Fundamental understanding of the drying and crystallisation kinetics and shape of resultant crystalline particles produced via droplet evaporation is essential across several applications. Population balance modelling provides a deterministic framework to predict crystal size distribution (CSD) by considering nucleation, growth, and diffusion of crystals within a drying droplet. This study models crust formation in a levitating saline droplet by mathematical modelling of its evaporation and crystallisation. Numerical predictions are obtained for the water evaporation, heat transfer and internal solute (NaCl) diffusion. The CSD is predicted by solving a one-dimensional population balance equation (PBE) using both the discrete method and the method of moments (MoM), considering the impact of crystal diffusion. The predicted change in droplet size over time aligns well with experiments on an acoustically levitated saline droplet. The crystal birth and growth rates are estimated by matching the predictions with the measured time to reach crust formation and the number of crystals formed as observed by scanning electron microscopy. The MoM significantly reduces computational time and memory requirements compared to the discrete method. Both methods, with or without accounting for crystal diffusion, provide similar results on a uniform computational mesh, but refining the mesh at the droplet surface causes the MoM to fail to converge. While neglecting the crystal diffusion in the PBE improves numerical convergence, the predicted number of crystals tends towards zero for finer meshes. This study presents a suitable approach for solving the PBE in an evaporating droplet to ensure numerical accuracy.
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