Motion of a spherical particle in a viscous fluid along a slip wall

Near-wall hydrodynamic slip triggers swimming state transition of micro-organisms

“…In addition, the flow problem due to the tangential squirming modes on the surface of a stationary sphere adjacent to a plane wall with fluid slip has been solved for the first time. The solutions obtained from the numerical codes employed in the present study to obtain the full solution of the Stokes equation were first validated with various earlier works regarding a spherical particle motion near a no-slip surface (Brenner 1961;O'Neill 1964) as well as near a slippery surface (Goren 1973;Kezirian 1992;Loussaief et al 2015). Subsequently the force and torque values obtained from the full Stokes equation solution are rechecked with the aforementioned reciprocal theorem approach (appendix D).…”

“…Similar to the previous works related to a passive or active sphere moving near a no-slip wall, we also find that the decay of these constants becomes very slow as the swimmer comes close to the plane wall, which calls for a large number of terms to be retained to reach the desired accuracy (Lee & Leal 1980;Yazdi & Borhan 2017). Adding to this, the increased value of the slip length at the plane wall turns out to be another hurdle to obtain a uniform accuracy throughout the calculations (Kezirian 1992;Loussaief et al 2015). Thus, for extreme cases when the swimmer is very close to wall (e.g.…”

“…l S = 10) to cause V x to fall below the unbounded-medium velocity. A fall in swimming velocity with increasing l S is in contrast to intuition, since a spherical particle translating parallel to the wall experiences lower hydrodynamic resistance in the presence of slip (Davis, Kezirian & Brenner 1994;Loussaief et al 2015). To address this apparent anomaly, we consider the fact that the microswimmer velocity is dependent on a coupled effect of the hydrodynamic resistances to the simultaneous translational and rotational movement parallel to the wall as well as on the thrust generated due to the propulsive action.…”

“…where S w is the surface of the slippery plane wall. It was shown (Loussaief et al 2015) that the contributions of the extra terms due to non-vanishing fluid velocity at the plane wall, appearing in both sides of (D 2), become equal, i.e.…”

Effective viscosity of a dilute homogeneous suspension of spheres in Poiseuille flow between parallel slip walls

“…Pasol, Sellier & Feuillebois (2009) and references therein). Here we will use the results of Loussaief, Pasol & Feuillebois (2015) and Ghalia, Feuillebois & Sellier (2016) for a sphere suspended in linear and quadratic ambient shear flows, respectively. This article is organized as follows.…”