Electrohydrodynamically induced instabilities in parallel flows

The behavior of small disturbances in parallel flows of insulating liquids subjected to charge injection, with an imposed electric field orthogonal to the primary flow, is studied. The resulting convective patterns and the instability thresholds are determined for plane Couette and Poiseuille flows. In the case of Couette flow the instability is purely electrodynamic, and as a consequence the stability threshold does not vary with Reynolds number. The most unstable modes are always longitudinal rolls. The same is true for Poiseuille flow up to a certain Reynolds number for which the instability occurs in the form of transverse waves. This mode of instability is inertial and corresponds to the fact that pure plane Poiseuille flow is unstable when the fluid attains a certain velocity. Particular attention is given to the energy transfer between the primary flow and the secondary flow in order to gain physical insight into the way inertial and electric physical mechanisms act on the liquid.<>