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Mass Fractal Dimension (mass + fractal_dimension)

Distribution by Scientific Domains

Polymers and Materials Science	50%

Selected Abstracts

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

PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION, Issue 5 2005
Jimmy Y. H. Liao
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,,m) 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. [source]

Mass fractal dimension of soil macropores using computed tomography: from the box-counting to the cube-counting algorithm

EUROPEAN JOURNAL OF SOIL SCIENCE, Issue 3 2003
J.S. Perret
Summary Transport phenomena in porous media depend strongly on three-dimensional pore structures. Macropore networks enable water and solute to move preferentially through the vadose zone. A complete representation of their geometry is important for understanding soil behaviour such as preferential flow. Once we know the geometrical, topological and scaling attributes of preferential flow paths, we can begin computer simulations of water movement in the soil. The box-counting method is used in three dimensions (i.e. cube-counting algorithm) to characterize the mass fractal dimension of macropore networks using X-ray computed tomography (CT) matrices. We developed an algorithm to investigate the mass fractal dimension in three dimensions and to see how it compares with the co-dimensions obtained using the box-counting technique in two dimensions. For that purpose, macropore networks in four large undisturbed soil columns (850 mm × 77 mm diameter) were quantified and visualized, in both two and three dimensions, using X-ray CT. We observed an increasing trend between the fractal dimension and macroporosity for the four columns. Moreover, similar natural logarithm functions were obtained for the four cores by a least squares fit through plots of mass fractal dimension against macroporosity. [source]

Reaction-limited aggregation in presence of short-range structural forces

AICHE JOURNAL, Issue 4 2005
Venkataramana Runkana
Abstract A geometrically discretized sectional population balance model for reaction-limited aggregation of colloidal suspensions is presented. The two important model parameters are collision frequency factor and collision efficiency factor. The collision frequency factor is derived from physically realistic arguments proposed for collision of fractal aggregates. The collision efficiency factor is computed as a function of total interaction energy between particles, including short-range structural repulsion forces. The irregular and open structure of aggregates is taken into account by incorporating their mass fractal dimension. The characteristic time constant of reaction-limited aggregation, derived from dynamic scaling of mean aggregate size-aggregation time data, is found to correlate with electrolyte concentration. The population balance model is tested with published experimental data for aggregation of ,-alumina suspensions in the presence of different electrolytes. It is shown that the slow kinetics of aggregation under certain conditions of pH and electrolyte concentration require inclusion of short-range structural repulsion forces along with van der Waals attraction and electrical double layer repulsion forces in an extended DLVO theory. The model predictions are in good agreement with experimental data for time evolution of mean aggregate diameter in the reaction-limited aggregation regime. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source]

Preparation and Characterization of Trialkoxysilane-Containing Acrylic Resin/Alumina Hybrid Materials

MACROMOLECULAR MATERIALS & ENGINEERING, Issue 8 2006
Mingqi Li
Abstract Summary: In the present study (3-methacryloxypropyl)trimethoxysilane (MPMS) containing acrylic resin/alumina hybrid materials with various alumina contents were prepared. The effects of ethylacetoacetate (EAA) content, catalyst type, and water content during sol,gel process for alumina sols on the microstructure and properties of the hybrid materials were investigated by SAXS, AFM, DSC, TGA, and nano-indentation tester, respectively. It was found that the hybrid materials exhibited a homogeneity and the alumina phase of the hybrids had mass fractal dimension and open structure. The thermal and mechanical properties of the hybrid materials were obviously improved when alumina was incorporated. The EAA contents, catalyst type, and water content during sol,gel process for alumina sols had obvious effects on the microstructure and properties of the hybrid materials. Typical load,displacement curves of the pure acrylic resin and hybrid materials with increasing alumina content. [source]