Representation of aggregates from their two-dimensional images for primary particles of different sizes

This study focused on representing the three-dimensional (3D) structure of individual aggregates based on their two-dimensional (2D) images. This starts with the determination of 2D box-counting fractal dimension ($D_{f,\mathrm{BC},2D}$), uses a previously derived empirical correlation to obtain 3D power law fractal dimension ($D_{f,\mathrm{PL}}$), and then builds the aggregate on the basis of $D_{f,\mathrm{PL}}$ by an existing algorithm. Validation of this procedure can be done in forward or backward manner. Forward validation requires the existence of tomographic measurements of $D_{f,\mathrm{PL}}$. It has been conducted on aggregates of large primary particles produced to this purpose in a spray fluidized bed and analyzed by X-ray micro-computed tomography (μ-CT). For the same agglomerates backward validation has also been exercised, starting the representation from 2D projections of the 3D objects and repeating the same procedure on the represented aggregates to see, how accurately the fractal dimensions of the original objects are reproduced. When the primary particles are too small in size to be resolved by X-ray μ-CT, only 2D imaging data by electron microscopy are usually available. Such images have been taken from literature for aggregates composed of submicron particles or nanoparticles and used for aggregate representation in 3D. Subsequently, backward validation of the procedure has been conducted. Both forward validation and backward validation results indicate a high level of consistency between the fractal characteristics and morphological structures of the represented aggregates and those of the original ones. Additionally, this study shows that the method is effective for aggregates of bidisperse and polydisperse particles.