Numerical Study on the Unstable Flow Dynamics of Wormlike Micellar Solutions past a Sphere in the Creeping Flow Regime

The flow dynamics of wormlike micellar solutions around a sphere is a fundamental problem in particle-laden complex fluids but is still understood insufficiently. In this study, the flows of the wormlike micellar solution past a sphere in the creeping flow regime are investigated numerically with the two species, micelles scission/reforming, Vasquez-Cook-McKinley (VCM) and the single-species Giesekus constitutive equations. The two constitutive models both exhibit the shear thinning and the extension hardening rheological properties. There exists a region with a high velocity that exceeds the main stream velocity in the wake of the sphere, forming a stretched wake with a large velocity gradient, when the fluids flow past a sphere at very low Reynolds numbers. We found a quasi-periodic fluctuation of the velocity with the time in the wake of the sphere using the Giesekus model, which shows a qualitative similarity with the results found in present and previous numerical simulations with the VCM model. The results indicate that it is the elasticity of the fluid that causes the flow instability at low Reynolds numbers, and the increase in the elasticity enhances the chaos of the velocity fluctuation. This elastic-induced instability might be the reason for the oscillating falling behaviors of a sphere in wormlike micellar solutions in prior experiments.