In this paper, we express the Chord Length Distribution (CLD) measure associated to a given Particle Size Distribution (PSD) when particles are modeled as suspended spheroids in a reactor. Using this approach, we propose two methods to reconstruct the unknown PSD from its CLD. In the single-shape case where all spheroids have the same shape, a Tikhonov regularization procedure is implemented. In the multi-shape case, the measured CLD mixes the contribution of the PSD associated to each shape. Then, an evolution model for a batch crystallization process allows to introduce a Back and Forth Nudging (BFN) algorithm, based on dynamical observers. We prove the convergence of this method when crystals are split into two clusters: spheres and elongated spheroids. These methods are illustrated with numerical simulations.
@article{arxiv.2012.08287,
title = {New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles},
author = {Lucas Brivadis and Ludovic Sacchelli},
journal= {arXiv preprint arXiv:2012.08287},
year = {2020}
}