Direct measurements of constrained Brownian motion of an isolated sphere between two walls

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Abstract
We report the results of direct measurements, using video microscopy in combination with optical tweezers, of constrained diffusion of an isolated uncharged PMMA sphere in a density-matched fluid confined between two parallel flat walls. Our experimental methodology allows us to study the hindered diffusion of the sphere as an explicit function of its distance from the walls, without interference from sedimentation or from electrostatic interaction between the particle and the walls. The measured diffusion coefficients are used to test the predictions of the wall drag effect predicted by several approximate theoretical analyses. We find a quantitative agreement with the behavior predicted using a hydrodynamic analysis that independently superimposes the wall drag effects arising from each wall. Our results imply, indirectly, that neglect of multiple interactions with the colloid sphere of the perturbations of the pressure and velocity fields induced by each wall leads to an underestimate of the influence of the wall on the drag force experienced by the particle.