Sedimentation of a sphere in a viscoelastic fluid: a multiscale simulation approach

Abstract

AbstractA long-standing problem in non-Newtonian fluid mechanics, namely the relationship between drag experienced by a sphere settling in a tube filled with a dilute polymeric solution and the sphere sedimentation velocity, is investigated via self-consistent multiscale flow simulations. Comparison with experimental measurements by Arigo et al. (J. Non-Newtonian Fluid Mech., vol. 60, 1995, pp. 225–257) have revealed that the evolution of the drag coefficient as a function of fluid elasticity can be accurately predicted when the macromolecular dynamics is described by realistic micromechanical models that closely capture the transient extensional viscosity of the experimental fluid at high extension rates. Specifically, for the first time we have computed the drag coefficient on the sphere at high Weissenberg number $\mathit{Wi}$ utilizing multi-segment bead–spring chain models with appropriate molecular parameters and have demonstrated that a hi-fidelity multiscale simulation is not only capable of accurately describing the drag on the sphere as a function of $\mathit{Wi}$ at various sphere-to-tube diameter ratios but also it can closely reproduce the experimentally observed velocity and stresses in the wake of the sphere.