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The two-phase microflow of conductive (electrolyte) and non-conductive (dielectric) viscous liquids bounded by two solid walls in an external electric field is scrutinized. The lower solid wall, which is adjoined to the electrolyte, is a charged dielectric surface; the upper wall which bounds the dielectric is insulated. The problem has a steady one-dimensional (1D) solution. The theoretical results for a plug-like velocity profile are successfully compared with available theoretical and experimental data from the literature. The linear stability of the steady-state flow is investigated numerically with spectral Galerkin’s method for solving linearized eigenvalue problem. This method was successfully applied for related problem of electroosmosis of ultrathin film. The numerical analysis provides insights on the coexistence of long and short-wave instabilities. The influence of control parameters such as the ratio of the viscosities of both liquids and the ratio of the channel heights on the stability of one-dimensional flow was investigated for different values of external electric field. The influence of an external pressure gradient on the flow stability is also investigated. The experimental facts established by other authors, according to which the system destabilizes if the electroosmotic flow is oppositely directed to the external pressure gradient, is confirmed in this work. Otherwise stabilization takes place.


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