The properties of fractal clusters

Smirnov, Boris M.

doi:10.1016/0370-1573(90)90010-y

Cited by 128 publications

(88 citation statements)

References 158 publications

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“…Correlations coincide for large k for different P * , indicating that consolidation essentially affects the large scale features of the microstructure. The slope of I(k) versus k on the logarithmic plot yields d F = 1.52 ± 0.04, which coincides with the fractal dimension (1.55±0.02) obtained in ideal ballistic aggregation [13], despite a different connectivity: z is well above 2, it increases with P * c from about 2.9 to 3.1. Correlation length ξ can be estimated from the abscissa of the intersection of the initial plateau with the line of slope −d F .…”

Section: Density Correlationssupporting

confidence: 82%

“…1 are frequent in colloid aggregation processes, and exhibit a self-similar structure characterized by a fractal dimension d F . Ideal aggregation processes (e.g., diffusionlimited, reaction-limited or ballistic) have been studied a lot [12] and lead to different values of d F [13]. Since the density of a fractal object vanishes in the thermodynamic limit, arbitrarily large systems of finite solid fraction Φ only display a fractal structure below some correlation length or "blob size" ξ , which satisfies (in 2D) [12] …”

Section: Density Correlationsmentioning

confidence: 99%

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Discrete simulation of model, loose cohesive powders: plastic consolidation, fractal microstructure and tensile strength

Gilabert¹,

Roux²,

Castellanos³

2009

AIP Conference Proceedings

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Abstract. Isotropic packings of cohesive disks in 2D are studied by discrete, stress-controlled numerical simulations. Depending on the assembling process and on whether contacts possess rolling resistance (RR), configurations form under low pressure P with varying solid fraction Φ and fractal dimension d F describing small scale correlations below some blob size ξ . The gradual collapse observed under growing P is described as a linear relation between ln P and 1/Φ within some range, once the influence of initial conditions has faded out, and until a maximum density is approached. This corresponds to a decrease of ξ that is compatible with the fractal blob model. The isotropic tensile strength is always considerably smaller than the naive Rumpf estimate, and grows with consolidation. Coordination numbers in systems with small RR change little while density increases by large amounts in consolidation.

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Section: Density Correlationssupporting

confidence: 82%

Section: Density Correlationsmentioning

confidence: 99%

Discrete simulation of model, loose cohesive powders: plastic consolidation, fractal microstructure and tensile strength

Gilabert¹,

Roux²,

Castellanos³

2009

AIP Conference Proceedings

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“…This is in contrast to other aggregate construction algorithms. In their review article, Smirnov (1990) summarized how the (simulated) growth process affects the fractal nature of the aggregate. While ballistic particle-cluster aggregation (BPCA) produces compact clusters with D ≈ 3, ballistic clustercluster aggregation (BCCA) results in an open structure with D ≈ 2.…”

Section: Aggregatesmentioning

confidence: 99%

Influence of porosity on collisions between dust aggregates

Gunkelmann

Ringl

Urbassek

2016

A&A

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Context. Collisions between dust particles may lead to agglomerate growth or fragmentation, depending on the porosity of the dust and the collision velocity. Aims. We study the effect of agglomerate porosity and collision velocity on aggregate fragmentation and agglomeration. Methods. Granular-mechanics simulations are used to study the outcome of head-on dust aggregate collisions. The aggregates are composed of silica grains of 0.76 µm radius and have filling factors of between 0.08 and 0.21. The simulations incorporate repulsive and viscoelastic, dissipative normal forces, and intergrain adhesion. The tangential forces are composed of gliding, rolling, and torsional friction. To study the effect of aggregate porosity, we prepared spherical aggregates with identical radius but differing particle numbers. Results. The threshold velocity for agglomerate fragmentation decreases with the porosity of the aggregates. Porous aggregates tend to fragment more easily, and the fragments are irregularly shaped. In the agglomeration regime, the merged aggregate is more compact than the initial collision partners. The collision velocity at which compaction is highest is independent of the initial porosity.

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“…Both theoretical and experimental studies have shown that mutual collisions lead dust aggregates to have their fractal dimension D ∼ 2, which is so-called ballistic cluster-cluster aggregation (BCCA ;Smirnov 1990;Meakin 1991;Kempf et al 1999;Blum & Wurm 2000;Krause & Blum 2004;Paszun & Dominik 2006). The dust aggregates would be gradually compacted or disrupted in coagulation because of the increase in impact energy.…”

Section: Introductionmentioning

confidence: 99%

Static compression of porous dust aggregates

Kataoka

Tanaka

Okuzumi

et al. 2013

A&A

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Context. In protoplanetary disks, dust grains coagulate with each other and grow to form aggregates. While these aggregates are growing by coagulation, their filling factor φ decreases to φ 1; however, comets, the remnants of these early planetesimals, have φ ∼ 0.1. Thus, static compression of porous dust aggregates is important in planetesimal formation. However, the static compressive strength has only been investigated for relatively high-density aggregates (φ > 0.1). Aims. We investigate and find the compressive strength of highly porous aggregates (φ 1). Methods. We performed three-dimensional N-body simulations of aggregate compression with a particle-particle interaction model. We introduced a new method of static compression: the periodic boundary condition was adopted, and the boundaries move with low speed to get closer. The dust aggregate is compressed uniformly and isotropically by themselves over the periodic boundaries. Results. We empirically derive a formula of the compressive strength of highly porous aggregates (φ 1). We check the validity of the compressive strength formula for wide ranges of numerical parameters, such as the size of initial aggregates, the boundary speed, the normal damping force, and material. We also compare our results to the previous studies of static compression in the relatively high-density region (φ > 0.1) and confirm that our results consistently connect to those in the high-density region. The compressive strength formula is also derived analytically.

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The properties of fractal clusters

Cited by 128 publications

References 158 publications

Discrete simulation of model, loose cohesive powders: plastic consolidation, fractal microstructure and tensile strength

Discrete simulation of model, loose cohesive powders: plastic consolidation, fractal microstructure and tensile strength

Influence of porosity on collisions between dust aggregates

Static compression of porous dust aggregates

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