Screening, Hyperuniformity, and Instability in the Sedimentation of Irregular Objects

Abstract

We study the overdamped sedimentation of non-Brownian objects of irregular shape using fluctuating hydrodynamics. The anisotropic response of the objects to flow, caused by their tendency to align with gravity, directly suppresses concentration and velocity fluctuations. This allows the suspension to avoid the anomalous fluctuations predicted for suspensions of symmetric spheroids. The suppression of concentration fluctuations leads to a correlated, hyperuniform structure. For certain object shapes, the anisotropic response may act in the opposite direction, destabilizing uniform sedimentation.PACS numbers: 47.57.E, 47.57.J, 05.70.Ln, Sedimentation, the settling of colloidal objects under gravity, is a fundamental and ubiquitous physical process whose details are still under debate (see reviews in Refs. [1,2]). The related process of bed fluidization is widely used in reactors, filtration, and water treatment [3]. Long-range hydrodynamic correlations among settling objects lead to complex many-body dynamics, exhibiting strong fluctuations and large-scale dynamic structures even for athermal (non-Brownian) objects with negligible inertia [4][5][6][7]. One of the key issues is the extent of velocity fluctuations of the sedimenting objects about their mean settling velocity. A famous prediction by Caflisch and Luke [8] stated that the magnitude of velocity fluctuations of individual objects should diverge with system size. Over the years there has been evidence from theory and simulations both in favor of [9][10][11][12][13][14] and against [1,[15][16][17] this prediction. Experimentally, the indefinite growth of velocity fluctuations with system size has not been observed [5,6].To resolve the Caflisch-Luke paradox, several screening mechanisms have been suggested: a characteristic screening length emerging from correlations between concentration fluctuations (the structure factor of the suspension) [15], e.g., as a result of stratification [14,18]; inertial effects [17]; side-wall effects [17]; and noise-induced concentration fluctuations [1,16].Earlier theories have considered symmetric objects, mostly spheres. Spheroids [19, 20], rod-like objects [21][22][23][24][25][26][27], and permeable spheres [28], were studied as well. In various scenarios, including applications involving fluidized beds, the suspensions contain objects of asymmetric shapes. In the present work we address the sedimentation of a large class of irregular objects which are selfaligning [29]. Under gravity, in addition to settling, such an individual object aligns an eigendirection with the driving force. This should be distinguished from symmetric objects like rods, which align with flow lines [19, 23] rather than with an external force of fixed direction. In general these objects are chiral and thus also rotate about the force direction in a preferred sense of rotation. Both

Hyperuniform states of matter

“…Long-range hydrodynamic correlations among settling particles in a viscous liquid lead to complex many-body dynamics, exhibiting very large density fluctuations and large-scale dynamic structures when the particles are spheres or other centrally symmetric objects [338][339][340][341]. Goldfriend, Diamant and Witten studied [342] the over damped sedimentation of non-Brownian objects of irregular shape using fluctuating hydrodynamics. They showed that the anisotropic response of the objects to flow, caused by their tendency to align with gravity, directly suppresses density and velocity fluctuations in certain directions with varying intensities.…”

Hidden multiscale order in the primes

“…All structurally perfect crystals and quasicrystals are hyperuniform, but typical disordered many-particle systems, including gases, liquids, and glasses, are not. Disordered hyperuniform many-particle systems are exotic states of amorphous matter that have attracted considerable recent attention [10,47,4,55,12,54,24,23,50,30,27,14,21,46]. (1.6)].…”

Two Diverging Length Scales in the Structure of Jammed Packings

“…However, studies of very large systems that explicitly identify a crossover length ξ ρ below which the system is uniform [39] suggest that ξ ρ might increase somewhat in the dual limit as the pressure is decreased towards the jamming transition and the equilibration time increases [39]. Density hyperuniformity has also been predicted for sedimentation [40] and periodically sheared suspensions [41,42].…”