Computer simulation of floc formation in a colloidal suspension

Vold, Marjorie J.

doi:10.1016/0095-8522(63)90061-8

Cited by 348 publications

(89 citation statements)

References 9 publications

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“…These methods are based on simple algorithms that mimic cluster-cluster or particle-cluster aggregation processes due to Brownian motion. Due to their relative simplicity, several investigators (e.g., Vold 1963;Hutchinson and Sutherland 1965;Sander 1981, 1983;Meakin 1983a,b) have adopted particle-cluster methods; however, the aggregates obtained cannot be considered fractals (Jullien and Botet 1987). A more physicallybased method was developed by Mountain et al (1986), who generated soot aggregates using a numerical simulation involving clustercluster aggregation based on the solution of the Langevin equations.…”

Section: Simulation Of Aggregatesmentioning

confidence: 99%

Evaluation of the Fractal Properties of Cluster?Cluster Aggregates

Brasil¹,

Farias²,

Carvalho³

2000

Aerosol Science and Technology

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ABSTRACT. While the fractal dimension of cluster -cluster aggregates, D f , appears to be a well-established property, the fractal prefactor, kg (also known as structural coef cient), continues to exhibit a large range of possible values. In the present paper, an attempt is made to clarify this issue which leads to conclusive results concerning the value to adopt for the fractal prefactor of simulated aggregates. Starting from a large population of "free" numerically simulated aggregates (i.e., where no restrictions to aggregate formation were imposed) the fractal properties obtained were estimated both using morphological concepts as well as light scattering theories. Furthermore, studies for aggregates having prede ned morphological k g values (namely, k g > 2 and ca. 1) were also performed in order to check the viability of these values. The results obtained for the three different populations of aggregates considered were used to infer, through a best-t analysis, the fractal properties. Our best estimates are k g ¼ 1.27 and D f ¼ 1.82, which are approximately independent of aggregate size and composition. These results are in very good agreement with numerical predictions reported by previous authors. However, experimental results systematically indicate k g > 2. This motivated the present authors to identify possible reasons for these large discrepancies. Present calculations indicate that partial sintering in conjunction with the polydispersity of aggregates (resulting in a cut-off function coef cient, k p , >1) contributes to a systematic increase in k g , possibly justifying the differences between numerical and experimental results.

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Section: Simulation Of Aggregatesmentioning

confidence: 99%

Evaluation of the Fractal Properties of Cluster?Cluster Aggregates

Brasil¹,

Farias²,

Carvalho³

2000

Aerosol Science and Technology

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“…Theoretical models of aggregating particles have been developed for different mechanisms (Vold, 1959(Vold, , 1963Sutherland, 1966Sutherland, , 1967Witten and Sander, 1981;Kolb et al, 1983;Witten and Meakin, 1983;Meakin, 1983aMeakin, -d, 1984aBall and Witten, 1984;Hentschel, 1984;Meakin and Wasserman, 1984), representing two distinctly different types of particle interactions-linear-trajectory coagulation or Brownian trajectory coagulation.…”

Section: Application Of Fractal Geometry To Fine Particlesmentioning

confidence: 99%

Fractal Characterization of the Structure of Aerosol Agglomerates Grown at Reduced Pressure

Reist

Hsieh

Lawless

1989

Aerosol Science and Technology

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Experimentally grown metallic aerosol particles were tal analysis was used to characterize these particles and found to form highly complex shapes. When the ambient their differences. The analysis was able to distinguish pressure at which they were grown was decreased, disseveral different growth regimes and explain some of the tinctive changes in their appearance were observed. Fracgrowth-pressure effects.

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“…In DLA model, particles released at a point distant from the cluster execute random walks until they find a neighbor site of the cluster and irreversible stick in this site. If the random walks are replaced by ballistic trajectories at random directions, we have the ballistic aggregation (BA) model [9]. In contrast to DLA, the BA model generates disordered nonfractal clusters with nontrivial scaling properties [2,10].…”

Section: Introductionmentioning

confidence: 99%

Morphological transition between diffusion-limited and ballistic aggregation growth patterns

et al. 2005

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In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter λ, which assumes the value λ = 0 (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For λ = 0, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles ρ in the region defined by a circle of radius r centered at the initial seed. As a function of r, ρ reaches the asymptotic value ρ0(λ) following a power law ρ = ρ0 + Ar −γ with a universal exponent γ = 0.46(2), independent of λ. The asymptotic value has the behavior ρ0 ∼ |1 − λ| β , where β = 0.26(1). The characteristic crossover length that determines the transition from DLA-to BA-like scaling regimes is given by ξ ∼ |1 − λ| −ν , where ν = 0.61(1), while the cluster mass at the crossover follows a power law M ξ ∼ |1 − λ| −α , where α = 0.97(2). We deduce the scaling relations β = νγ and β = 2ν − α between these exponents.

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Computer simulation of floc formation in a colloidal suspension

Cited by 348 publications

References 9 publications

Evaluation of the Fractal Properties of Cluster?Cluster Aggregates

Evaluation of the Fractal Properties of Cluster?Cluster Aggregates

Fractal Characterization of the Structure of Aerosol Agglomerates Grown at Reduced Pressure

Morphological transition between diffusion-limited and ballistic aggregation growth patterns

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