16722 DOI: 10.1021/la102273n Langmuir 2010, 26(22), 16722–16729 Published on Web 10/11/2010
pubs.acs.org/Langmuir
© 2010 American Chemical Society
Anisotropic and Hindered Diffusion of Colloidal Particles
in a Closed Cylinder
H. B. Eral,* J. M. Oh, D. van den Ende, F. Mugele, and M. H. G. Duits
Physics of Complex Fluids group, IMPACT institute University of Twente
PO Box 217, 7500 AE Enschede, The Netherlands
Received June 4, 2010. Revised Manuscript Received August 19, 2010
Video microscopy and particle tracking were used to measure the spatial dependence of the diffusion coefficient (D
R
)
of colloidal particles in a closed cylindrical cavity. Both the height and radius of the cylinder were equal to 9.0 particle
diameters. The number of trapped particles was varied between 1 and 16, which produced similar results. In the center of
the cavity, D
R
turned out to be 0.75D
0
measured in bulk liquid. On approaching the cylindrical wall, a transition region
of about 3 particle diameters wide was found in which the radial and azimuthal components of D
R
decrease to respective
values of 0.1D
0
and 0.4D
0
, indicating asymmetrical diffusion. Hydrodynamic simulations of local drag coefficients for
hard spheres produced very good agreement with experimental results. These findings indicate that the hydrodynamic
particle-wall interactions are dominant and that the complete 3D geometry of the confinement needs to be taken into
account to predict the spatial dependence of diffusion accurately.
1. Introduction
Understanding how confinement affects the diffusive behavior
of colloidal particles is crucial to understanding various dynamic
processes in biological and microfluidic systems.
1-3
The first class
of examples is given by particles that have to diffuse toward a flat
wall before they become immobilized as needed for coating
applications or for biomedical diagnostics in microfluidic chips.
4,5
Here, diffusive processes under confinement have been found to
have a direct influence on measurable quantities such as reaction
rates and retardation times.
6,7
Also, the confinement of particles
in more than one dimension and/or involving wall curvature
occurs; examples are the synthesis of colloids inside droplets,
8
the
trapping of particles inside pores,
9,10
and the diffusion or directed
transport of biomolecules or particles inside biological cells
(or model systems for these
11,12
). For each of these cases, under-
standing the time-dependent particle dynamics is connected to the
question of how confinement influences diffusion.
13
Surprisingly, a majority of fundamental studies referring to this
problem have been limited to simple geometries such as a particle
approaching a flat wall or quasi-2D systems.
14-17
Theoretically,
the classical problem of a particle translating in the vicinity of
a rigid flat wall was first treated in 1907 by Lorentz
18
and then
Faxen,
19,20
which was later improved by Brenner
21
and extended
to the double-wall case by Goldman.
22
The drag force along the
axis of the cylinders was studied theoretically by Sano.
23
For some
geometries, the quantitative correspondence between differently
obtained analytical expressions is still an issue, as evidenced by
recent papers on methods to improve the analytical solution.
24-26
*To whom correspondence should be addressed. E-mail: h.b.eral@
utwente.nl.
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