New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles

TL;DR

This paper introduces new inversion techniques to reconstruct particle size distributions from chord length distributions for spheroid particles, employing regularization and dynamical observer methods with proven convergence.

Contribution

It presents novel methods for PSD reconstruction from CLD data for spheroids, including a Tikhonov regularization for single-shape particles and a BFN algorithm for multi-shape particles with convergence proof.

Findings

Methods successfully reconstruct PSD from CLD data in simulations.

Convergence of the BFN algorithm is proven for two particle shape clusters.

Numerical simulations demonstrate the effectiveness of the proposed approaches.

Abstract

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.