Calculation of the fractal dimension of aggregates

Gmachowski, Lech

doi:10.1016/s0927-7757(02)00278-9

Cited by 70 publications

(42 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A correlation providing a d f -dependent prefactor, k = k(d f ), has been proposed by Gmachowski [6]. Some of the colloidal fractals reported in the literature can be appreciated in Fig.…”

Section: Introductionmentioning

confidence: 83%

Fractal-like structures in colloid science

Lazzari

Nicoud

Jaquet

et al. 2016

Advances in Colloid and Interface Science

174

126

View full text Add to dashboard Cite

a b s t r a c tThe present work aims at reviewing our current understanding of fractal structures in the frame of colloid aggregation as well as the possibility they offer to produce novel structured materials. In particular, the existing techniques to measure and compute the fractal dimension d f are critically discussed based on the cases of organic/inorganic particles and proteins. Then the aggregation conditions affecting d f are thoroughly analyzed, pointing out the most recent literature findings and the limitations of our current understanding. Finally, the importance of the fractal dimension in applications is discussed along with possible directions for the production of new structured materials.

show abstract

“…A correlation providing a d f -dependent prefactor, k = k(d f ), has been proposed by Gmachowski [6]. Some of the colloidal fractals reported in the literature can be appreciated in Fig.…”

Section: Introductionmentioning

confidence: 83%

Fractal-like structures in colloid science

Lazzari

Nicoud

Jaquet

et al. 2016

Advances in Colloid and Interface Science

174

126

View full text Add to dashboard Cite

show abstract

“…This is why the present investigation is limited to a maximum D f value of 2.1. Such a restriction in the selection of D f and k f in tunable algorithms for fractal aggregation generation is likely a manifestation of the possible relationship between D f and k f , as suggested in several studies (Sorensen and Roberts 1997;Gmachowski 2002;Lapuerta et al 2006;Heinson et al 2012). …”

Section: Theory Numerical Generation Of Fractal Aggregatesmentioning

confidence: 99%

Investigation of Absorption and Scattering Properties of Soot Aggregates of Different Fractal Dimension at 532 nm Using RDG and GMM

Liu¹,

Wong

Snelling³

et al. 2013

Aerosol Science and Technology

View full text Add to dashboard Cite

Radiative properties of numerically generated fractal soot aggregates of different fractal dimensions were studied using the numerically accurate generalized Mie-solution method (GMM) and the Rayleigh-Debye-Gans (RDG) approximate theory. Fractal aggregates of identical prefactor but different fractal dimensions, namely, 1.4, 1.78, and 2.1, were generated numerically using a tunable algorithm of cluster-cluster aggregation for aggregates containing up to 800 primary particles. Radiative properties of these aggregates were calculated at a wavelength of 532 nm assuming a soot refractive index of 1.6 + 0.6i. Four commonly used structure factors in the RDG approximation were used to investigate the effect of structure factor on the differential and total scattering cross-sections and the asymmetry factor. The differential and total scattering properties calculated using the RDG approximation become increasingly sensitive to the structure factor with increasing the fractal dimension. Primary particle interactions are the fundamental mechanism for the aggregate absorption enhancement for small aggregates and the shielding effect for larger aggregates. The extent of these two competing factors is dependent on the fractal dimension and aggregate size. RDG reasonably predicts the effect of fractal dimension on the scattering properties, but fails to account for the effect of aggregation or fractal morphology on the absorption property of fractal soot aggregates, though the error is in general less than 15%.

show abstract

“…d is normally defined as a diameter of the sphere circumscribed the aggregate (Gmachowski, 2002) straight trajectories (Chan & Dahneke, 1981). Using G sh and the limiting large Kn p form of the primary particle's Cunningham correction factor C ¼l(AþQ)/d p , one obtains for the agglomerate drag in the free molecular regime…”

Section: Properties Of Fractal Agglomeratesmentioning

confidence: 99%