Modeling of the vacuum-sublimation drying process of a highly porous material in a microwave field

The paper presents a comprehensive mathematical model of heat and mass transfer for the process of vacuum-sublimation drying of a highly porous material in a super-high frequency (microwave) field. The model is developed to adequately describe the intensive and non-stationary processes characteristic of this drying method. The materials and methods section justifies the consideration of key process features: the volumetric nature of drying and microwave heating, the changing porous structure of the material, the presence of three forms of moisture, and the necessity to analyze temperature, moisture content, and pressure fields. The process is presented as a combination of interrelated elementary processes. The main result is a system of differential equations in cylindrical coordinates, describing internal heat and mass transfer, accounting for thermal conductivity, vaporization, phase transitions, and microwave heating. The system is supplemented with boundary conditions. For practical calculations, simplifications are proposed, e.g., neglecting liquid transport after the completion of material swelling. Sub-models for describing accompanying processes are specified. A heuristic model of material swelling is proposed, linking the expansion coefficient to the minimum temperature, and formulas are derived for determining the variable radius of the material strand, the volumetric concentration of dry matter, and porosity. A model of phase transitions (crystallization/melting) based on local conditions is developed, and a corresponding term is introduced into the heat conduction equation. For modeling microwave heating, formula is proposed, accounting for the selective absorption of energy by different material components. A method for the analytical estimation of the dielectric loss coefficient through the volume fractions of components is introduced. The main conclusion of the study is the creation of a holistic mathematical framework that allows for modeling the complex drying process, considering the mutual influence of thermophysical, structural, and electrodynamic factors. The model enables the analysis of the distribution of key parameters (temperature, humidity, pressure) within the material volume at all process stages, forming a basis for optimizing technological regimes.