Initiation of motion for an isolated finite size particle in a rotating tank flow

Abstract

The initiation of motion of an isolated finite size particle within a rotating fluid in a tank is investigated experimentally. The study leverages on the absence of slip velocity to explore the impact rotation has on the initiation of the motion of a particle. Results show that the motion, when it occurs, is purely radial. It is initiated when the centrifugal force acting on the particle overcomes the friction force exerted on it by the tank bottom. A model of friction force that reproduces the experimental data quite well is proposed. It is based on the classical Coulomb’s friction law and pressure considerations. Denoting rc as the radial position of a particle when its motion starts, the critical radius r∗c=rc/d essentially depends on the density ratio γ, the Froude number Frω=ω2d/g but also the ratio of the tank radius to the particle size: α=R/d . Frω is based on the particle diameter d, the shear velocity ΔU=ωd with ω the rotation rate and g the acceleration due to gravity. The agreement of the model with the experimental data is obtained for the same friction coefficient λ = 0.019 whatever the particles. The value is not far from the value 0.05 generally expected for lubricated smooth plastic/plastic friction coefficients. The model also shows that for a given tank radius a critical rotation speed exists below which, no initiation of motion can be expected.