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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.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/8454 To cite this version :Antoine DESPEYROUX, Abdelhak AMBARI, Abderrahim BEN RICHOU -Wall effects on the transportation of a cylindrical particle in power-law fluids -Journal of Non-Newtonian Fluid Mechanics -Vol. 166, n°19-20, p.1173-1182 -2011 Any correspondence concerning this service should be sent to the repository b s t r a c tThe present work deals with the numerical calculation of the Stokes-type drag undergone by a cylindrical particle perpendicularly to its axis in a power-law fluid. In unbounded medium, as all data are not available yet, we provide a numerical solution for the pseudoplastic fluid. Indeed, the Stokes-type solution exists because the Stokes' paradox does not take place anymore. We show a high sensitivity of the solution to the confinement, and the appearance of the inertia in the proximity of the Newtonian case, where the Stokes' paradox takes place. For unbounded medium, avoiding these traps, we show that the drag is zero for Newtonian and dilatant fluids. But in the bounded one, the Stokes-type regime is recovered for Newtonian and dilatant fluids. We give also a physical explanation of this effect which is due to the reduction of the hydrodynamic screen length, for pseudoplastic fluids. Once the solution of the unbounded medium has been obtained, we give a solution for the confined medium numerically and asymptotically. We also highlight the consequence of the confinement and the backflow on the settling velocity of a fiber perpendicularly to its axis in a slit. Using the dynamic mesh technique, we give the actual transportation velocity in a power-law ''Poiseuille flow'', versus the confinement parameter and the fluidity index, induced by the hydrodynamic interactions.