakdown occurs at their edges and is manifested as inability of the system to satisfy the equilibrium conditions there. When the membranes are sufficiently close together and are charged to a certain level, they touch at their mid-points and the equilibrium breaks down. Our results are compared with an approximate solution of this problem, presented by two other authors. The approximate solution ignores the edge effects of the membranes and overestimates the amount of charge that the membranes can carry before breakdown occurs. In the special case when the gap between the membranes is much less than their width, our results are in quantitative agreement with the approximate solution but as the gap between the membranes increases, the accuracy of the approximate solution decreases.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1976 Royal Society