Hydrodynamic Boundary Effects on Thermophoresis of Confined Colloids

Abstract

We study hydrodynamic slowing-down of a particle moving in a temperature gradient perpendicular to a wall. At distances much smaller than the particle radius, h a, lubrication approximation leads to the reduced velocity u/u0 = 3 h a ln a h , with respect to the bulk value u0. With Brenner's result for confined diffusion, we find that the trapping efficiency, or effective Soret coefficient, increases logarithmically as the particle gets very close to the wall. This provides a quantitative explanation for the recently observed enhancement of thermophoretic trapping at short distances. Our discussion of parallel and perpendicular thermophoresis in a capillary, reveals a very a good agreement with five recent experiments on charged polystyrene particles. PACS numbers:The motion of a colloid close to a solid boundary is strongly influenced by hydrodynamic interactions. Thus the like-charge attractions observed for confined colloidal assemblies [2], were shown to arise from hydrodynamic fluctuations [1]. Similarly, a surface-active particle with a flow field perpendicular to the wall, induces lateral advection of nearby neighbors and cluster formation [3][4][5][6][7]. More recently, the collision patterns observed for selfpropelling Janus particles close to a wall [8], were related to hydrodynamic interactions. Quite generally, the latter are relevant where surface forces and confined geometries are combined for sieving [11], trapping [12,13], and assembling colloidal beads [14].A generic example is provided by a surface-active particle moving towards a wall. If hydrodynamic effects on Brownian motion are well understood in terms of Brenner's solution for confined diffusion [15], this is not the case for the drift velocity u. At distances h much larger than the particle radius a, electrophoresis slows down by the factor u/u 0 = 1 − 5 8 a 3 /h 3 [16]. At short distances h < a, the wall-solvent-particle permittivity contrast strongly alters the local electric field; this electric coupling is difficult to separate from hydrodynamic interactions; a similar effect influences diffusiophoresis [17]. A more favorable situation occurs for thermophoresis, where the drift velocity is proportional to the temperature gradient [18,19]: Since the heat conductivity of silica or polystyrene (PS) particles is not very different from that of water, the thermal gradient is hardly affected by the presence of the wall [7], and velocity changes can be unambiguously attributed to hydrodynamic interactions.Here we study the vertical motion of a particle that is confined to the upper half-space z ≥ 0, as illustrated in Fig. 1; applications are thermophoresis across a capillary and self-propelling Janus particles that preferentially orient toward the wall, or "pullers" [10]. In the steady state, drift and diffusion currents cancel each other, −uc − D∇c = 0, and the particle concentration satisfiesAt large distances h a, there are no boundary effects FIG. 1: Schematic view of a particle moving towards a confining wall at velocity u. a) The arrow...

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“…(107). We also note the our expression becomes same as the analytical result of the singular term in [51] for the parallel interaction between a squirmer and a wall, that is F z in our notation. We did not compute the O(1) terms and instead use the values of an isolated squirmer as was done in [48] for a Stokesian Dynamics simulation.…”

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