Backflow-Induced Inertial Arrest of Velocity Fluctuations in Sedimenting Suspensions
Abstract
A self-contained hydrodynamic theory is proposed to reconcile the discrepancy between divergent Stokesian velocity fluctuations and finite experimental measurements in sedimenting suspensions. We show that the compensating backflow induces non-negligible inertia, giving rise to an emergent screening length ξ∼ aϕ−1/3Rep−1/3 far exceeding the mean interparticle spacing aϕ−1/3 even at vanishingly small particle Reynolds numbers. This backflow inertial screening, together with finite-time viscous diffusion, arrests the indefinite spatiotemporal growth of large-scale velocity fluctuations. The resulting velocity fluctuations scale as δu ∼ ϕ1/3VsRep−1/6, together with the viscous correlation time τc=ξ2/ν, reproducing the well-known hydrodynamic self-diffusivity scaling DH∼ Vs a. The theory predicts the prefactors of these scaling laws without adjustable parameters, in good quantitative agreement with experimental measurements. It also successfully captures the experimentally observed crossover from the finite-correlation regime to the finite-system regime as the screening length becomes comparable to the system size.
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BibTeX
@misc{wei2026backflowinduced,
title = {{Backflow-Induced Inertial Arrest of Velocity Fluctuations in Sedimenting Suspensions}},
author = {Hsien-Hung Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23997},
eprint = {2608.23997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23997},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Backflow-Induced Inertial Arrest of Velocity Fluctuations in Sedimenting Suspensions
AU - Hsien-Hung Wei
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2608.23997
UR - https://arxiv.org/abs/2608.23997
AB - A self-contained hydrodynamic theory is proposed to reconcile the discrepancy between divergent Stokesian velocity fluctuations and finite experimental measurements in sedimenting suspensions. We show that the compensating backflow induces non-negligible inertia, giving rise to an emergent screening length ξ∼ aϕ^−1/3Re_p^−1/3 far exceeding the mean interparticle spacing aϕ^−1/3 even at vanishingly small particle Reynolds numbers. This backflow inertial screening, together with finite-time viscous diffusion, arrests the indefinite spatiotemporal growth of large-scale velocity fluctuations. The resulting velocity fluctuations scale as δu ∼ ϕ^1/3V_sRe_p^−1/6, together with the viscous correlation time τ_c=ξ^2/ν, reproducing the well-known hydrodynamic self-diffusivity scaling D_H∼ V_s a. The theory predicts the prefactors of these scaling laws without adjustable parameters, in good quantitative agreement with experimental measurements. It also successfully captures the experimentally observed crossover from the finite-correlation regime to the finite-system regime as the screening length becomes comparable to the system size.
ER -