Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments

Abstract

The surface tension driven breakup of viscoelastic filaments into droplets is qualitatively different from that of Newtonian liquid filaments. Disturbances on filaments of dilute polymer solutions often grow to a configuration consisting of nascent droplets connected by a thin ligament; the breakup time for this configuration is much longer than that predicted by extensions of Rayleigh's linear stability theory. We present here a nonlinear analysis of surface tension driven breakup of viscoelastic filaments using two complementary approaches that given equivalent results: a transient finite element solution and a one-dimensional thin filament approximation. We show that significant nonlinear effects lead to the experimentally-observed nascent droplet-ligament configuration, and we predict the entire evolution of the filament profile. Agreement with available experimental data for profile evolution and breakup of jets of Newtonian fluids and dilute polymer solutions is excellent.