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This paper presents a numerical model to describe the evaporation and drying of liquid droplets containing dissolved solids, relevant to processes like spray drying and spray pyrolysis in the food and pharmaceutical industries. A one-way coupled Euler–Lagrange approach is developed, where the gas flow inside the dryer is addressed in the Eulerian framework while the droplet dynamics and motion are tracked using the Lagrangian framework. In the Lagrangian framework, a novel and detailed kinetics-based multi-stage drying model is developed. The droplet level model is validated against experimental data for skim-milk droplet drying, showing strong agreement. Effects of different activation energy models are also analyzed and it is found that one model predicts the drying characteristics better than the other. Finally, large-scale three-dimensional simulations are performed on a lab scale spray dryer drying Maltodextrin solution in water. It is demonstrated that the model correctly predicts variation in final particle size distribution due to changes in drying air characteristics, paving way for the deployment of the model in predicting final particle characteristics in a spray dryer. 

In this paper, we present a mathematical model and numerical simulation for the evaporation and drying of a liquid droplet containing suspended solids, relevant to processes such as spray drying and spray pyrolysis in the food and pharmaceutical industries. The model comprises three stages: first is the evaporation of the liquid droplet consisting of solid particles, followed by the second stage starting with the formation of a porous crust around a wet-core region and, finally, the third stage with sensible heating of the dry particle. Using a finite difference method with a moving grid, we account for the moving interface between the crust and wet core. Our model incorporates spatial temperature variations and is validated against experimental data on colloidal silica droplet drying, showing good agreement. We examine model assumptions and analyze the impact of drying conditions on drying rate and final particle morphology. Along with the temperature and velocity of the drying gas, we also find that the shape of suspended solid particles inside the droplet and assuming continuum flow of vapor through the crust influence drying quality. Finally, we develop a regime map to predict whether the final particle will be solid or hollow based on operating conditions.