Hydrodynamic interactions of spherical particles in a fluid confined by a rough no-slip wall

Abstract

In this paper we develop a theoretical framework to study the hydrodynamic interactions in the presence of a nonflat and no-slip boundary. We calculate the influence of a small amplitude and sinusoidal deformations of a boundary wall in the self-mobility and the two-body hydrodynamic interactions for spherical particles. We show that the surface roughness enhances the self-mobility of a sphere in a way that, for motion in front of a local hump of the surface, the mobility strength decreases while it increases for the motion above a local deep of the rough surface. The influence of the surface roughness in the two-body hydrodynamic interactions is also analyzed numerically.

Rectified motion in an asymmetric channel: The role of hydrodynamic interactions with walls

“…In addition to interaction between particles, the long range hydrodynamic interaction with confining walls is proved to have essential effects on the motion of either passive colloidal particles [13,14] or active systems [15][16][17]. It is the main goal of this article to address how the interaction with walls will influence the functionality of a Brownian ratchet.…”

General aspects of hydrodynamic interactions between three-sphere low-Reynolds-number swimmers

“…(2), the fluid velocity can be eliminated and replaced by the sphere velocity. Therefore, it is possible to expand the velocity of each sphere in terms of the hydrodynamic forces exerted on the other spheres [18],…”

Rough wall effect on micro-swimmers

“…It remains to prove that there exists X 0 such that A(X 0 ) is non-zero. By calling K int 4 the function (s, r, r ) → ∂ ∂z s → K 0 (s, r) ∂ ∂z s → K 0 (s, r ) , we have (see (22))…”