The Prevention of Wave Motions in a Liquid Layer under a Vertical Periodic Motion Due to a Superposed Thin Viscous Liquid Layer

Abstract

Instabilities of a liquid layer, over which a thin viscous liquid layer is superposed, are investigated theoretically and experimentally under vertical periodic motion. It is assumed that the depth of the lower layer is finite and that of the upper one is very small. Thus, the motions of the lower and upper liquids are treated as an irrotational flow and a viscous flow, respectively. The neutral stability curves, which separate the stable region from the unstable one in the plane of the frequency and the amplitude of an externally imposed acceleration, are drawn by using a linear theory. The neutral curves depend on the Reynolds number, the depth ratio, the density ratio, the Weber number and the ratio of the surface tension coefficient. The motion of the ideal fluid layer is found to be stabilized by superposing a thin viscous liquid layer. The theoretical results are fully confirmed by the experimental ones obtained in the water-oil liquid layer.