Free Motion of a Slender Particle in Lubricating Channel Flow

Lubricating fluid motion is analysed in the context of Stokes flow through a channel containing a freely moving, relatively dense particle. The typical particle thickness is a finite fraction of the channel width, whereas the longitudinal length scale is larger, with the particle having otherwise arbitrary shape. The fluid dynamics in the gaps are coupled with the particle motion. Analysis and numerical results show that direct ’impact’ of the particle can occur with a channel wall within a finite time; however, strictly this represents the onset of impact, yielding new local physics. Dependent on the values of various model parameters, such as the particle’s initial lateral and rotational position, these impacts take place at the leading or trailing edge of a flat-plate particle, or mid-body for a smooth particle. Other parameter regimes indicate long-lasting particle oscillations, rather than a direct impact with a channel wall. For a flat-plate particle, analysis indicates that the critical centre of mass position is the midpoint, (subcritical positions yield oscillations), rather than the 1/6-or 1/3-chord position of high-Reynolds number flows. For a smooth bodied particle, the critical centre of mass position is dependent on the geometry of the particle body.