Space-Charge Dynamics of Liquids

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Abstract
The propagation and instability characteristics of small‐signal electro‐fluid‐mechanical space‐charge and polarization waves in nonhomogeneous fluids are developed. Stratified equilibrium configurations with fluid properties and space‐charge density constant within planar, cylindrical, and spherical surfaces, are emphasized. Equilibrium electric fields due both to charges in the fluid and to externally imposed potentials are normal to these surfaces. The liquid is modeled as incompressible, inviscid, and perfectly insulating, with domains of sufficiently high frequency or growth rate to validate the last assumption defined in terms of electrical conductivity or mobility. A general set of relations for perturbation field and flow variables on the perturbed surfaces of fluid layers having constant properties and space charge are derived in each of the configurations. A detailed description of wave dispersion and instability for interactions in the following situations exemplifies how these relations are used in representing a broad class of discretely stratified equilibria: (a) perfectly conducting interface stressed by normal field and bounded from above by fluid supporting uniform space charge; (b) two planar layers of differing properties and space charge; (c) uniformly charged liquid jet; and (d) uniformly charged liquid drop.

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