Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

Abstract

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite.

Keywords

• non-Brownian sedimentation
• stability
• BBGKY hierarchy
• hydrodynamic screening
• correlation functions
• low-Reynolds-number hydrodynamics