Effects of confinement on hydrodynamic interactions between a suspended sphere and stationary obstacles

Via Lattice Boltzmann simulations we have derived an empirical relation for the hydrodynamic interaction between a sedimenting sphere and an obstacle in narrow confining flow channels. This relation is of importance for particle tracking in microfluidic devices used for fractionation of suspensions. The hydrodynamic interaction is a function of the dimensionless gap, the degree of confinement, and the ratio of the principal curvatures of the sphere and obstacle. The degree of confinement is defined as the ratio of particle diameter and the length scale, which enters the mobility of the confined sphere, and is described by a generalisation of the Haberman–Sayre correlation. For gaps larger than a certain the screening length, the hydrodynamic interaction changes over from a 1/¿ to a 1/¿2 scaling. The screening length is dependent on the degree of confinement.