Ultimate particle size distribution of granular materials based on fractal scaling: Definition and its application

IF 4.6 2区工程技术 Q2 ENGINEERING, CHEMICAL

Powder Technology Pub Date : 2025-06-11 DOI:10.1016/j.powtec.2025.121232

Jiru Zhang, Biwen Zhang

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Abstract

The concept of relative breakage has been increasingly used for the quantitative analysis of particle breakage in granular materials, and its calculation relies significantly on the ultimate particle size distribution. However, a precise characterization of this distribution remains unresolved. This study introduced a novel concept of the ultimate particle size distribution, defined by the ultimate space-filling capacity of the particles, employing fractal theory. High-pressure confined compression tests were conducted on quartz sand and gravel to investigate the evolution of the particle size distribution due to particle breakage. Fractal scaling served as a modeling tool to track the change in the particle number during particle breakage. The findings revealed a transition from diverse initial distributions to a fractal distribution with increasing breakage. A finite particle size scale exhibited an ultimate fractal distribution, where the ultimate fractal dimension was a function calculating the ratio of the minimum to maximum particle size, with values in the range of 1.5 to 3. The ultimate fractal distribution characteristics depended on the measurement scale of the maximum and minimum particle sizes, regardless of the uniformity of the initial distribution. The transition from a particle size distribution to a fractal distribution in the confined compression tests was characterized by a constant ratio between volumetric strain and relative breakage. This ratio held promise for accurately estimating relative breakage. This study provides insights into the ultimate particle size distribution and enhances relative breakage measurement in granular materials.

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基于分形标度的颗粒材料极限粒径分布：定义及其应用

相对破碎量的概念越来越多地用于颗粒材料中颗粒破碎量的定量分析，其计算很大程度上依赖于最终粒度分布。然而，这种分布的精确特征仍然没有得到解决。本研究采用分形理论，引入了由颗粒的极限空间填充能力定义的极限粒径分布的新概念。对石英砂和砾石进行了高压密闭压缩试验，研究了颗粒破碎对粒径分布的影响。分形尺度作为一种建模工具来跟踪颗粒破碎过程中颗粒数的变化。研究结果表明，随着破碎量的增加，岩石的初始分布从多样化向分形分布转变。在有限粒径尺度下，最终分形维数为最小与最大粒径之比的函数，取值范围为1.5 ~ 3。最终的分形分布特征取决于最大和最小粒径的测量尺度，而与初始分布的均匀性无关。在密闭压缩试验中，颗粒尺寸分布向分形分布的转变表现为体积应变与相对破碎率的比值为常数。这一比率有望准确估计相对破损。这项研究提供了最终粒度分布的见解，并加强了颗粒材料的相对破碎测量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Powder Technology 工程技术-工程：化工

CiteScore

9.90

自引率

15.40%

发文量

1047

审稿时长

46 days

期刊介绍： Powder Technology is an International Journal on the Science and Technology of Wet and Dry Particulate Systems. Powder Technology publishes papers on all aspects of the formation of particles and their characterisation and on the study of systems containing particulate solids. No limitation is imposed on the size of the particles, which may range from nanometre scale, as in pigments or aerosols, to that of mined or quarried materials. The following list of topics is not intended to be comprehensive, but rather to indicate typical subjects which fall within the scope of the journal's interests: Formation and synthesis of particles by precipitation and other methods. Modification of particles by agglomeration, coating, comminution and attrition. Characterisation of the size, shape, surface area, pore structure and strength of particles and agglomerates (including the origins and effects of inter particle forces). Packing, failure, flow and permeability of assemblies of particles. Particle-particle interactions and suspension rheology. Handling and processing operations such as slurry flow, fluidization, pneumatic conveying. Interactions between particles and their environment, including delivery of particulate products to the body. Applications of particle technology in production of pharmaceuticals, chemicals, foods, pigments, structural, and functional materials and in environmental and energy related matters. For materials-oriented contributions we are looking for articles revealing the effect of particle/powder characteristics (size, morphology and composition, in that order) on material performance or functionality and, ideally, comparison to any industrial standard.