Journal
SYMMETRY-BASEL
Volume 14, Issue 1, Pages -Publisher
MDPI
DOI: 10.3390/sym14010063
Keywords
non-Brownian sedimentation; stability; BBGKY hierarchy; hydrodynamic screening; correlation functions; low-Reynolds-number hydrodynamics
Categories
Funding
- National Science Centre [UMO-2018/31/B/ST8/03640]
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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.
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.
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