Abstract

Nonlinear Behavior of an Annular Liquid Sheet

T.Yoshinaga, K.Kotani (Department of Mechanical Science, Osaka University, Osaka, Japan)

e-mail: yoshinag@me.es.osaka-u.ac.jp

Behavior of a gas-cored annular liquid sheet is analytically studied when the effect of finite thickness of the sheet is considered. Nonlinear evolution equations for an axisymmetric ring element of the sheet are derived by means of the membrane approximation under the influence of its own inertia, surface tension and gaseous hydrostatic pressure. The linear dispersion relation of the equations shows the existence of two temporally unstable modes - dilational and sinuous types - for long waves, one of which disappears in a thin limit of the sheet thickness, while an isolated unstable mode additionally appears for short waves in a range of the sheet thickness. It is numerically shown that characteristic behavior of the sheet, which is blown up like a spherical balloon, closed by sealing off the inner gas and broken up into ligaments, is mainly due to nonlinearity as well as pressure difference between both sides of the sheet, inertia and surface tension.

Section : 7