Study of Cylindrical Jet Breakup Using One-Dimensional Approximations of the Euler Equations

Abstract

We study the phenomenon of pinching of inviscid incompressible jets when surface tension is important. This is done by analyzing one-dimensional models derived by use of slender jet theory. Equations are derived for both single- and two-fluid arrangements. Higher-order terms are retained for regularization purposes. In the absence of a surrounding fluid these equations are the inviscid Cosserat system. It is shown that the leading order system terminates in infinite-slope singularities before pinching happens---this is achieved by studying a 2 X 2 system of conservation laws in the complex plane and by numerical solution of the evolution equations. Inclusion of higher-order terms changes the order of the evolution equations and enables the one-dimensional models to produce the phenomenon of pinching and drop formation in many cases. The evolution equations are solved numerically, and the numerical experiments suggest that the interface develops a cusp locally as the jet pinches. Local similarity solutions valid near pinching are suggested, and scaling exponents are compared with the simulations. Numerical solutions of models which include the full curvature term are found to terminate in infinite-slope singularities, before pinching can take place, for a range of initial conditions which produce pinching for the slice models. If the initial amplitudes are small enough, however, pinching is supported.