Determination of fractal dimension and prefactor of agglomerates with irregular structure

Abstract

Agglomerates are often composed of amorphous and irregular primary particles, especially in the food industry. The spatial morphology of this kind of soft agglomerate, here maltodextrin, can be quantified by fractal dimension. Previous research in this regard was focused on simulated agglomerates or studied 2D projected images of real agglomerates. In this work 3D volume images of agglomerates are generated with the help of X-ray computed tomography. Primary particles are distinguished and separated by means of a sequence of image processing steps. Thus center coordinates and volume of each particle are extracted. Based on this information, the radius of gyration is calculated and compared for either monodisperse or polydisperse primary particles. The primary particles comprising the maltodextrin agglomerates follow a broad size distribution, hence considering the polydispersity is highly recommended. Next, radii of primary particles are determined in order to calculate 3D fractal dimension and prefactor from power law equation. Due to the irregular shape of primary particles, two different ways of calculating primary particle radius are investigated. It is observed that differences in primary particle radius affect the partial overlapping of particles which mostly influences the prefactor value, while only slight changes are noticed in the fractal dimension. Further, the gyration radius and fractal dimension are obtained directly from voxel data. Though voxel based method is more accurate, it requires more effort and time. Therefore, by considering some error in the values of fractal dimension and gyration radius, the separated polydisperse primary particle model is suggested as a proper option. Finally, fractal dimension is also calculated by the box counting method. The proper implementation of this method for 3D structures is discussed and the results are compared with the classical power law function.