Computer Modeling of Milk Spray Drying under Combined Convective and Radiative Heating

Introduction: Spray drying is a critical unit operation in milk powder production, strongly affecting product quality, storage stability, and process energy efficiency. Although computational fluid dynamics (CFD) has been widely applied to drying analysis, many existing models do not adequately capture internal droplet structural transformations or the effect of combined convective and radiative heating on heat and mass transfer kinetics. As a result, their predictive capability and usefulness for process optimization remain limited.

Purpose: To develop and numerically implement a CFD-oriented mathematical model of milk spray drying that describes the evolution of droplet temperature and moisture content under combined convective and radiative heating and identifies rational operating conditions.

Materials and Methods: The model was formulated as a system of differential equations describing heat conduction, moisture diffusion, and the kinetics of structural transformations within the particle. Numerical simulations were performed in Python (PyCharm environment) using the SciPy, NumPy, and Matplotlib libraries. Calculations were carried out for a single milk droplet under different specific heat input levels ranging from 0.000156 to 0.000273 J over a treatment time of 120 s. Structural and morphological changes were incorporated through a correction coefficient, K₁.

Results: The model generated temperature and moisture profiles as functions of energy input. Increasing the heat input raised the droplet surface temperature from 331 to 360 K, but did not result in a proportional increase in drying intensity. In all tested regimes, the final moisture content remained within a narrow range of 4.9-5.1%. Incorporation of the structural coefficient K₁ made it possible to adequately describe the reduction in moisture diffusivity at the final stage of drying associated with crust formation at the particle surface.

Conclusion: Higher energy input levels appear unjustified from an energy-efficiency perspective, as they may impose excessive thermal stress without providing a substantial increase in drying rate. The proposed model can be used to optimize spray-drying conditions, support dryer design, and develop digital twins of dehydration processes for food emulsions and suspensions.

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