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
We study the properties and symmetries governing the hydrodynamic interaction between two identical, arbitrarily shaped objects, driven through a viscous fluid. We the orientational effect, we find that the two objects usually repel each other. In this case the mutual degradation weakens as the two objects move away from each other, and full alignment is restored at long times.
We study the slow relaxation of isolated quasi-integrable systems, focusing on the classical problem of Fermi-Pasta-Ulam-Tsingou (FPU) chain. It is well-known that the initial energy sharing between different linear-modes can be inferred by the integrable Toda chain. Using numerical simulations, we show explicitly how the relaxation of the FPU chain toward equilibration is determined by a slow drift within the space of Toda's integrals of motion. We analyze the whole spectrum of Toda-modes and show how they dictate, via a Generalized Gibbs Ensemble (GGE), the quasi-static states along the FPU evolution. This picture is employed to devise a fast numerical integration, which can be generalized to other quasi-integrable models. In addition, the GGE description leads to a fluctuation theorem, describing the large deviations as the system flows in the entropy landscape. *
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