Stationary nonlinear waves at the surface of a thin liquid layer under inverted gravitation conditions

Abstract

Instability of the flat surface of a thin liquid layer wetting a solid substrate under inverted gravitation conditions is discovered. The development of this instability leads to formation of a new stationary nonuniform liquid surface state. It looks like a solitary hill with characteristics sensitive to the liquid film parameters, particularly to the layer thickness at which the instability begins to develop. By application of a variational approach the mechanical stability of such a hill (droplet) in the one-dimensional approximation is proved. A variational picture of the shape evolution for a cylindrical charged droplet in an external electric field is constructed, too. The results obtained are compared with an experiment on liquid hydrogen droplets [A.A. Levchenko, G.V. Kolmakov, L.P. Mezhov-Deglin, M.G. Mikhailov, and A.B. Trusov, Low Temp. Phys. 25, 242 (1999)]. The theory developed is in good agreement with the results of experiments.