Simulations of a sphere sedimenting in a viscoelastic fluid with cross shear flow

Abstract The settling rate of heavy spheres in a shear flow of viscoelastic fluid is studied by numerical simulation. Experimental data [Tonmukayakul et al., US Patent Application US20110219856 (2011); van den Brule and Gheissary, J. Non-Newton. Fluid Mech. 49 (1993) 123–132] have shown that both shear thinning and the elasticity of the suspending polymeric solutions affect the settling rate of the solids. In the present work, simulations of viscoelastic flow past a single, torque-free sphere with a cross shear flow are used to study the effect of the elasticity of the carrying fluid on the sphere’s settling rate. The FENE-P constitutive model is used to represent a viscoelastic Boger fluid, with parameters obtained by fitting rheological data. A twofold increase in drag, i.e. a decrease in settling rate, is obtained with increase in the cross shear Weissenberg number, Wi  ⩽ 15, even though the shear viscosity of the solution decreases over this same range. At small Weissenberg number, Wi τ 11 component of the viscous stress (with 1, the sedimentation direction) is the primary cause of the increase in sphere drag.