Evaluating transport in irregular pore networks

Permeability of polydisperse solid foams

The effect of polydispersity on foam permeability is investigated by numerical simulations. Foam structures are first generated by Laguerre tessellations via the Neper software and relaxed to minimize the surface energy via the Surface Evolver software. The fluid flow and permeability are then calculated by means of pore-network simulations, by considering either fully open-cell foams or foams with randomly selected closed windows. Different configurations of window aperture are used, including identical window aperture size, identical window aperture ratio, or random window aperture ratio. The main results are obtained for the case of foams having identical and uniform window aperture ratios. For such foams and at constant mean pore size, foam permeability is found to strongly increase with the polydispersity degree. The numerical results are employed to discuss the validity of the mean pressure field assumption used to calculate the foam permeability, the effect of small pores, and the definition of an equivalent Kelvin foam size. We show that as long as the fluctuations of the window aperture ratio remain low, foam permeability can be estimated by using the mean pressure field hypothesis. The weak effect of small pores on permeability is related to their small contribution to the overall fluid volume fraction. Finally, various estimations of the equivalent Kelvin foam size based on pore-size distribution are proposed.

Heterogeneous continuous-time random walks

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.