Nature of branching in electrohydrodynamic instability

Abstract

Using weak nonlinear analysis, it is shown that an electric field imposed on a bilayer of fluids in the presence of gravity can only lead to subcritical instability of the interface. We see that no matter the horizontal dimension of the fluid layers or the Bond number, subcritical branching necessarily results. A simple expression for the case of deep layers reveals that the subcritical nature of the instability is contributed dominantly by electrostatic forcing, which is of $O(k)$, and diminished curvature which is of $O({k}^{3})$, both being enough to offset the supercritical nature offered by gravity, which is of $O({k}^{2})$.