A Physical Interpretation of the use of Fractional Operators for Modelling the Drying Process
Résumé
Fractional order derivatives provide useful alternatives to their integer order counterparts due to their ability to model memory and other properties of the porous medium, such as nonlocal behaviour. These phenomena are driven by the constrained interactions within the complex and non-homogeneous microstructures evident at the pore scale.In this work, we investigate the suitability of time and space fractional operators for modelling drying processes and provide a physical interpretation of these operators. At first, the concept and the general formulation in the case of a 1-D finite domain is summarised. Then a selection of simulations allowed us to analyse the physical effects of these operators on the solution. In particular, we elucidate:(I )the ability of these operators to break the fundamental relationship between mean square displacement and time in the simple example of diffusion in an open space, (ii) the caution to be taken with the formulation of boundary conditions and source terms to obtain consistent balance equations, (iii) the effect of fractional in space diffusion as a way to alter the MC profiles compared to standard diffusion, therefore potentially avoiding the dependence of the diffusivity on the variable