Hindered Brownian diffusion in a square-shaped geometry

We study the spatial dependence of the mobility of microparticles diffusing close to an edge of a square microtube. Confocal particle tracking is used to measure the local diffusion coefficients of fluorescent latex 1.1 μm particles suspended in an aqueous solution in a borosilicate square capillary of 50 μm section side. Observations are made for a set of planes obtained by confocal sectioning of the capillary volume. The translational diffusion coefficients parallel to the axis channel and perpendicular to one of the walls are measured as a function of the distance from both the two channel walls concurring in an edge. A complete 3D spatial map of the colloid diffusion coefficients is thus obtained. Near the corner, the diffusion is hindered up to about 40% as compared to its bulk value. The three translational diffusion coefficients pertaining to the motions along the channel axis and within the channel cross-section turn out to be different from each other and differently affected by the confinement, i.e., we are in the presence of an anisotropic diffusion. The hindered diffusion phenomenon is also examined by finite element numerical simulations, and the numerical predictions fairly agree with the measured diffusion coefficients.