We show that the Euclidean Wasserstein distance between two compactly supported solutions of the one–dimensional porous medium equation having the same center of mass decays to zero for large times. As a consequence, we detect an improved L1–rate of convergence of solutions of the one–dimensional porous medium equation towards well–centered self–similar Barenblatt profiles, as time goes to infi...

For the case of flame thickness being of the order of the pore linear dimension, the flame structure and speed in adiabatic, premixed methane-air combustion in porous media are examined. The local, volume-averaged conservation equations that assume a local thermal equilibrium between the solid and the gas phases (i.e. the single-medium treatment) or allow for a thermal nonequilibrium (i.e. the ...

Porous zirconium alginate beads as a novel adsorbent were prepared for fluoride removal and characterized by SEM, FTIR, TG, EDX and XPS. The effect of solution pH, adsorbent dose, initial fluoride concentration, contact time, medium temperature and the coexisting ions on adsorption capacity of fluoride ion has been studied. The presence of HCO3 , SO4 2and PO4 3had a large negative impact on flu...

The pressure drop across metallic porous medium is a critical element in cooling aerospace engineering application. This paper presents a metamodel based on artificial neural networks (ANN) for estimating the pressure drop through metallic porous media. The ANN is developed using experimental data obtained from an experimental bench, developed at PRISME laboratory, which ensure the monitoring o...

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient t...

Using large scale computer simulations and pore network models of porous rock, we investigate the e€ect of correlated heterogeneity on two-phase ̄ow through porous media. First, we review and discuss the experimental evidence for correlated heterogeneity. We then employ the invasion percolation model of two-phase ̄ow in porous media to study the e€ect of correlated heterogeneity on rate-control...

The growth of a cell population within a rigid porous scaffold in a perfusion bioreactor is studied, using a three-phase continuum model of the type presented by Lemon et al. (2006, Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol., 52, 571-594) to represent the cell population (and attendant extracellular matrix), culture medium and porous scaffold. The bioreac...

Porous media has interesting features in compared with free flame combustion due to the extended of the lean flammability limits and lower emissions. Advanced new generation of internal combustion (IC) engines are expected to have far better emissions levels both gaseous and particulate matter, at the same time having far lower fuel consumption on a wide range of operating condition. These c...