Experiments and modeling in viscoelastic fluids dimpled drops and beaded filaments /
Abstract (Summary)iv We investigate the effect of viscoelasticity on the shape of drops and the break up of filaments through experiment and theory. We find that an immiscible drop of a dilute polymer solution falling through a quiescent viscous Newtonian fluid may exhibit a stable dimple at its trailing edge. At higher volumes the dimple extends far into the interior of the drop, and pinches off via a Rayleigh-type instability, injecting oil droplets into the polymer drop. At even larger volumes, a stable toroidal shape develops. We show that the dimpled shape can be reproduced mathematically with axisymmetric solutions for Stokes flow past a non-Newtonian drop, using the constitutive equation for a Simple Fluid of Order Three. This modeling has been generalized to give an analytical prediction of the rise discontinuity for air bubbles in a polymeric fluid. We also present experimental results on the dynamics of wormlike micellar filaments surrounded by an immiscible viscous bulk fluid. For certain concentrations, these filaments develop a beads-on-string structure previously observed only in polymer jets and filaments surrounded by air. By taking advantage of the longer time scales present in this experiment, we are able to quantify the evolution of individual beads. We also investigate the stability of these filaments and the robustness of the beads-on-string structure by stretching the filament within a rotating flow. Using a slender body approximation, we derive an integro-differential evolution equation that governs the development of a viscoelastic filament. A stability analysis shows that there is a critical parameter for which these filaments will be linearly stable at short time.
School Location:USA - Pennsylvania
Source Type:Master's Thesis
Date of Publication: