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. (1) Happel, J. ; Brenner, H. 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