On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates

Abstract

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, Df, 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 Df 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 Df 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 Df 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 Df 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.

The use of LDS as a tool to evaluate flocculation mechanisms

“…Another traditional technique to monitor flocculation and to assess the performance of flocculants is based on settling tests in the absence of turbulence, monitored by different means [5,6], which can supply indirect information on flocs average size and structure [21] (namely the mass fractal dimension) for the conditions prevailing in a sedimentation system.…”

“…LDS not only allows the determination of the aggregate mean size and size distribution, but gives also the mass fractal dimension of the flocs, d F [4,21,23]. The mass fractal dimension provides a mean of expressing the degree to which primary particles fill the space within the nominal volume occupied by an aggregate and is, therefore, a convenient parameter to characterize the density of the flocs [24].…”

Using Light Scattering to Screen Polyelectrolytes (PEL) Performance in Flocculation

“…The individual particles could be considered to follow the Rayleigh-Gans-Debye approximation [17]. Additionally, since secondary aggregates resulting from the aggregation of primary aggregates can be formed, the scattering exponent, SE, [17], corresponding to the larger particles, was also computed from the scattering pattern, as a function of time. Thus, the kinetics of the flocs structure evolution could be computed off-line, through the mathematical processing of the scattering matrix.…”

“…LDS not only allows the determination of the aggregates mean size and size distribution, but gives also the mass fractal dimension of the flocs as a function of time [3,[15][16][17]. Mass fractal dimension provides a mean of expressing the degree to which primary particles fill the space within the nominal volume occupied by an aggregate according to Equation 1: for solid non-porous particles d F = 3 and for porous particles 1 < d F < 3 [17].…”

“…Information about the flocs structure must then be provided by the so called scattering exponent, SE, which is also obtained from the scattering pattern as shown in Figure 1 [17]. Biggs et al [3] indicate that scattering patterns at small length scales refer to the light scattered from primary aggregates, whereas at large length scales they correspond to the light scattered from secondary aggregates that resulted from the aggregation of the primary ones.…”