Kinematics of a symmetrically confined cylindrical particle in a “Stokes-type” regime

Abstract

To contribute to the study of the influence of the hydrodynamic interactions governing the dynamics of solid particles such as fibers in nondilute regimes, we consider in this work a cylindrical particle confined between two parallel walls at low Reynolds numbers. The particle moves with its axis always parallel to both walls. Our numerical results, derived with a projection method and a finite-volume approach, turn out to be very accurate and enable us to solve different problems using the matrix resistance technique. The first problem considers the consequences of these interactions on the settling velocity of a particle. In such confined situations, the hydrodynamic interactions are expressed by a backflow leading to a decrease of the settling velocity when the confinement increases with an asymptotical behavior varying like ε5∕2, where ε stands for the gap between the plane walls and the cylinder. The second problem consists in the accurate determination of the actual velocity of a neutrally buoyant particle transported in a Poiseuille flow, with its axis perpendicular to the mean flow. The hydrodynamic interactions lead to the existence of a relative velocity between the free particle and the flow unperturbed by the particle. This result reconsiders the assumption commonly used in some studies (same velocity for the particle and the unperturbed fluid) to analyze the transportation of fibers in the processing of composite materials (extrusion, injection molding) for concentrated regimes. In the third problem describing the transportation of a non-neutrally buoyant particle in a vertical Poiseuille flow, as in a fluidized bed, for instance, we obtain two regimes depending on the relative magnitude of the sedimentation velocity to the mean Poiseuille flow, and this suggests a potential method to separate the particles according to their density or size. On this occasion, we give the various flow patterns arising with each problem.