Sedimentation dynamics of spherical particles in confined geometries

Abstract

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing L x . By systematically varying L x we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of L x . We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to L x . We also find that the behavior of the corresponding diffusion coefficients as a function of L x is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.

Statolith Sedimentation Kinetics and Force Transduction to the Cortical Endoplasmic Reticulum in Gravity-SensingArabidopsisColumella Cells

“…The cell wall or other finite boundaries exert a retarding effect on the sedimentation of particles in a viscous medium and can introduce an asymmetry in the drag force (Vogel, 1994;Brenner, 1999;Lin et al, 2000;Kuusela et al, 2004). These so-called wall effects will significantly affect statolith velocities and the relative motion of statoliths and, therefore, statolith membrane interactions and consequently gravitropic signaling events.…”

“…During sedimentation, the statoliths will produce a velocity field around them in the cytosol, which, at low Reynolds numbers, decays as r 21 where r is the distance from the particle center (Brenner, 1999;Kuusela et al, 2004). Along the cytosolstatolith interface, the velocity of the immediately adjacent cytosol will be the same as that of the moving statolith, the cytosol tends to move with the statolith, and further away a velocity gradient with respect to distance extends as a consequence of the no-slip boundary condition (Vogel, 1994(Vogel, , 2003Pickard, 2003).…”

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

“…The equations of motion for both internal and external fluid are then solved on a fixed finite-element grid. The work of Kuusela et al 17 is similar except that the particle-fluid interaction is treated in an explicit manner by integrating hydrodynamic stresses over the particle surface, and the equations are solved using a finitedifference method. A general difficulty with such fixed grid methods is their inability to resolve the hydrodynamic lubrication stresses in the gaps between particles whose separation is comparable to or smaller than the grid spacing.…”

“…A general difficulty with such fixed grid methods is their inability to resolve the hydrodynamic lubrication stresses in the gaps between particles whose separation is comparable to or smaller than the grid spacing. Thus, lubrication interactions are usually not fully resolved, and either elastic collisions 14,15,17 or repulsive forces 16 are used to prevent particle overlap.…”

Non-equilibrium sedimentation of colloids: confocal microscopy and Brownian dynamics simulations

“…in quasitwo-dimensional suspensions [23][24][25], and screened hydrodynamic interactions in a narrow channel [26]. Steady-state sedimentation dynamics of spherical particles was studied when the system was confined between upright plates [27] and Brownian dynamics simulation of the final stage of sedimentation was considered in a soft sphere model [28].…”