Inertial Screening in Sedimentation

TL;DR

This study investigates how inertial effects influence sedimentation dynamics of non-Brownian spheres, identifying a critical Reynolds number where inertial screening alters velocity fluctuations and spatial correlations.

Contribution

It extends sedimentation analysis into the inertial regime, revealing the inertial screening length's role and proposing a modified force balance model for fluctuation behavior.

Findings

Inertial corrections become significant at Re ≈ 0.05.

Inertial screening reduces velocity fluctuations and their spatial extent.

A modified Hinch model links fluctuation magnitudes to correlation sizes.

Abstract

We use particle image velocimetry to measure the sedimentation dynamics of a semi-dilute suspension of non-Brownian spheres at Reynolds numbers, $0.001\le Re\le 2.3$, extending from the Stokes to the moderately inertial regime. We find that the onset of inertial corrections to Stokes sedimentation occurs when the inertial screening length $l=a/Re$ becomes similar to the Stokes sedimentation length $\xi_0$, at $Re_c= a/\xi_0\approx 0.05$. For $Re>Re_c$, inertial screening significantly reduces both the magnitude and spatial extent of the particle velocity fluctuations. A modified Hinch force balance model connects the fluctuation magnitudes $\sigma_V/V$ to the correlation sizes $\xi$.