Unsteady Sedimentation of a Colloidal Sphere in a Horizontal Channel

The elementary system of a sphere sedimenting through a viscous fluid under gravity becomes remarkably difficult to treat analytically when the host fluid is bounded by parallel horizontal walls. The simplest treatment, due to Oseen, involves linear superposition of Faxén’s classic single-wall correction to the mobility. We investigate the limits of the Oseen superposition approximation in this canonical system by measuring the trajectories of colloidal spheres sedimenting through water in slit pores. Measurements are performed by lifting solid or liquid droplets to the top glass-water interface with holographic optical tweezers and tracking their descent with nanometer precision by interpreting holographic video microscopy data with the Lorenz-Mie theory of light scattering. This analysis also yields precise measurements of the particles’ refractive indexes that can be interpreted with Maxwell Garnett effective medium theory to estimate the particles’ buoyant masses. Agreement between the hydrodynamic theory and these measurements establishes the limits of validity of the measurement technique and the hydrodynamic model.