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Internal electrohydrodynamic instability of liquids with collinear field and conductivity gradients

Bulk-coupled instability at the interface between miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium normal electric field is studied experimentally and theoretically. Observations of fluid motions permit measurement of an instability wavenumber and growth rate. A model with a layer of diffusive conductivity distribution coupled to uniform bounding half-spaces is developed. Numerical integration of linearized electromechanical equations leads to a set of growing eigenfrequencies with corresponding eigenmodes, pure real for small wavenumber and complex (propagating) for large wavenumber. The fastest growing wavenumber and corresponding growth rate are characterized as a function of the conductivity ratio and a time-constant ratio, which reflects the importance of inertial and viscous effects. In the viscous-dominated limit, the description agrees with a corresponding surface-coupled theory. The model is evaluated for parameters corresponding to experimental observations.