A Spherical Particle Settling Towards a Corrugated Wall

Abstract

Based on the assumption of low Reynolds number, the flow around a spherical particle settling towards a corrugated wall in a fluid at rest is described by Stokes equations. In the case of the small amplitude of wall roughness, the asymptotic expansion coupled with the Lorentz reciprocal theorem are used to derive analytical expressions of the hydrodynamic effects due to wall roughness. The evolution of these effects in terms of roughness parameters and also the sphere-wall distance are discussed.

A mathematical model to study the wall roughness effects on the migration of inertial particles in a shear flow

“…y,R i y . The analytical and numerical results of the friction factors of the forces and torques of the first and second order have been obtained by various authors, see [15,16,18]. In a similar way, the components of translational and rotational velocities of the particle are expanded as…”

“…In earlier studies, we have studied the problems of influence of wall roughness on a shear flow [14] and its influence on a freely moving spherical particle near a rough wall in a shear flow [15], and the problem of a particle settling towards a rough wall in a fluid at rest [16]. Based on these results, we will evaluate the effect of wall roughness on the separation of spherical particles entrained by a simple linear shear flow.…”

A Sphere Held Fixed in a Poiseuille Flow near a Rough Wall

“…This relationship appears as a slip boundary condition for the unknown flow field on a fictitious plane wall located at Z = 0. This technique is called the flattening of the boundary condition, and it has already been used in various earlier studies [17,20]. The substitution of V…”

“…They calculated the effects of second-order flow, forces, torque, and also the sphere velocities, generated by the wall roughness. Lamzoud et al [17] studied the problem of a sphere settling towards a corrugated wall, in a fluid at rest.…”