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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(2):209-234; doi:10.1093/qjmam/44.2.209
© 1991 by Oxford University Press
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INTERFACIAL STRESS FIELDS AND THE ELECTROHYDRODYNAMICAL BOUNDARY CONDITION

R. CADE

( Department of Mathematics and Research Centre, Catholic University Santiago, Dominican Republic )

The boundary between two fluid media, one a conducting liquid and the other an insulator, is taken to be under the influence of an electric field, and its mechanics is studied by treating it as a thin boundary layer, so that there is continuous, if rapid, change, on passing from one medium to the other. These considerations lead to a different result from the classical one for the pressure difference between the two sides, a result in which both the electric double layer and fluid velocity are represented, and which reduces to the latter if the system is at rest and the double layer ignored. The difference indicates error in some existing work in the field of electrohydrodynamics in which the classical formula has been assumed to hold, and is the motivation for the derivation of axisymmetric and two-dimensional versions of a new electrohydrodynamical boundary condition; one which, it is hoped, offers possibilities of future application to particular problems.


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