Stretch and hold: The dynamics of a filament governed by a viscoelastic constitutive model with thixotropic yield stress behavior

Abstract

The transient behavior of filament stretching is studied for a viscoelastic constitutive model that combines a partially extending strand convection model with a Newtonian solvent. The vertical filament is fixed at the bottom and the top is pulled up and held. Gravity and surface tension are also included in the model though they are not the primary mechanisms in this study. An axisymmetric circular slender jet approximation is applied. An asymptotic analysis for the initial stages of evolution is performed for large relaxation time, so that an interplay of fast and slow time scales emerges, and gives a criterion for whether the fluid yields immediately or whether slow dynamics ensues, depending on elastic stresses, gravity, and capillary stress. The analysis guides the choice of parameters to exemplify thixotropy and yield stress behavior through numerical simulations of the full governing equations from start to finish of the filament evolution. Elastic effects promote a spring back of the filament toward its initial shape, while pulling at the top stretches the filament locally to promote yielding, with the lower portion of the filament remaining unyielded. In addition, a parameter regime that models extensional experiments in the literature for yield stress fluids sheds light on the differences in filament shapes.