Drag force on spheres confined on the center line of rectangular microchannels

Via Lattice Boltzmann simulations we show there is a great deal of universality in the reduced mobility of spheres moving along the centre line of capillaries or rectangular microchannels. The reduced mobility follows a generalization of the Haberman–Sayre correlation, which is a function of the degree of confinement, e. This quantity e = dp/De, is defined as the ratio of the particle diameter and the length scale De, which is a weighted mean of the square root of the cross section area DA, and the hydraulic diameter Dh. The force experienced by spheres in pressure driven flow can be described by a generalized Faxen theorem, combined with effective medium theory. This force can be decomposed in a drag force and a pressure gradient force, both inversely proportional to the reduced mobility.