Homogeneous nucleation of carbon dioxide by molecular simulation - PowerPoint PPT Presentation

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Homogeneous nucleation of carbon dioxide by molecular simulation Martin Horsch, Kai Langenbach, Katrin Stöbener, Stephan Werth, Zengyong Lin, Thorsten Windmann, Jadran Vrabec, Hans Hasse Laboratory of Engineering Thermodynamics, University of Kaiserslautern Thermodynamics and Energy Technology, University of Paderborn XIX. Symposium on Thermophysical Properties Boulder, Colorado, 25 th June 2015

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Molecular modelling of carbon dioxide Comparison of literature models Merker et al. (2010), JCP 132: 234512. 300 temperature [K] 280 CO 2 (Vrabec et al. ) 260 Merker et al. Vrabec et al. Harris and Yung 240 Möller and Fischer CO 2 (Merker et al. ) Zhang and Duan 220 0 5 10 15 20 25 density [mol / l] Multicriteria optimization requires characterizing a whole class of models. 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 2

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Molecular modelling of carbon dioxide Comparison of literature models Pareto set for 2CLJQ models Merker et al. (2010), JCP 132: 234512. 300 temperature [K] 280 260 Merker et al. Vrabec et al. Harris and Yung 240 Möller and Fischer Zhang and Duan 220 0 5 10 15 20 25 2CLJQ model by Vrabec et al. density [mol / l] Multicriteria optimization requires massively-parallel molecular modelling. 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 3

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Massively-parallel MD on hermit (Stuttgart) CO 2 ( T = 280 K and ρ = 17.2 mol/l) http://www.ls1-mardyn.de/ 100 000 000 interaction sites, 110 592 cores l arge s ystems “ 1 ”: m olecul ar dyn amics 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 4

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Massively-parallel MD: Cavitation Scale-up to the entire hermit cluster for canonical simulation of cavitation in carbon dioxide. Evaluation of local density at 180 x 180 x 180 grid points: ≤ 5 ? (6 mol/l) Liquid phase detected for more than 5 neighbours within a radius CO 2 ( T = 280 K and ρ = 17.2 mol/l) of 6.9 Å around the grid point. 100 000 000 interaction sites, 110 592 cores 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 5

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Cavitation in a subsaturated liquid Yasuoka-Matsumoto method: Count nuclei exceeding a threshold size ℓ. N = 2.5 x 10 7 , V = 2.41 x 10 -21 m 3 , T = 280 K Three consecutive regimes: ℓ = 36 nm 3 ℓ = 18 nm 3 ● relaxation (equilibration) ℓ = 270 nm 3 ● homogeneous cavitation ● growth and aggregation 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 6

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Cavitation in a subsaturated liquid Yasuoka-Matsumoto method: Count nuclei exceeding a threshold size ℓ. N = 2.5 x 10 7 , V = 2.41 x 10 -21 m 3 , T = 280 K ℓ = 36 nm 3 ℓ = 18 nm 3 C N T ℓ = 270 nm 3 Classical nucleation theory predicts critical cavity sizes from 10 to 30 nm 3 . 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 7

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Cavitation rates from simulation and CNT Cavities with a volume greater than 250 nm 3 are certainly supercritical. carbon dioxide (3CLJQ) Diemand et al. (2014), PRE 90: 052407. 10 20 nucleation rate x m 3 s J / J CNT C L N J T a ℓ ≥ 250 nm 3 n d s 10 10 i m i l a r this T = 280 K work J = J CNT 10 0 1 T / T c 0.4 0.6 0.8 For cavitation at high temperatures, CNT is a good approximation. 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 8

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Nucleation in supersaturated vapours Cluster criterion: Stillinger type, single s e l u neighbour within radius c e l o 1.5 σ + L /4, i.e. 5.1 Å. m 5 7 = ℓ Critical size predicted by CNT in region of interest: 40 to 60 molecules. 2CLJQ 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 9

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Nucleation in supersaturated vapours Cluster criterion: CO 2 269 K 250,2 K 238,4 K 228,4 K 10 34 -1 Stillinger type, single nucleation rate / m -3 s -1 -3 s neighbour within radius Nukleationsrate in m 10 33 1.5 σ + L /4, i.e. 5.1 Å. 10 32 CNT (nonisothermal) 10 31 ℓ = 50 molecules ℓ = 75 molecules 2CLJQ ℓ = 250 molecules 10 30 1 2 3 4 Dichte / Sättigungsdichte supersaturation (in terms of density) 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 10

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse The carrier gas effect on nucleation Scenario: ● Vapour contains k components ● Liquid phase approximately pure Wedekind et al. ● k – 1 components: Carrier gas Carrier gas effect (Wedekind et al. ): ● Thermalization → J increases ● Greater pressure → J decreases 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 11

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse The air pressure effect on nucleation Quaternary system CO 2 , N 2 and O 2 (2CLJQ) Ar (LJ) Air components with CNT following Wedekind et al. relative mole fractions as in air. ℓ = 050 ℓ = 100 ℓ = 150 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 12

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse The air pressure effect on nucleation Quaternary system CO 2 , N 2 and O 2 (2CLJQ) Ar (LJ) Air components with relative mole fractions as in air. ℓ = 050 ℓ = 100 ℓ = 150 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 13

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Is a carrier gas only present in the vapour? Light boiling compounds (i.e. “carrier gases”) often adsorb at the interface: For very small droplets, a bulk-like Γ CO2 = 0 region (with little air) is absent. The interfacial region contains Γ O2 great amounts of air due to inter- facial enrichment . Droplet growth and decay is domi- nated by heat and mass transfer through the interface. Interfacial enrichment probably influences nucleation in fluid mixtures. 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 14

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Adsorption and surface tension Gibbs adsorption equation: dγ = −Σ Γ i dμ i − ζ dT . adsorption surface tension CO 2 + O 2 CO 2 + O 2 CO 2 + O 2 CO 2 + O 2 Γ O2 / μmol m -2 γ / g s -2 x O2 / mol mol -1 x O2 / mol mol -1 Even small liquid mole fractions of a carrier gas can reduce γ significantly. 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 15

Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Conclusion With optimized and validated molecular models , e.g. from multicriteria optimization, quantitatively reliable predictions can be made. Massively parallel MD simulation of large systems makes activated processes like homogeneous nucleation directly accessible. In this way, over 100 000 cores of a supercomputer can be used efficiently. For pure carbon dioxide , homogeneous nucleation of bubbles in a metastable liquid and of droplets in a metastable vapour is well described by CNT, without the need for a curvature correction. The influence of a carrier gas cannot be reduced to its presence in the vapour phase, due to the possibility of interfacial enrichment . 25 th June 2015 M. Horsch, K. Langenbach, K. Stöbener, S. Werth, Z. Lin, T. Windmann, J. Vrabec, and H. Hasse 16