Mathematical and physical foundations of drying theories

In this paper a survey is given concerning to the stochastic modelling appr oaches in transport processes with a special emphasis on application possib ilities for simultaneous heat and mass transfer in drying. First, the mostl y used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (state-independent ) conductivity coefficients. Powerful discretisation methods are shown for their solution. Basic principles of variational calculus are discussed then with an attenti on on direct methods. As a simple application a first-order approximation e xample is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivit y coefficients has a crucial influence on the flow pattern of the coupled h eat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefficients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statist ical properties of percolative system the dynamic scaling theory was applie d. Characterising the system decay a correlation length was introduced as a parameter. Finally, a simple case of two fields is described together with relevant transfer functions.