Electrical conductivity and tortuosity of solid foam: Effect of pore connections

Abstract

Numerical and analytical methods at both micro-and mesoscales are used to study how the electrical resistivity and the high frequency tortuosity of solid foam are modied by the presence of membranes that partially or totally close the cell windows connecting neighbor pores. Finite element method (FEM) simulations are performed on two pores connected by a single-holed membrane and on well-ordered Kelvin foam. For two pores connected by a single-holed membrane, we show that the equation for pore access resistance obtained by Sahu and Zwolak (Phys. Rev. E 98, 012404, 2018) can predict, after a few modications, the electrical resistivity at the membrane scale for a large range of membrane apertures. In the second part, considering these analytical results, we build a pore-network model by using two kinds of conductances at the pore scale -inter-pore conductance and intra-pore conductance. Local inter-pore resistances govern foam electrical conductivity at small membrane aperture size, but when the membrane aperture has the same order of magnitude as the pore size, the intra-pore resistances are no longer negligible. An important success of this pore-network model is that it can be used to study the eects of percolation on the foam electrical conductivity by using pore-network simulations on larger samples containing a few thousands of pores and having dierent proportions of closed membrane randomly distributed over the sample.The tortuosity is found to be drastically larger than one in foam containing membranes with small apertures or a signicant fraction of closed membranes.

Acoustics of monodisperse open-cell foam: An experimental and numerical parametric study

“…C. Microstructure of real foam samples compared to numerical bcc foam In addition to solid volume fraction and pore size, the mean size hd o i of apertures between pores and the mean number N v of open windows per pore are important microstructural parameters for macroscopic properties such as permeability and tortuosity (Despois and Mortensen, 2005;Johnson et al, 1987;Kirkpatrick, 1973;Langlois et al, 2018Langlois et al, , 2019. For some real foam samples, binocular microscope observations were used to determine the distribution of the aperture sizes.…”

“…Recent studies proposed pore-network models for permeability and electrical conductivity of solid foam (Langlois et al, 2018(Langlois et al, , 2019. For permeability, the model considers that the fluid flow through solid foam is governed by the pressure drops that occur when the fluid flows through the windows.…”

“…As a consequence, the problem for electrical conductivity is very similar to the ones for permeability. Hereafter, we recall the expressions for permeability and tortuosity (where the bulk electrical resistance of the pore is neglected) regarding foam having a bcc structure (Langlois et al, 2018(Langlois et al, , 2019:…”

“…From these measurements, the visco-thermal parameters-namely, viscous permeability, tortuosity, viscous characteristic length, thermal permeability, and thermal characteristic length-are determined for an extensive number of foam samples. By combining Surface Evolver and finite-element method calculations, the visco-thermal parameters of body centered cubic (bcc) foam numerical samples are also calculated on the whole range of solid volume fraction (from 0.5% to 32%), compared to measured values and to theoretical model predictions [Langlois et al (2019). Phys.…”

Percolation and tortuosity in heart-like cells

“…One of the directions in which percolation theory has evolved is the so-called forest fire model (FFM) 2 , 3 , a part of a general "directed percolation" (DP) models, where the percolation can only move in a single forward direction and backwards movement is prohibited, such as for fire propagation. Electrical and thermal passage through different media have also been investigated by percolation methods 4 . For a review see Ref.…”