Brownian dynamics of a sphere between parallel walls

Abstract

Abstract. – We describe direct imaging measurements of a colloidal sphere’s diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere’s hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis. Stationary surfaces modify the flow field set up by a moving particle, thereby increasing the particle’s hydrodynamic drag. Calculating this influence remains a vexing problem in all but the simplest geometries because complicated boundary conditions usually render the problem intractable. For example, Faxén derived a single sphere’s hydrodynamic coupling to a rigid planar surface [1] as early as 1924. Adding a second parallel wall, however, is so much more challenging that a definitive formulation is not yet available. This is particularly unsatisfactory in that many biologically and industrially relevant processes are governed by particles ’ dynamics in confined geometries. This letter describes measurements ofa single colloidal sphere’s diffusion through water in a slit pore formed by two parallel glass surfaces. We use optical tweezers [2] to position the