Nonlinear stability of conducting viscous film flowing down an inclined plane at moderate Reynolds number in the presence of a uniform normal electric field

The stability of a perfectly conducting viscous film flowing down an inclined plane at a moderate Reynolds number in the presence of an applied normal electric field is studied in the finite amplitude regime. Due to the presence of the interface, the normal electric field produces an additional stress, which affects the flow dynamics considerably. Using the momentum integral method a nonlinear evolution equation for the development of the free surface is derived. The study reveals that the electric parameter introduces instability into the flow field. Further, nonlinear studies show that both a subcritical unstable zone and a supercritical stable zone may exist along with unconditional stable and explosive zones, depending on the wavenumber versus Reynolds number plane.