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Integral representation of hydraulic permeability

2022
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Proceedings of the Royal Society of Edinburgh. Section A Mathematics
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In this paper, we show that the permeability of a porous material (Tartar (1980)) and that of a bubbly fluid (Lipton and Avellaneda. Proc. R. Soc. Edinburgh Sect. A: Math. 114 (1990), 71–79) are limiting cases of the complexified version of the two-fluid models posed in Lipton and Avellaneda (Proc. R. Soc. Edinburgh Sect. A: Math. 114 (1990), 71–79). We assume the viscosity of the inclusion fluid is $z\mu _1$ and the viscosity of the hosting fluid is $\mu _1\in \mathbb {R}^{+}$ , $z\in \mathbb

doi:10.1017/prm.2022.25
fatcat:gyussr6mwnhxvchq4qfb4dh2ve