Rotational Liquid Film Interacted with Ambient Gaseous Media

Abstract

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. The experimental study of annular liquid jets shows existing tulip and bubble jet shapes and also predicts the existence of periodic shape. However, sufficient simplifications of mathematical models of the flow details were made: the effects of the forces of surface tension of the longitudinal motion and the variability of the tangential velocity component of the centrifugal forces in the field were neglected. In this work, the equations described the flow of rotational annular jets of viscous liquid in an undisturbed medium with allowance of the abovementioned effects. The basic model was obtained through the use of quasi-two-dimensional momentum balance equations in the metric space with the co- and contravariant basis vectors suitable for surfaces with complicated shape. The pressure difference outside and within the jet was obtained and analyzed. The results of calculations show the dependence of the jet shape on the relative contributions of the initial rotation rate, viscosity, surface tension, gravity forces, and pressure difference. An exact solution to the problem of the motion of a thin cylindrical shell due to different internal and external pressures is obtained. Analysis of nonlinear instabilities of the Rayleigh–Taylor type in meridional cross section was carried out. It is shown that the instabilities, which appear due to pressure drop, cannot be stabilized by rotation.