Capillary pinch-off in inviscid fluids

The axisymmetric pinch-off of an inviscid drop of density rho(1) immersed in an ambient inviscid fluid of density rho(2) is examined over a range of the density ratio D=rho(2)/rho(1). For moderate values of D, time-dependent simulations based on a boundary-integral representation show that inviscid pinch-off is asymptotically self-similar with both radial and axial length scales decreasing like tau(2/3) and velocities increasing like tau(-1/3), where tau is the time to pinch-off. The similarity form is independent of initial conditions for a given value of D. The similarity equations are solved directly using a modified Newton's method and continuation on D to obtain a branch of similarity solutions for 0less than or equal toDless than or equal to11.8. All solutions have a double-cone interfacial shape with one of the cones folding back over the other in such a way that its internal angle is greater than 90degrees. Bernoulli suction due to a rapid internal jet from the narrow cone into the folded-back cone plays a significant role near pinching. The similarity solutions are linearly stable for 0less than or equal toDless than or equal to6.2 and unstable to an oscillatory instability for Dgreater than or equal to6.2. Oscillatory behavior is also seen in the approach to self-similarity in the time-dependent calculations. Further instabilities are found as D increases and the steady solution branch is lost at a stationary bifurcation at D=11.8. (C) 2003 American Institute of Physics.