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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.
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Submitted on : Thursday, October 31, 2019 - 5:05:54 PM
Last modification on : Thursday, March 19, 2020 - 11:52:05 AM
Long-term archiving on: : Saturday, February 1, 2020 - 5:31:13 PM

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V. Langlois, V. Trinh, C. Perrot. Electrical conductivity and tortuosity of solid foam: Effect of pore connections. Physical Review E , American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.013115⟩. ⟨hal-02338216⟩

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