发表机构
National Cheng Kung University（国立成功大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出自洽流体动力学理论，揭示回流诱导惯性屏蔽抑制沉降悬浮液速度波动发散，预测标度律 prefactors 并吻合实验，捕捉关联 regime 与系统 regime 的 crossover。
AI 中文摘要
本文提出了一套自洽的流体动力学理论，以调和沉降悬浮液中发散的斯托克斯速度波动与有限实验测量值之间的矛盾。研究表明，补偿回流会引发不可忽略的惯性效应，进而产生一个 emergent 屏蔽长度ξ~aφ^(-1/3)Re_p^(-1/3)，即便在粒子雷诺数极小的情况下，该长度也远大于平均粒子间距aφ^(-1/3)。这种回流惯性屏蔽与有限时间粘性扩散共同作用，阻止了大尺度速度波动在时空上的无限增长。最终的速度波动标度为δu~φ^(1/3)V_sRe_p^(-1/6)，结合粘性关联时间τ_c=ξ²/ν，重现了著名的流体动力学自扩散系数标度D_H~V_sa。该理论无需可调参数即可预测这些标度律的 prefactors，与实验测量值的定量吻合度良好；还成功捕捉到实验观测到的、随屏蔽长度与系统尺寸相当而出现的、从有限关联 regime 到有限系统 regime 的 crossover。
英文摘要
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 $ξ\sim aϕ^{-1/3}Re_p^{-1/3}$ 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 $δu \sim ϕ^{1/3}V_sRe_p^{-1/6}$, together with the viscous correlation time $τ_c=ξ^2/ν$, reproducing the well-known hydrodynamic self-diffusivity scaling $D_H\sim V_s a$. 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.
