Non-Fickian Transport in Porous Media: Always Temporally Anomalous?

Fractional diffusion model for emission and adsorption prediction of TXIB from wallpaper

Mercury injection test shows that wallpaper is a porous building material with a complex fractal mass transfer channel. Therefore, fractional Fick's law is employed to investigate sub-diffusion of 2,2,4 trimethy1-1,3-pentanediol diisobutyrate (TXIB) from wallpaper. In view of the fact that a small amount of TXIB has been released from the wallpaper before the environmental chamber experiment, the non-uniform initial concentration is introduced. Based on fractional Fick's law, both fractional convective mass transfer equation and fractional mass balance equation have been firstly proposed. Combining the finite difference method and L1 algorithm, the fractional diffusion model is solved numerically. Numerical simulation results show that the present model matches well with the experimental data. Compared with the previous model based on Fick's law, the present model is in better agreement with experimental data of di-2-ethylhexyl phthalate (DEHP) released from polyvinyl chloride (PVC) flooring. The influence of key parameters on the concentration of TXIB is analyzed graphically. In addition, the absorption amount and absorption rate of TXIB on the environmental bulkhead are numerically simulated for the first time.

The Effects of Pore Geometry on Late Time Solute Transport with the Presence of Recirculation Zone

The solute transport process in porous media is central to understanding many geophysical processes and determines the success of engineered applications. However, fundamental understanding of solute transport in heterogeneous porous media remains challenging especially when inertial effects are significant. To address this challenge, we employed direct numerical simulations in a variety of intrapore geometries at a high Reynolds number (Re = 10) flow regime, where recirculation zones (RZs) are present with significant inertial effects. We find that the volume of RZs depends on pore geometries. Moreover, RZs serve as an immobile domain that can trap and release solutes that lead to non-Fickian transport, characterized by the early arrival and heavy tailing of breakthrough curves and bimodal residence time distributions (RTDs). Lastly, the late time portion of RTDs is fitted to the power law function with determined exponent n, where n depends on the pore geometries and consequently the volume of RZs. Our study sheds light on the mechanisms of an immobile zone on the solute transport, especially improving our understanding of late time transport tailing in pressurized heterogeneous porous media.

Fractal Stochastic Processes on Thin Cantor-Like Sets

We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with the use of non-local fractal derivatives. The fractal Hurst exponent is suggested, and its relation with the order of non-local fractal derivatives is established. We relate the Gangal fractal derivative defined on a one-dimensional stochastic fractal to the fractional derivative after an averaging procedure over the ensemble of random realizations. That means the fractal derivative is the progenitor of the fractional derivative, which arises if we deal with a certain stochastic fractal.

Advanced materials modelling via fractional calculus: challenges and perspectives

Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.