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Instabilities in a two-phase electromagnetohydrodynamic (EMHD) flow between a pair of parallel electrodes are explored. A linear stability analysis has been performed based on a coupled Orr-Sommerfeld system generated from the conservation laws. The study shows the presence of a finite-wave-number EMHD mode of instability in addition to the two commonly observed instability modes in the pressure-driven two-layer flows, namely, the long-wave interfacial mode arising from the viscosity or density stratification and the finite-wave-number shear flow mode engendered by the Reynolds stresses. This extra EMHD mode originates from the additional stresses generated by the Lorenz force acting at the liquid layers and is found to exist under all conditions beyond a critical strength of the externally applied magnetic field. The EMHD mode either can exist as a singular dominant mode or can coexist as a dominant or subdominant mode with the conventional interfacial mode or shear flow instabilities in the two-layer flows. The EMHD flow studied here has numerous potential applications in fluid transport, enhanced heat and mass transfer, mixing, and emulsification because of the low energy requirement, flow reversibility, absence of moving parts, and facile control over flow rate. The parametric study presented here on the instabilities in the two-layer EMHD flow will thus be of great practical use.

Parametric study on instabilities in a two-layer electromagnetohydrodynamic channel flow confined between two parallel electrodes