Movement of a Sphere on a Flat Wall in Non-Newtonian Shear Flow

Abstract

For a particle on a wall or cuttings bed in a multiphase flow in confined geometries a condition for onset and lift-off is very important. In this case, a fundamental problem of hydrodynamic forces and torque acting on a particle moving near and on the wall in a viscous fluid needs to be solved. In this paper, systematical simulation of a flow was performed around a perfect rolling or sliding spherical particle near the wall. A shear flow of Newtonian and Herschel-Bulkley fluids was investigated. The simulation was conducted for Reynolds numbers up to 200 and the dimensionless positive particle velocity Vp < 1.4. The relative particle velocity was made dimensionless by dividing it by the incoming flow velocity in front of the particle. The simulation was performed using the open-source CFD package OpenFOAM. The simulation results for Newtonian fluid agree with data presented in the literature. For the particle’s low translational velocity the drag force coefficient in the non-Newtonian fluid is lower than in Newtonian fluid, but for increasing translational velocity the drag force coefficient increases. The lift force coefficient behavior is non-monotonic versus rheology parameters. Lift and drag force show a sudden drop for very small translational velocities. Our simulation shows that in the case of large Bingham numbers the particle’s lift force can be negative for steady perfect particle rolling. Thus, friction between particle and surface prevents particle’s take-off in some cases. Knowing the dependence of the lift force on Reynolds number and rheological parameters allows one to determine incipient motion and take-off conditions for a spherical particle.