Abstract
Vacuum freeze-drying is a preferred method for converting mare's milk into a shelf-stable powder while retaining its nutritional and sensory qualities.However, the process remains time-consuming and energy-intensive.This study presents a validated three-dimensional numerical model that simulates conjugate heat-and mass-transfer during vacuum freeze-drying under industrially relevant conditions.The governing equations for heat conduction, water-vapour transport (Darcy's law), and latent-heat removal were solved in COMSOL™ 6.3 using the Deformed Geometry interface to track phase-front motion without remeshing.Simulations were performed on a 50 × 45 × 0.7 cm slab frozen to -50 • C, with a shelf temperature of -20 • C and chamber pressure rangingfrom 15 to 35 Pa.Validation was conducted in a 0.45 m 2 pilot dryer using centre-line temperature measurements and gravimetric moisture-loss data.The model reproduced experimental temperature profiles (R 2 = 0.96) and predicted sublimation-front motion within 4% of image-based observations.Thinner samples (3 mm vs. 7 mm) and lower pressures (15 Pa vs. 35 Pa) significantly reduced drying time, though gains diminished below 15 Pa.This model offers a practical framework for optimising freeze-drying conditions and is extendable to other porous food and biopharmaceutical products.