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

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.

Automated summary

We qualitatively investigate a stationary state of a non-Brownian sedimenting suspension. By analyzing the BBGKY hierarchy derived from the Liouville equation, we find that the assumption of plasma-like screening relations can eliminate some long-range terms in the hierarchy, but it does not lead to integrable solutions for correlation functions. This suggests the breaking of translational symmetry in the system, allowing the development of a non-uniform structure to suppress velocity fluctuations and limit the range of correlations.