Long-wave instability of stratified two-phase MHD channel flow

Instability of a stratified two-phase MHD parallel flow between two infinite plates is addressed. We examine the effect of the transverse magnetic field on the base flow and long wave instability of a two-layer system consisting of conductive liquid and non-conductive gas. Both perfectly insulating and perfectly conducting boundaries are considered. To capture the behavior at small but finite wavenumbers, the conventional first-order long-wave stability analysis is extended to higher order terms. Using mercury-air system as a representative test case, the results demonstrate distinct and non-similar base flow and disturbance profiles, as well as different stability maps for insulating versus conducting boundaries. The stability diagrams reveal a non-monotonic influence of the magnetic field on flow stability, showing that, in addition to its expected stabilizing effect, the field can also induce destabilization under certain conditions. Inspection of the disturbance profiles indicates that despite the strong damping of mercury flow by the magnetic field, interaction of the two fluids at the interface and the shear-induced instabilities in the gas layer dominate and can lead to flow destabilization as the magnetic field strength increases.