Explosive Instability of the Surface of a Conducting Fluid in an Electric Field in Confined Axisymmetric Geometry

摘要

We consider the nonlinear dynamics of the free surface of a conducting fluid (liquid metal for applications) in an applied vertical electric field for the case of confined axisymmetric geometry: the region occupied by the fluid is limited laterally. Amplitude equation describing the evolution of a fluid boundary is derived in the weakly nonlinear approximation. In the framework of this equation, it is shown that quadratic nonlinearities accelerate the development of electrohydrodynamic instability. Also, it is demonstrated both numerically and analytically that high-order nonlinearities play a destabilizing role. Consequently, the instability takes an explosive character: the surface perturbation amplitude grows faster than exponentially.