Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Lee, Chunwoo; Kramer, Timothy A.

doi:10.1016/j.cis.2004.07.001

Cited by 105 publications

(98 citation statements)

References 23 publications

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“…[16] Several experimental results have confirmed that aggregates have a fractal geometry [e.g., Vicsek, 1992;Li et al, 1998;Lee and Kramer, 2004;Burd and Jackson, 2009]. For an aggregate formed from initially identical primary particles having an effective diameter d j , the number of primary particles (N j ) in an aggregate can be estimated using a well-known fractal relationship [Jullien and Botet, 1987;Frenklach, 2002;Lee and Kramer, 2004]:…”

Section: A Simplified Aggregation Modelmentioning

confidence: 99%

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A model for wet aggregation of ash particles in volcanic plumes and clouds: 1. Theoretical formulation

2010

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[1] We develop a model to describe ash aggregates in a volcanic plume. The model is based on a solution of the classical Smoluchowski equation, obtained by introducing a similarity variable and a fractal relationship for the number of primary particles in an aggregate. The considered collision frequency function accounts for different mechanisms of aggregation, such as Brownian motion, ambient fluid shear, and differential sedimentation. Although model formulation is general, here only sticking efficiency related to the presence of water is considered. However, the different binding effect of liquid water and ice is discerned. The proposed approach represents a first compromise between the full description of the aggregation process and the need to decrease the computational time necessary for solving the full Smoluchowski equation. We also perform a parametric study on the main model parameters and estimate coagulation kernels and timescales of the aggregation process under simplified conditions of interest in volcanology. Further analyses and applications to real eruptions are presented in the companion paper by Folch et al.

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Section: A Simplified Aggregation Modelmentioning

confidence: 99%

“…For an aggregate formed from initially identical primary particles having an effective diameter d j , the number of primary particles (N j ) in an aggregate can be estimated using a well-known fractal relationship [Jullien and Botet, 1987;Frenklach, 2002;Lee and Kramer, 2004]:…”

Section: A Simplified Aggregation Modelmentioning

confidence: 99%

A model for wet aggregation of ash particles in volcanic plumes and clouds: 1. Theoretical formulation

2010

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“…The sphericity and solidity of the colloids (see Supplementary information for definitions) determined from TEM-micrographs were similar at the three sites, implying that no significant difference in colloid shape or porosity between the sites could be shown. In addition, the fractal dimensions of the colloids determined using a simplified approach described by Lee and Kramer (2004) (Supplementary information, Table S1), were in the range 1.77-1.86 at all four sites, indicating that they had been formed by diffusion-limited aggregation, e.g., without any strong repulsion between the smaller components forming the colloids (Lin et al, 1998). No significant difference could be shown between TEM and AFM fractal dimensions at sites B and C, but there was a small but significant difference at site A, and a highly significant difference at site D (Mann-Whitney U-test with P = 0.05 significance level).…”

Section: Total and Filterable Fraction Of Major And Microelements In mentioning

confidence: 99%

Metallic nanoparticle enrichment at low temperature, shallow CO2 seeps in Southern Italy

et al. 2012

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a b s t r a c t a r t i c l e i n f oWe report on metal enrichment along a natural pH gradient owing to increased CO 2 degassing at cold, shallow seeps of Vulcano Island in the Mediterranean Sea, off Sicily. We assessed composition of unfiltered and filtered seawater (b100 nm) along acidic zones ranging between ambient and pH 5, and showed that most seep derived elements are present as nanoclusters which then aggregate into larger colloids while mixing with ambient seawater along a pH gradient. Size and elemental composition of such naturally occurring nanoparticles assessed by modern characterisation methods were in good agreement with the results from conventional analytical methods. We provide analytical evidence for the presence in the water column of a large fraction of seep derived elements (e.g. approximately 50% of iron, over 80% of Mn, 100% of Cr, S and Zn) in the form of nano sized particles (e.g. b 100 nm) even at typical open ocean pHs. We launch in situ sampling protocols and sample preparation procedures for multi-method suitable to obtain accurate measurements on nanoparticles from environmental samples. Based on our results a first insight to the formation of natural nanoparticles at cold CO 2 seeps is presented and the persistence of such nano-clusters in the surrounding seawater is stipulated.

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“…Then, the fractal dimension is calculated using the number of primary particles in the system that are detected using videomicroscopy. The relation of the values of D f and the two dimensional fractal dimensions is not an straightforward matter as has been pointed out in [19,20,21].…”

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confidence: 98%

Morphology of anisotropic chains in a magneto-rheological fluid during aggregation and disaggregation processes

Domínguez-García¹,

Melle²,

Rubio³

2009

Journal of Colloid and Interface Science

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We study the morphology of the chain-like aggregates formed when a external constant and uniaxial magnetic field is applied to a magneto-rheological (MR) fluid. In order to characterize the conformation of the aggregates, we study the evolution of various fractal dimensions during aggregation and disaggregation processes (i.e., when the applied field is switched on and off), using video-microscopy and image analysis. Experiments have been performed by varying the values of two external parameters: the magnetic field amplitude and particle concentration. We found that the box-counting dimension, related with how the aggregates occupy the surrounding space, depends on the ratio R 1 /R 0 . During the first stage of the disaggregation process, when the particles are moving by Brownian motion inside the aggregate, Family-Vicsek scaling function is verified.

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Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Cited by 105 publications

References 23 publications

A model for wet aggregation of ash particles in volcanic plumes and clouds: 1. Theoretical formulation

A model for wet aggregation of ash particles in volcanic plumes and clouds: 1. Theoretical formulation

Metallic nanoparticle enrichment at low temperature, shallow CO2 seeps in Southern Italy

Morphology of anisotropic chains in a magneto-rheological fluid during aggregation and disaggregation processes

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