Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

摘要

The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electro_hydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic_Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.