PINCHING THREADS, SINGULARITIES AND THE NUMBER 0.0304

The dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier-Stokes equations. Eggers [Phys. Rev . Lett. 71, 3458 (1993)] recently proposed a single universal similari ty solution for a viscous thread pinching with an inertial-viscous-cap illary balance in an inviscid environment. In this paper it is shown t hat there is actually a countably infinite family of such similarity s olutions which are each an asymptotic solution to the Navier-Stokes eq uations. The solutions all have axial scale t'(1/2) and radial scale t ', where t' is the time to pinching. The solution obtained by Eggers a ppears to be special in that it is selected by the dynamics for most i nitial conditions by virtue of being less susceptible to finite-amplit ude instabilities. The analogous problem of a thread pinching in the a bsence of inertia is also investigated and it is shown that there is a countably infinite family of similarity solutions with axial scale t' (beta) and radial scale t', where each solution has a different expone nt beta. (C) 1996 American Institute of Physics.