Dynamics of Slender Viscoelastic Free Jets

Previous studies of slender viscoelastic and Newtonian free surface jets have focused mainly on steady state predictions, guided primarily by industrial textile applications. Dynamical analyses and simulations of fiber flows, even the linearized stability analysis of nontrivial steady states, have lagged behind considerable experimental and textile processing observations and advances. The foundational work of Chang and Lodge [Rheol. Acta., 10 (1971), pp. 448–449] and Petrie [Rheol. Acta., 14 (1975), pp. 955–957], [Elongational Flows, Pitman, London, 1979] has been extended by the axisymmetric modeling and simulation of Beris and Liu [J. Non-Newtonian Fluid Mech., 26 (1988), pp. 363–394], [Comput. Methods Appl. Mech. Engrg., 76 (1989), pp. 179–204], for Maxwell fluids, and Markovich and Renardy [J. Non-Newtonian Fluid Mech., 17 (1985), pp. 13–22] for Johnson–Segalman fluids. The model in [Markovich and Renardy] is a single, nonlinear parabolic equation in which elastic retardation provides dominant smooth...