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Molecular simulation and theory of homogeneous cavitation
Martin Horsch,1, 2 Kai Langenbach,1, 3 Martin Lautenschläger,1, 4 Hans Hasse1
1Laboratory of Engineering Thermodynamics, University of Kaiserslautern,2Department of Chemical Engineering, Indian Institute of Technology Kanpur,3Department of Chemical and Biomolecular Engineering, Rice University,4Department of Mechanical Engineering, University of California, Berkeley
ProcessNet MolMod ConferenceFrankfurt am Main, 10th March 2017
Homogeneous liquid to vapour nucleation
210 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Bubble formation
MD simulation of nucleation requires large systems and performant codes.
Carbon dioxide
density [mol / l]0 10 20
tem
pera
ture
[K]
220
240
260
280
300
Merker et al., J. Chem. Phys. 132, 234512, 2010.
15 255
Merker et al.Vrabec et al.
Zhang and DuanMöller and FischerHarris and Yung
3CLJQ
Scalable molecular dynamics simulation
310 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Collaboration within
IMEMO (2008 – 2011)
SkaSim (2013 – 2016)
TaLPas (2017 – 2020)
Scalable molecular dynamics simulation
410 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Spatial domain decomposition
Dynamic load balancing
Communication (almost) only with neighbour processes
large systems “1”: molecular dynamics http://www.ls1-mardyn.de/
Linked-cell data structurenear-field pair potentials
Summation techniques, e.g.Janeček, FMM, for far field
(non-blocking,overlapping MPI
send/receiveoperations)
Scalable molecular dynamics simulation
510 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Scaling of ls1 mardyn examined on SuperMUC up to 146 016 cores.1
ideal strong scaling
observed strong scaling
number of cores
homogeneous LJTS liquidwith 4.8 billion molecules
128
1024
8192
65536
spe
edu
p (
fro
m 1
28 c
ore
s)
128 512 2048 8192 32768 131072
1W. Eckhardt, A. Heinecke, et al., Proceedings of ISC 2013, Springer, LNCS 7905, 1 – 12, 2013.
Scalable molecular dynamics simulation
610 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Up to N = 4 · 1012
on SuperMUC1
number of cores
spe
edup
weak scalingwith 31.5 million
molecules per core
MD simulation world record achieved for a liquid Lennard-Jones system.1
1Eckhardt et al., ISC 2013, LNCS 7905, 1 – 12, 2013.
Bubble formation in metastable liquid CO2
710 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
metastable liquid carbon dioxideCanonical MD simulation of cavitation in carbon dioxide.
Evaluation of local density at180 x 180 x 180 grid points:
Liquid phase: More than five neighbours present within a rad-ius of 6.9 Å around the grid point. up to 100 million interaction sites
Nucleation rate from population statistics
810 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
3CLJQ model by Merkeret al.1 for carbon dioxide
simulation time t / ps
num
ber
of b
ubbl
es w
ith V
II >
θ
θ =
1 nm
3θ
= 5
nm3
θ =
20 n
m3
θ =
100
nm3
θ = 500 nm3
N = 13 000 000, ρ = 23.6 mol/l, T = 220 K
Observation of● metastable relaxation,● nucleation,● growth of supercritical
bubbles,● ripening / coalescence
θ = 1, 2, 5, 10, 20, 50, 100, 200, and 500 nm3
1Merker et al., J. Chem. Phys. 132, 234512, 2010.
Nucleation rate from population statistics2
910 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
θ =
1 nm
3θ
= 5
nm3
θ =
20 n
m3
θ =
100
nm3
θ = 500 nm3
N = 13 000 000, ρ = 23.6 mol/l, T = 220 K
Observation of● metastable relaxation,● nucleation,● growth of supercritical
bubbles,● ripening / coalescence
θ = 1, 2, 5, 10, 20, 50, 100, 200, and 500 nm3
simulation time t / ps
num
ber
of b
ubbl
es w
ith V
II >
θ
3CLJQ model by Merkeret al.1 for carbon dioxide
2Yasuoka and Matsumoto, J. Chem. Phys. 109, 8451, 1998.
1Merker et al., J. Chem. Phys. 132, 234512, 2010;
Nucleation rate from population statistics
1010 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
rate
of f
orm
atio
n J(
V II >
θ)
/ m-3s-1
≈ V*
threshold bubble size θ / nm3
Objective: Determine themacroscopic nucleation rate J.
The rate of formation J(V II > θ)
from the method of Yasuokaand Matsuomoto depends onthe threshold size θ.
Two types of finite-size effectsare present, due to bubble sizeand due to system size.
Nucleation rate from population statistics
1110 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Subcritical bubbles are formed at a higher rate.
For large bubbles, the rate of formation is limited by the system volume.
≈ V*
threshold bubble size θ / nm3
Objective: Determine themacroscopic nucleation rate J.
The rate of formation J(V II > θ)
from the method of Yasuokaand Matsuomoto depends onthe threshold size θ.
Two types of finite-size effectsare present, due to bubble sizeand due to system size.
rate
of f
orm
atio
n J(
V II >
θ)
/ m-3s-1
Comparison to classical nucleation theory
1210 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
CNT → capillarity approximationγ = γ
planar(T ) independent of the bubble radius
metastable liquid density ρ / mol l -1
nuc
lea
tion
rate
J /
m -3
s -1
order parameter
fre
e e
ne
rgy
/ kT
Density gradient theory
1310 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
1 L. D. Landau, E. M. Lifshitz, Phys. Z. Sowjet. 8, 153, 1935;2 J. W. Cahn, J. E. Hilliard, J. Chem. Phys. 28, 258, 1958;3 C. I. Poser, I. C. Sanchez, Macromol. 14, 361, 1981;4 M. P. A. Fisher, M. Wortis, Phys. Rev. B 29, 6252, 1984;5 H. Kahl, S. Enders, Phys. Chem. Chem. Phys. 4, 931, 2002.
γ+κ(∇ρ)2
order parameter
fre
e e
ne
rgy
/ kT
Density gradient theory + PC-SAFT EOS
1410 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
1 L. D. Landau, E. M. Lifshitz, Phys. Z. Sowjet. 8, 153, 1935;2 J. W. Cahn, J. E. Hilliard, J. Chem. Phys. 28, 258, 1958;3 C. I. Poser, I. C. Sanchez, Macromol. 14, 361, 1981;4 M. P. A. Fisher, M. Wortis, Phys. Rev. B 29, 6252, 1984;5 H. Kahl, S. Enders, Phys. Chem. Chem. Phys. 4, 931, 2002.
6 J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40, 1244, 2001;7 J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 41, 5510, 2002.
A = Aideal+Ahard chain+Adispersion+Aassociation
Perturbed-Chain StatisticalAssociating Fluid Theory
γ+κ(∇ρ)2
adjustedto model
properties
Hybrid Nucleation Theory
1510 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
J = J0 exp(−Δ A *kT )
thermodynamic factor from densitygradient theory with the PC-SAFT EOS
kinetic factor from molecular dynamics
ρ / mol l -12015
280 KCO
2
1040
1030
1020
1010
J /
m-3s-1
CNT
HyN
T
extrapolationby the hybrid
nucleation theory
τnucl
τS
τ = 1 – T / Tc
J = 1
06 m
-3 s-1
0 0.04 0.080.02
0.02
0.04
0.06
satu
rate
d liq
uid
iso-choric
HyNT
experimental data:Straub (1973)Huang et al. (1975)
Conclusion
1610 Mar 2017 Martin Horsch, Kai Langenbach, Martin Lautenschläger, Hans Hasse
Molecular modelling and simulation of bubble formationby homogeneous nucleation requires the efficient useof HPC resources by scalable MD simulation.
Here, ls1 mardyn was employed on over 100 000 coresto simulate metastable liquid carbon dioxide in sys-tems containing up to 100 000 000 interaction sites.
The classical nucleation theory predicts an unphysical temperaturedependence of the thermodynamic factor which determines the nucleation rate in the spinodal limit.
A hybrid nucleation theory was developed by combining density gra dient theory and the PC-SAFT equation of state with MD simulation results.