Collisional Aggregation Due to Turbulence

Pumir, Alain; Wilkinson, M.

doi:10.1146/annurev-conmatphys-031115-011538

Cited by 105 publications

(110 citation statements)

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“…The largest aegagropilae collected for this study have a major axis of approximately 9 cm, whereas the largest ever reported aegagropilae have a diameter around 20 cm. The existence of a maximal size raises the question of the influence of a surrounding turbulent flow on aggregation and fragmentation of objects of sizes in the inertial range of turbulence scales, whereas most of previous studies were dealing with sub-Kolmogorov flocs (31,32).…”

Section: [7]mentioning

confidence: 99%

Structure and mechanics of aegagropilae fiber network

Verhille

Moulinet

Vandenberghe

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Fiber networks encompass a wide range of natural and manmade materials. The threads or filaments from which they are formed span a wide range of length scales: from nanometers, as in biological tissues and bundles of carbon nanotubes, to millimeters, as in paper and insulation materials. The mechanical and thermal behavior of these complex structures depends on both the individual response of the constituent fibers and the density and degree of entanglement of the network. A question of paramount importance is how to control the formation of a given fiber network to optimize a desired function. The study of fiber clustering of natural flocs could be useful for improving fabrication processes, such as in the paper and textile industries. Here, we use the example of aegagropilae that are the remains of a seagrass (Posidonia oceanica) found on Mediterranean beaches. First, we characterize different aspects of their structure and mechanical response, and second, we draw conclusions on their formation process. We show that these natural aggregates are formed in open sea by random aggregation and compaction of fibers held together by friction forces. Although formed in a natural environment, thus under relatively unconstrained conditions, the geometrical and mechanical properties of the resulting fiber aggregates are quite robust. This study opens perspectives for manufacturing complex fiber network materials.fiber network | fiber aggregation | Posidonia oceanica | fibrous material A egagropilae are a natural aggregate of fibers produced by the decomposition of leaves and roots of Posidonia oceanica. The fibers are entangled by sea motion until the clusters reach the shore (1) (Fig. 1). P. oceanica is an endemic plant of the Mediterranean Sea with very long and thin leaves (about 1-m long, 1-cm wide, and less than 1-mm thick). The name aegagropilae originates from the Greek [αίγαγρoς (wild goat) and πιλoς (fur)] and refers to the resemblance between the shape of these balls and those regurgitated by goats. Natural fiber clustering occurs for different species of aquatic plants, such as the so-called seaballs that can be found on the Atlantic Ocean and lake shores (2, 3).P. oceanica meadows play an important ecological role in the preservation of Mediterranean coasts. They constitute plant barriers that promote sediment trapping and oxygen production in seabed, and the accumulated remains protect the beaches from erosion. Moreover, aegagropilae fibers are suitable materials for insulation in construction and automotive industries. After submitting them to various tests, they recently landed in the marketplace under the name of Neptutherm. Beyond the curiosity that these natural objects can provoke, aegagropilae samples found on beaches raise several fundamental questions. The first set of questions is on their formation process. How can fibers be entangled and packed by a flow without any confinement? How long does it take to form a cluster? Can one explain the size distribution of these aggregates? The second set of q...

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Section: [7]mentioning

confidence: 99%

Structure and mechanics of aegagropilae fiber network

Verhille

Moulinet

Vandenberghe

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…In d spatial dimensions the radial distribution function reads ( ) (ˆ) = = g r P R r r t d 1 [81,87,97], wherê | | d = x R t t is the spatial separation between the centres of mass of the two particles. In one spatial dimension, g(r) is identical to the distribution of separations (| | ) d = P x r t discussed in section 6.…”

Section: Heavy Particles In Turbulencementioning

confidence: 99%

“…For heavy particles in turbulence, there may be sub-regions of high particle concentration that temporarily expand into particle void regions, without being affected by the boundaries of the system. These are in a transient (non-steady) state, where caustics contribute to collision rates between particles not only through the rate of caustic formation J and an increased collision velocity [87,97], but possibly also through finite-time contributions to the radial distribution function g(r).…”

Section: Heavy Particles In Turbulencementioning

confidence: 99%

Fractal catastrophes

et al. 2020

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We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes ('caustics') in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents (FTLEs). Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor ('fractal catastrophes') make a distinct and universal contribution to the distribution of spatial FTLEs. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of FTLEs for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media. in configuration space. These singular points are cusp or fold catastrophes, also called 'caustics' [46,47], due to their similarities with the random focusing of light in geometrical optics [49,50]. For smooth phase-space manifolds, catastrophes are known to lead to finite-time singularities in the spatial particle density ñ t (x) ( figure 1(b)), suggesting that caustics may increase spatial clustering [46]. These consideration are, however, too imprecise to quantify spatial clustering. More importantly, these arguments rest on the notion of a smooth manifold, and it is unclear to which extent they apply to fractal phase-space attractors(figure 1(c)). In other words, it is not understood how caustic folds affect the spatial fractal dimensions, although it is generally assumed that they do. Computing the effect of caustics in the long-time limit is challenging because they give rise to non-perturbative effects [51], and are therefore thought to cause perturbation expansions for spatial fractal dimensions [6, 7, 51-55] to fail.Here we show how to describe the effect of caustics on spatial clustering from first principles by projecting the phase-space FTLEs to configuration space. We demonstrate our method by deriving the spatial FTLE distribution for inertial particles accelerated by a spatially smooth but random force field in one spatial dimension. Our main result is that caustics give rise to a distinct and universal contribution to the spatial FTLE distribution, independent of the details of the force field. This caustic contribution results in an exponentially increased probability of observing dense clusters of particles. Furthermore, we demonstrate how caustics affect the distribution of spatial separations, and we show that ...

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“…Globally speaking, it is the rate at which the phase-space manifold of the particles folds over. The rate of caustic formation is of particular importance for the calculation of collision rates between particles, where it leads to corrections to the Saffman-Turner formula for advected particles [10,[20][21][22]. We compute J from the magnitude of the tail of the steady-state distribution P s (Z = z), which behaves as P s (Z = z) ∼ J z 2 for large z:…”

Section: Rate Of Caustic Formationmentioning

confidence: 99%

Heavy particles in a persistent random flow with traps

Meibohm

Mehlig

2019

Phys. Rev. E

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We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modelled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spatial trapping regions where particles tend to accumulate. We determine the statistics of fluid-velocity gradients in the vicinity of these traps and show how this allows to determine the spatial Lyapunov exponent and the rate of caustic formation. We compare our analytical results with numerical simulations of the model and explore the limits of validity of the theory. Finally, we discuss implications for higher-dimensional systems. arXiv:1902.04354v2 [physics.flu-dyn]

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Collisional Aggregation Due to Turbulence

Cited by 105 publications

References 97 publications

Structure and mechanics of aegagropilae fiber network

Structure and mechanics of aegagropilae fiber network

Fractal catastrophes

Heavy particles in a persistent random flow with traps

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