(354g) Sphere Sedimentation in Wormlike Micelles: Effect of Micellar Relaxation Spectrum and Gradients in Micellar Extensions

Recent studies have shown that beyond a critical extensional Deborah number, a falling sphere in wormlike micelles never reaches a constant terminal velocity, instead it settles with an unsteady velocity. This behavior is linked to the wormlike micellar chain scission in the wake of the sphere. Similar instabilities in viscoelastic polymer solutions, where polymer chain scission is highly unlikely, are thought to be the results of a single-mode relaxation spectrum of the polymer chains or the asymmetry in the polymer chain extensions on flanks of the falling sphere. In this paper, we examine the effect of micellar relaxation spectrum and gradients in micellar extensions on the sphere instability in wormlike micelles over a wide range of elasticity (10^-2 < De_E < 15) and inertia (10^-6 < Re < 10). Falling spheres exhibit fluctuating behavior in wormlike micelles with a single-mode relaxation spectrum for De_E ≥ 2.6. However, for similar conditions (2.5 ≤ De_E ≤ 15, and 10^-2 < Re < 10), spheres never exhibit the unsteady motion in the wormlike micelles with a broad relaxation spectrum (i.e. a multi-mode Maxwell model). This indicates the importance of the micellar relaxation spectrum on dynamics of the sphere sedimentation in wormlike micelles. We show that a criterion based on the ratio of dissipated energy to the stored elastic energy of micelles can successfully describe the effect of micellar relaxation spectrum on sphere sedimentation dynamics. In addition, for conditions that give rise to sphere instability, flow induced birefringence indicates no sign of gradients in micellar extensions on sphere sideways.