Quantum mechanics

Electrical resistivity and conductivity

Neuroscience

Biology

Statistics

Materials science

Thermal diffusivity

Percolation (cognitive psychology)

Percolation theory

Porosity

Thermodynamics

Physics

Psychology

Mathematics

Percolation threshold

Porous medium

Conductivity

Composite material

Tortuosity

Monte Carlo method

Mechanics

Directed percolation

International Journal of Engineering Science

Understanding the effects of porous network characteristics including the percolation and tortuosity on transport properties of porous materials is of great importance for the design and optimization of such materials, e.g., for superior resistance to degradation due to the transfer of corrosive fluids. Meanwhile, the percolation and tortuosity of porous networks are strongly affected by the geometrical shape of pores. In this work, we devise a generic theoretical framework for the accurate predictions of the percolation threshold and tortuosity of porous networks and a variety of transport properties of two-phase porous materials composed of three-dimensional (3D) interpenetrating non-spherical pores randomly distributed in a homogeneous solid matrix. Our framework contains three major components: (1) a coupled scheme of Monte Carlo simulations and a rigorous excluded-volume percolation model for determining of the percolation threshold of porous networks; (2) a continuum percolation-based tortuosity model (CPTM) for deriving the geometrical tortuosity of porous networks near the percolation threshold and above; and (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting various effective transport properties including the effective diffusivity, permeability, electrical and thermal conductivity of porous materials over the entire range of porosities. The theoretical framework yields accurate predictions of the percolation threshold, tortuosity and various effective transport properties, which are verified and validated using extensive experimental, numerical and analytical data for a wide spectrum of different porous materials reported in literature. Our framework is readily applicable to other non-spherical percolating networks composed of interpenetrating discrete objects like cracks, particles, interfaces, capsules and tunneling networks though 3D spherocylindrical porous networks are used as an introductory example in this work. Finally, we utilize the framework to explore the influences of the pore geometrical configurations on the tortuosity and effective diffusivity of porous materials. The results shed light on the intrinsic and complex interplay of components, structures and transport properties in porous materials, which in turn can provide novel insights for understanding degradation of porous materials in practical applications.

Theoretical framework for percolation threshold, tortuosity and transport properties of porous materials containing 3D non-spherical pores