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On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates
Author(s) -
Liao Jimmy Y. H.,
Selomulya Cordelia,
Bushell Graeme,
Bickert Götz,
Amal Rose
Publication year - 2006
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.200500978
Subject(s) - fractal dimension , fractal , dimension (graph theory) , coal , statistical physics , geology , mineralogy , biological system , mathematics , geometry , environmental science , chemistry , physics , mathematical analysis , pure mathematics , biology , organic chemistry
Several methods to measure the structures of coal aggregates are compared. Loose and compact coal aggregates were generated through flocculation of ultrafine coal particles (mean volume diameter of 12 μm) under specific shearing conditions. Aggregate structure in terms of mass fractal dimension, D f , was determined using various methods; namely 2D and 3D image analysis, interpretation of intensity patterns from small angle light scattering, changes in aggregation state through light obscuration, and settling behavior. In this study, the measured values of D f ranged from 1.84–2.19 for coal aggregates with more open structures, and around 2.27–2.66 for the compact ones. All of these approaches could distinguish structural differences between aggregates, albeit with variation in D f values estimated by the different techniques. The discrepancy in the absolute values for fractal dimension is due to the different physical properties measured by each approach, depending on the assumptions used to infer D f from measurable parameters. In addition, image analysis and settling techniques are based on the examination of individual aggregates, such that a large number of data points are required to yield statistically representative estimations. Light scattering and obscuration measure the aggregates collectively to give average D f values of the particulate systems; consequently ignoring any structural variation between the aggregates, and leaving possible small contaminations undetected (e.g. by dust particles or air bubbles). Appropriate utilization of a particular method is thus largely determined by system properties and required data quality.