Diffusiophoretic Motion of an Axially Symmetric Colloidal Particle in Nonelectrolyte Gradients along Its Axis of Revolution and Perpendicular to Two Plane Walls
Date Issued
2011
Date
2011
Author(s)
Wan, Yi-Wei
Abstract
The axisymmetric diffusiophoretic motion of a colloidal particle of revolution in a nonelectrolyte solution situated between two infinite parallel plane walls are studied theoretically in the quasisteady limit with small Peclet and Reynolds numbers. The applied solute concentration gradient is uniform and perpendicular to the plane walls. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle size and to the particle-wall gaps, but the polarization effect of the solute is incorporated in the thin interfacial layer caused by the strong adsorption of the solute. The presence of the confining walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is altered by the walls, thereby speeding up or slowing down the particle; secondly, the walls enhance the viscous retardation of the moving particle.
To solve the solutal and hydrodynamic governing equations of the system, a method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the solute concentration distribution and fluid velocity field. The apparent slip condition on the particle surface is satisfied by applying a boundary collocation technique to these general solutions. Numerical results for the diffusiophoretic velocity of the colloid particle relative to that under identical conditions in an unbounded fluid solution are presented for various cases. The collocation results of a spherical particle agree well with the approximate analytical solutions obtained by using the method of reflections. The presence of the walls always reduces the spherical particle velocity, irrespective of the surface properties of the particle or the relative particle-wall distances.
The diffusiophoretic velocity of a confined spheroid along its axis of revolution in general increases with an increase in its axial-to-radial aspect ratio, but there are exceptions. The presence of the walls can reduce or enhance the spheroid velocity, depending upon the polarization parameter and aspect ratio of the particle as well as the relative particle-wall separation distances. For a constant relative separation between the two plane walls, the diffusiophoretic mobility of the spheroid has a maximum when it is located midway between the walls and decreases as it approaches either of the walls. When a spheroid with a fixed aspect ratio is located near a first plane wall, the approach of a second wall far from the particle can first increase the diffusiophoretic mobility to a maximum, then reduce this mobility when the second wall is close to the particle, and finally lead to a minimum mobility when it reaches to the same distance from the particle as the first wall.
Subjects
Diffusiophersis
Axisymmetric particle
Colloid spheroid
Boundary effects
Plane walls
Type
thesis
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