Flow of a wormlike micelle solution past a falling sphere

Abstract With the increasing use of wormlike micelle solutions as rheological modifiers in many consumer products, the prediction of the behavior of these fluids has grown increasingly important in recent years. In this paper, the flow past a sphere falling at its terminal velocity through a column of a wormlike micelle solution is experimentally studied. The working fluid is an entangled wormlike micelle solution of 0.05 mol/l cetyletrimethylammonium bromide and 0.05 mol/l sodium salicylate dissolved in water. The rheology of the fluid is characterized in both shear and transient homogeneous uniaxial extension. Sphere-to-tube ratios of a / R =0.0625 and a / R =0.125 are investigated over a wide range of Deborah numbers. The drag on the sphere is initially found to decrease with increasing Deborah number because of shear thinning effects. As the Deborah number is increased, the establishment of a strong extensional flow in the wake of the sphere causes the drag to increase to a value larger than that of a Newtonian fluid with the same viscosity. At a critical Deborah number, the flow becomes unstable and fluctuations in the sedimentation velocity of the sphere are observed. Particle image velocity measurements are used to analyze the flow fields around the falling spheres. These measurements show the presence of a strong negative wake. For the unstable flows, the velocity flow field is observed to fluctuate between a negative and extended wake. Pointwise and full-field flow-induced birefringence measurements are used to track the evolution in the deformation of the wormlike micelle chains. Strong evidence is found that suggests that the flow instability is the result of a breakdown of the wormlike micelle network structure in the wake of the sphere. This breakdown is related to the filament rupture observed in the extensional rheology experiments.

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