Self-similarity study based on the particle sizes of coal-series diatomite

Abstract Coal-series diatomite (CSD) is widely distributed in China and has poor functional and structural properties and exhibits limited utilization of high value-added materials, resulting in a serious waste of resources and tremendous pressure on the environment. Moreover, due to differences in the mineralogical characteristics of CSD, different particle size scales (PSSs) have different functional structures and exhibit different self-similarities. In this study, we took CSD as the research object and PSS as the entry point and carried out a self-similarity study based on gas adsorption and an image processing method to illustrate the microstructures and self-similarities of different PSSs. The results showed that the pore structure of the CSD was dominated by mesopores and macropores and basically lacked micropores. The fractal dimensions were calculated with the Frenkel-Haisey-Hill (FHH) model and Menger model, and the D F1 values for − 0.025 mm and − 2 mm were 2.51 and 2.48, respectively, and the D M1 values were 3.75 and 3.79, respectively, indicating that the mesopore structure of the fine PSS was complex, whereas macropores were present in the coarse PSS. MATLAB was programmed to obtain grayscale thresholds, binarized images, grayscale histograms, three-dimensional (3D) reconstruction images and box dimensions, which enabled us to observe the microstructures and self-similarities of the CSD. Self-similarity studies based on particle sizes are very important for functional application of CSD.Please note that article title mismatch between MS and JS we have followed MS, kindly check and cofirm.Yes, I have checked and confirmed.Kindly check and confirm corresponding author mail id are correctly identified.Yes, I have checked and confirmed.