Molecular Dynamics Simulation of Nucleation of Liquid Droplet on Solid Surface
Tatsuto KIMURA1 and Shigeo MARUYAMA1,2Department of Mechanical Engineering, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Engineering Research Institute, The University of Tokyo,
2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan
TEL: +81-3-5841-6421 FAX: +81-3-5841-7702
E-mail: [email protected]
Key Words: Molecular Dynamics Method, Heterogeneous Nucleation, Liquid Droplet, Solid Surface, Nucleation Rate
ABSTRACT
1. Introduction
The droplet nucleation on a solid surface is very important phenomena from the viewpoint of the dropwise condensation theory, and also very interesting related to the nanotechnology such as the quantum dot generation. We have simulated the equilibrium liquid droplet on solid surface by the molecular dynamics method, and have clarified the relationship between potential parameter of molecular scale and macroscopic quantity such as contact angle(1). In addition, we also carried out the molecular dynamics simulation on the bubble nucleation process on the solid surface(2). In the meantime, direct simulations of the homogeneous nucleation process of the Lennard-Jones fluid(3) and the water(4) by the molecular dynamics method were reported and a large discrepancy to the classical nucleation theory was reported. Here, a heterogeneous nucleation of liquid droplet on a solid surface was simulated by the molecular dynamics method and the nucleation rate was compared with the classical nucleation theory.
2. Simulation Method
As shown in Figure 1, vapor argon consisted of 5760 molecules contact with plane solid surface was prepared. The potential between argon molecules was represented by the
Figure 1 Simulation system.
well-known Lennard Jones (12-6) function. The solid surface was represented by one layer of harmonic molecules in fcc (111) surface. We have controlled the temperature of the solid surface by arranging a layer of phantom molecules beneath the ‘real’ surface molecules. The phantom molecules modeled the infinitely wide bulk solid kept at a constant temperature Twall with proper heat conduction characteristics. The potential between argon and solid molecule was also represented by the Lennard-Jones potential function with various energy scale parameter to change the wettability. As an initial condition, an argon fcc crystal was placed at the center of the calculation domain. We used the velocity-scaling temperature-control directly to argon molecules for initial 100 ps. Then, switching off the direct temperature control, the system was run for 500 ps with the temperature control from the phantom molecules until the equilibrium argon vapor was achieved. The classical momentum equation was integrated by the Verlet’s leap-frog method with the time step of 5 fs. After the equilibrium condition at 160 K was obtained, the setting temperature of phantom was lowered to 100K or 80 K, and the system was cooled from the solid surface. The supersaturation ratio was estimated at about 10.
3. Results and Discussions
After 500 ps from the start of the calculation, solid surface was rapidly cooled by the temperature control of phantom molecules, and the temperature of argon gradually drop afterward, then the clusters were formed and grew as shown in Figure 2. Here we define the
“cluster” as a group of molecules whose intermolecular distance are less than 1.2?AR. The
(a) 500 ps (b) 1000 ps (c) 1500 ps
Figure 2 Snapshots of clusters larger than 5 atoms.
0 1 2
0 1 2
0 10 20 30 40 50
0 1 2
Cluster Size
?G [?10–20J]
E1
E2
E3
0 1 2
0 1 2
0 10 20 30 40 50
0 1 2
Cluster Size E1–L
E2–L
E3–L
(a) Twall = 100 K (b) Twall = 80 K
Figure 3 Cluster formation free energy. Circles and triangles represent free energy calculated from clusters distributions near wall and far from the wall, respectively. Solid line and dotted line
represents heterogeneous nucleation theory and homogeneous nucleation theory, respectively.
nucleation rate was calculated from the gradient of the number of the clusters larger than some threshold. The observed nucleation rate was not much different from the prediction of the classical heterogeneous nucleation theory. We also calculated the free energy need for cluster formation from the cluster size distribution and compared with that of nucleation theory as in Figure 3. When the surface was suddenly cooled to 100 K, the simulated free energy distribution agreed with the classical theory. Here, it should be noticed that the comparison is meaningful in the smaller cluster size range than the maximum of free energy. When the surface was cooled to 80 K (higher cooling rate), there was much difference in the free energy from the classical theory, especially for larger wettability. It can be understand that the difference from the classical theory tended to increase with the increase in the cooling rate because of the spatial temperature distribution.
4. References
(1) S. Maruyama, et al., Microscale Thermophysical Engineering, 2-1 (1998), 49-62.
(2) S. Maruyama and T. Kimura, Int. J. Heat & Technology, 18-1 (2000), 69-74.
(3) K. Yasuoka and M. Matsumoto, J. Chem. Phys., 109-19 (1998), 8451-8462.
(4) K. Yasuoka and M. Matsumoto, J. Chem. Phys., 109-19 (1998), 8463-8470.
