Motion of a spherical particle along a rough wall in a shear flow

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

“…This expression (2.4) is identical to that found by Assoudi et al [16] in the case of a linear shear flow.…”

“…The various integrals in (4.10), (4.11) are calculated by using the Gauss -Laguerre algorithm with 128 nodes, so that each integral is calculated with a precision better than O(10 −4 ) for L 3. These results will be compared with those obtained by Assoudi et al [16] in the case of a sphere held fixed, near a rough wall with a same roughness, in a linear shear flow (s). Indeed, according to Ho and Leal [2], we will limit our study to the case λ 1 in order to neglect the effect of the upper wall.…”

“…The flow of second order generated by the wall roughness of small amplitude has been calculated in a previous study by Assoudi et al [15]. After that, Assoudi et al [16] treated the motion of a spherical particle along a rough wall in a shear flow. They calculated the effects of second-order flow, forces, torque, and also the sphere velocities, generated by the wall roughness.…”

A Spherical Particle Settling Towards a Corrugated Wall

“…This technique is called the flattening of the boundary condition, it allows us to convert the no-slip condition on a surface with relief to a fictitious smooth wall with a slip condition that appears variable. This technique has already been used in several previous studies [21,23]. The complexity of these boundary conditions makes the analytical resolution of velocity and pressure fields difficult.…”

“…They considered a periodic roughness (which varies in one direction) under the assumption that the period is weak compared to the radius of the sphere, and their study is limited to the lubrication region. In a previous investigation [21], we have studied the problem of a freely spherical particle, in a shear flow parallel to a rough wall. The roughness considered is periodic and varies in one direction.…”