Inertial Screening in Sedimentation

Abstract

Using particle image velocimetry we have measured the sedimentation dynamics of non-Brownian spheres over a wide range of Reynolds numbers (Re) between 0.001 and 2.5. Particle velocity fluctuations about the mean settling velocity show large-scale correlations whose spatial extent and magnitude Delta V/V are independent of Re up to a critical value Re less than Re(sub c). For Re greater than Re(sub c) the fluctuations substantially diminish with increasing Reynolds number due to inertial screening of the long-range hydrodynamic interactions (HI). The onset of inertial affects is found to occur when the Oseen length l(sub o)=v/V becomes of order the correlation length. In the inertial regime, the velocity fluctuations follow -(Delta V/V)(sup 2) approaching ln(Re), in agreement with an integration of the (l/r) HI over a narrow region extending up to the Oseen length l(sub o). A simple "blob" model connects the measured correlation lengths to the magnitudes of the velocity fluctuations.