Abstract
Consider a gas-bubble liquid mixture with β the gas volume fraction p the pressure and ρ the density of the mixture. Let ceff be the effective sound speed of the mixture and τ = ρ−1 the specific volume. We have that
where the compressibility κ is defined by
i.e. the change of volume with respect to pressure. Now let us assume that density and compressibility of the mixture are simply the averages over the two component values
where subscripts denote liquid or gas. The density of the gas is typically 1000 times smaller than that of the liquid while the compressibility of the liquid is negligible. Combining (1.1) and (1.3) with this simplification gives the formula
If now p = const. ργ for the gas with γ the ratio of specific heats, we have κ −1g =γp and hence
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© 1986 Springer-Verlag New York Inc.
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Caflisch, R., Miksis, M., Papanicolaou, G., Ting, L. (1986). Waves in Bubbly Liquids. In: Ericksen, J.L., Kinderlehrer, D., Kohn, R., Lions, JL. (eds) Homogenization and Effective Moduli of Materials and Media. The IMA Volumes in Mathematics and its Applications, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8646-9_8
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DOI: https://doi.org/10.1007/978-1-4613-8646-9_8
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