Kinematics of a Cylindrical Particle at Low Reynolds Numbers in Asymmetrical Conditions
Résumé
This paper concerns the hydrodynamic interactions on a cylindrical particle in non-dilute regime at low Reynolds numbers. The particle moves between two parallel walls with its axis parallel to the boundaries. A numerical finite-volume procedure is implemented and a generalized resistance matrix is built by means of the superposition principle. Three problems are solved: the settling of the particle, the transport of a neutrally and of a non-neutrally buoyant particle in a Poiseuille flow. Concerning sedimentation, the settling velocity is maximal off the symmetry plane and decreases when the confinement increases. The particle rotates in the direction opposite to that of contact rolling. The particle induces a high pressure zone in the front and a low pressure zone in the back, the difference of which is maximal in the symmetry plane. For a neutrally-buoyant particle, the hydrodynamic interactions lead to a velocity lag between the particle and the undisturbed flow. The magnitude of the velocity lag increases with confinement and eccentricity. The angular velocity and pressure difference are opposite to the previous case. For a non-neutrally buoyant particle, three situations are found depending on a dimensionless parameter similar to an inverse Shields number. For its extreme low and high values, the particle is respectively either carried by the flow or settles against it whatever its position. For intermediate values, the particle either settles close to the walls or is dragged by the flow close to the symmetry plane. Similar results are obtained for the angular velocity and the pressure difference. All these results question
the assumption usually met in particulate transport in which the kinematics of the particle is often supposed to be that of the flow.
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