Space-Charge Dynamics of Liquids

Abstract

The propagation and instability characteristics of small-signal electro-fluid-mechanical space charge and polarization waves in nonhomogeneous fluids is 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.Two types of stratification for the mass density, dielectric constant, and space charge density are distinguished and related: discrete layers and continuous distributions. A general set of relations for perturbation field and flow variables on the perturbed surfaces of fluid layers having constant properties and snace charge are derived in each of the configurations. 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; d) Uniformly charged liquid drop. It is shown that the general relations can be used to represent systems of coupled layers which approximate continuous distribution by a series of step functions. Specific examples of weak-gradient and exponential distributions are presented showing that the solution found directly from the distributed theory is approached by the system of coupled layers, if the limit is taken in which the number of layers becomes large while the layer thickness approaches zero. Experiments are described which attempt to delineate the coupling of space charge to electrohydrodynamic surface waves on a perfectly-conducting interface in the configuration of (a), above.

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