The contraction of liquid filaments

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Abstract
In this paper the evolution of a free liquid filament of arbitrary viscosity, contracting under the action of surface tension forces, is studied by numerical means. A finite- element discretization procedure is used to obtain approximate solutions to the Navier-Stokes equations. A Lagrangian approach is employed to deal with the large domain deformations which occur during the evolution of the filament. Typically we find that during the contraction a bulbous region forms at the end of the filament. The character of the evolution of the filament is found to be crucially dependent on the value of the Ohnesorge number Oh (a measure of viscous and surface tension forces). For large Ohnesorge numbers (Oh [Gt ] O(1)) it is found that the liquid filament remains stable during contraction, even when the initial length of the filament is much longer than the Rayleigh stability limit. The bulbous end becomes more localized with decreasing Ohnesorge number while at the same time a clear neck forms in front of the bulbous end. In addition we find that the region in which the pressure is minimum moves towards the neck. For sufficiently small Ohnesorge numbers (Oh [Lt ] O(0.01)) the filament becomes unstable with the radius of the neck decreasing and, eventually, the bulbous end breaking away from the filament.

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