The proper use of mass diffusion equation in drying modelling: from simple configurations to non-fickian behaviours
Résumé
This keynote paper intends to clearly define the possibilities and limitations offered by a simple diffusion approach of drying. Actually, many works use a simple diffusion equation to model mass transfer during drying, probably because a simple analytical solution of this equation does exist in the case of simple boundary conditions. However, one has to be aware of the limitations of this approach. Using a comprehensive formulation and a relevant computational solution, the most frequent assumptions of the diffusion approach were rigorously tested. It is concluded that analytical solutions must be discarded for several reasons:-Dirichlet boundary conditions are not realistic,-In the drying process, the coupling between heat and mass transfer is mandatory,-Non-linearity (variation of diffusivity with moisture content) cannot be avoided for mass transfer. The second part of the paper is devoted to the solution of configurations that exhibit a non-Fickian behavior. The first case study concerns the long-term behavior of wood during transient diffusion. Explained by the mobility of macromolecules, this behavior can be formulated through relevant boundary conditions. The second example shows how a diffusion equation solved in a dual-scale porous medium is able to produce a non-Fickian behavior at the macroscopic scale.
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