The approach of a sphere to a wall at finite Reynolds number

Abstract

The approach to a wall of a non-Brownian rigid spherical particle, settling in a viscous fluid with a Reynolds number of the order of unity, is studied experimentally. Far from the wall, the fluid motion around the particle is driven by inertia and viscosity forces. The particle Stokes number is also of the order of unity, so that the particle motion far from the wall is driven by inertia. In the close vicinity of the wall, however, the particle–wall hydrodynamic interaction decelerates the particle significantly. An interferometric device is used to measure the vertical displacement of a millimetric size spherical bead at distances from the wall smaller than 0.1 sphere radius, with a spatial resolution of 100 nm. For the range of impact Stokes number (St*, based on the limit velocity of the sphere in an unbounded fluid) explored here (up toSt* ≅ 5), the measurements reveal that a small region of negligible particle inertia still exists just prior to contact of the sphere with the wall. In this lubrication-like region, the particle velocity decreases linearly with decreasing particle–wall distance and vanishes at contact, ruling out the possibility of a rebound. The vertical extent of this region decreases with increasing Stokes number and is e.g. only 10 μm large at impact Stokes numberSt* ≅ 5.