Sphere sedimentation in wormlike micelles: Effect of micellar relaxation spectrum and gradients in micellar extensions

We report experiments on the flow of wormlike micellar solutions based on cetylpyridinium chloride/sodium salicylate past a falling sphere via a combination of particle tracking velocimetry, particle image velocimetry, rheology, and flow induced birefringence (FIB). 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 the flanks of the falling sphere. In this paper, we examine the effect of micellar relaxation spectrum and gradients in micellar extensions on sphere instability in wormlike micelles over a wide range of flow parameters (10(-2) < De(E) < 40.7 and 10(-6) < Re < 10). In wormlike micelles with a single-mode relaxation spectrum, the sphere instability occurs for De(E) >= 2.6. However, for similar conditions (2.5 <= De(E) <= 40.7 and 10(-2) < Re < 10), spheres never exhibit unsteady motion in the wormlike micelles with a broad spectrum of relaxation times. This indicates the importance of the micellar relaxation spectrum on dynamics of 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, FIB indicates that micellar extensions on sphere sideways are perfectly symmetric. (C) 2018 The Society of Rheology.