Table 2 Based on the classical nucleation theory (CNT), critical radii, nucleation energy barriers, and corresponding homogeneous nucleation rates of both water and CO2 after adiabatic expansion. To evaluate the critical radii, homogeneous nucleation energy barriers, and nucleation rates of both ice water and dry ice CO2 clusters, their respective surface energy, and density were used (i.e., \({\sigma }_{{{\rm{H}}}_{2}{\rm{O}}}\approx 0.106\,{\rm{J}}\,{{\rm{m}}}^{-2}\), \({\sigma }_{{{\rm{C}}{\rm{O}}}_{2}}\approx 0.08\,{\rm{J}}\,{{\rm{m}}}^{-2}\), \({\rho }_{{{\rm{H}}}_{2}{\rm{O}}}\approx 920\,{\rm{kg}}\,{{\rm{m}}}^{-3}\), and \({\rho }_{{{\rm{CO}}}_{2}}\approx 1600\,{\rm{kg}}\,{{\rm{m}}}^{-3}\) 29).
From: Unveiling CO2 heterogeneous freezing plumes during champagne cork popping
Storage temperature of bottles (in K) | 279 | 285 | 293 |
|---|---|---|---|
Saturation ratio of gas-phase CO2 after adiabatic expansion, \({S}_{{{\rm{CO}}}_{2}}\) | 0.92 | 1.44 | 2.53 |
Saturation ratio of water vapor after adiabatic expansion, \({S}_{{{\rm{H}}}_{2}{\rm{O}}}\) | 2 376 | 7 023 | 27 400 |
Critical radius for water clusters after adiabatic expansion, \({r}_{{{\rm{H}}}_{2}{\rm{O}}}^{\ast }\) (in m) | \(2.9\times {10}^{-10}\) | \(2.6\times {10}^{-10}\) | \(2.3\times {10}^{-10}\) |
Critical radius for CO2 clusters after adiabatic expansion, \({r}_{{{\rm{CO}}}_{2}}^{\ast }\) (in m) | / | \(7.7\times {10}^{-9}\) | \(3.1\times {10}^{-9}\) |
Nucleation energy barrier for water clusters after adiabatic expansion, \({\rm{\Delta }}{G}_{{{\rm{H}}}_{2}{\rm{O}}}^{\ast }\) (in J) | \(3.4\times {10}^{-20}\) | \(2.8\times {10}^{-20}\) | \(2.2\times {10}^{-20}\) |
Nucleation energy barrier for CO2 clusters after adiabatic expansion, \({\rm{\Delta }}{G}_{{{\rm{CO}}}_{2}}^{\ast }\) (in J) | / | \(2.0\times {10}^{-17}\) | \(3.3\times {10}^{-18}\) |
Molecular concentration of water vapor in the bottleneck after adiabatic expansion, \({N}_{{\rm{G}}}^{{{\rm{H}}}_{2}{\rm{O}}}\) (in molecules cm−3) | \(7.4\times {10}^{16}\) | \(9.2\times {10}^{16}\) | \(1.2\times {10}^{17}\) |
Molecular concentration of gas-phase CO2 after adiabatic expansion, \({N}_{{\rm{G}}}^{{{\rm{CO}}}_{2}}\) (in molecules cm−3) | \(3.7\times {10}^{19}\) | \(3.8\times {10}^{19}\) | \(3.9\times {10}^{19}\) |
Homogeneous nucleation rate for water clusters after adiabatic expansion, \({J}_{{\rm{\hom }}}^{{{\rm{H}}}_{2}{\rm{O}}}\) (in cm−3 s−1) | \(8\times {10}^{17}\) | \({10}^{19}\) | \({10}^{20}\) |
Homogeneous nucleation rate for CO2 clusters after adiabatic expansion, \({J}_{{\rm{\hom }}}^{{{\rm{CO}}}_{2}}\) (in cm−3 s−1) | / | \(\approx 0\) | \(\approx 0\) |
