Oscillatory dynamics of inviscid planar liquid sheets

摘要

One-dimensional models of inviscid, planar liquid sheets surrounded by dynamically passive gases are obtained by means of perturbation methods, integral formulations, series expansions and variational principles. It is shown that integral formulations, series expansions and variational principles provide analogous one-dimensional models under certain approximations for the velocity and pressure fields. The equations for slender and thin sheets obtained from integral formulations are shown to be asymptotically equivalent to the exact equations of inviscid, planar liquid membranes. Algebraic and differential methods are employed to determine the singularities of the steady equations obtained from integral formulations, and indicate that the liquid does not leave the nozzle with an angle equal to that of the exit if the Weber number is equal to or less than one. Numerical studies of the time-dependent governing equations are presented in order to illustrate the nonlinear dynamics and bifurcations of confined, inviscid, planar liquid sheets when they are subjected to time-dependent pressure differences or gases are injected on either side of the sheet, in the absence of heat and mass transfer between the gases and the liquid.