Characteristic functions of drying material system and its theoretical solution

Drying system can normally be subject to momentum, heat, and mass transfer, three of which describe a single behavior. In drying process, there are no strictly mathematical solutions of models based on the laws, due to multiple transfer behaviors concurrently occur in a drying, particularly confined by various conditions of geometry, physics, time, and boundary. If some comprehensive factors of process were reduce to constant coefficients, mathematical models can obtain an approximate solution with some simplified actual conditions. However, diffusion-based drying function is difficult to quantify, due to activation energy, pre-finger factor and process index. It is necessary to explore theoretical solution of drying process since ancient times. Since drying can be defined as a process of spontaneous vaporization, and moisture migration, energy transfer and conversion can be measured by the changes in the drying rate and moisture content. Drying capacity of a system usually depends on water activity and external constraints, which can be characterized by free energy transfer and conversion. Taking free energy transfer and conversion as a unified scale, the present work aims to establish a characteristic function for a universal dry system and its theoretical solution under energy balance and external constraints, further to reveal drying mechanism. The results can be introduced: Theoretical expression of drying function was established using water activity in an initial state, water activity under phase equilibrium, and the relative humidity of medium, and the drying rate of the actual process. When time coordinates were introduced, the theoretical expressions were modified by the ratio of free water, and drying rate change with time. The characteristic function was also used to reveal water vaporization and pressure changes in the mixing process and their locations. An accurate solution can be achieved, particularly on the moisture content, and the distribution of water activity inside a material in the drying process. An analytical solution on a state point of a material can also be obtained from the established function for the actual drying process under various external conditions. Therefore, the theoretical solution can be gained at a state change process for a material under any external conditions, indicating breaking the description of a single behavior, such as the transfer coefficient in the transfer rate. The present work can provide a high theoretical basis for the transfer mechanism heat, mass, and momentum, in order to evaluate the energy efficiency of process system, and thereby formulate scientific evaluation standards.