An anomalous non-self-similar infiltration and fractional diffusion equation

Problems of anomalous infiltration in porous media are considered. As follows from the analysis of experimental data, modification of the infiltration equation is necessary. A fractional diffusion equation with variable order of the time-derivative operator for describing the liquid infiltration in porous media is proposed. The physical meaning of this fractional equation is explained. This equation provides good agreement with existing experimental data for both the subdiffusion and the superdiffusion. The treatment of experimental data for the absorption of water in a fired-clay brick and for water infiltration in cement mortar using this fractional equation of diffusion is presented. Various formulae, which can be useful for applications, have been developed.