(296f) Molecular Dynamics of Heterogeneous Bubble Nucleation and Growth : Study of Contact Line Motion Relevant to Nucleate Pool Boiling
Nucleate boiling is recognized as an ideal and effective technique to drastically cool a hot surface applied. It is attractive due to its stable, efficient heat transfer at a relatively low thermal driving force associated with nucleate boiling incipience. It's the dramatic heat transfer enhancements in this regime have attracted intensive interest since the 1930's. However, current proposed mechanisms rarely explicitly recognize the importance of the three-phase contact line at the edge of the vapor bubble on the solid heating surface. We argue its appearance and the motion of the contact line is essential to explain the large observed heat enhancement in nucleate boiling.
We model the transport process by the quasi-steady heat conduction equation for the growth of a single bubble at the interface of solid and liquid layers, each of finite extent under the assumptions of small Reynolds, thermal Peclet, Capillary and Bond numbers. Coupled with somewhat ad hoc contact line motion models (1) equilibrium contact angle (2) kinematic CL motion, we found that after an initial, short parameter- and model-dependent growth phase, the volume of the bubble as a function of time approaches an apparently universal time to the 3/2 power, which is in agreement with laser-doppler experimental data and other literature reported results. This stems from our simulation finding that almost 95% of total heat to the vapor bubble transfers to the very small region close to the contact line and the radius of CL growth linearly with the radius of the vapor bubble.
As noted, a direct continuum description based on quasi-steady heat conduction equation and boundary conditions does not fully incorporate all of the atomic-scale effects that control certain crucial aspects of bubble dynamics in boiling. The most obvious issue is CL motion. Although this information is in principle available experimentally, in practice such measurements on a rapidly growing bubble in the interior of a liquid close to a surface would be very difficult indeed. As an alternative, we employed molecular dynamics simulation to simulate a heterogeneous nucleation and growth of a vapor bubble on a solid surface due to heat transfer from the bottom of the heating solid.
Our simulations consider a fluid made of argon atom interacting with a Lennard-Jones (LJ 12-6) potential function with energy scale parameter e=1. There also has the same L-J potential function with energy scale parameter e=1 between the solid atoms, and in order to tether them at their lattice positions we apply harmonic force (k=50) to the solid atoms. We also apply L-J potential function form between argon and solid atom molecule with a different energy scale parameter that is delicately chosen due to the balance between the heat transfer to the liquid close to S-L interface and nucleation. We set potential cut-off distance 2.5s. The simulation domain we set for the program of interest is a cuboid, which is composed of the two solid walls and fluid region sandwiched between two walls. The solid wall lies on the bottom of simulation box and right above it is the fluid region, which is fully occupied by molecules. We have periodic boundary conditions in other 4 vertical boundaries of the domain. We adopted 5th-order gear algorithm to integrate Newton equation for the molecules in the computation with time step 5fs. Initially, we set the simulation box of 45.05s*45.05s*30.65s that composes of 40560 argon atoms and 23104 solid atoms, which all atoms are at their lattice position.
Firstly we achieve thermal equilibrium of all the phases in the simulation domain (solid walls and liquid argon) at uniform reduced temperature T=0.75. Then we expend the top wall gradually in the constant system reduced temperature T=0.75 until we find the nucleation at the S-L interface. We define local density lower than 0.15 as the vapor region and plot 3D iso-density profile to mark the possible nucleation. Finally we instantaneously increase the temperature at the bottom of the solid to a higher temperature and maintain the lower temperature at the top wall with the constant pressure that we obtained from the second step by adjusting the position of the top wall. At this step, the heat transfers through solid to the liquid and evaporates the liquid from the layer adjacent to the solid. Small vapor patches initially appear and disappear randomly in space and time. Finally at some point, one of these patches successfully grows to a stable vapor bubble and afterwards it grows with the time until heat tansfer stops.
We define the contact angle by azimuthally averaging the 2-dimensional density distribution about the center of the bubble in certain time interval. We track the growth of the vapor bubble and the associated changes in its contact line and contact angle, we found bubble growth at t1.27-1.30 which is agreement with our ad hoc model calculations. It also shows that the bubble grows slowly enough to maintain its equilibrium contact angle and the radius of CL grows linearly with the radius of bubble. Furthermore, we apply body forces for molecular atoms to mimic terrestrial Bond numbers, as the effective gravity to pull the bubble deformed and upwards and to calculate the corresponding CL motion. Finally we plug this into continuum conduction calculation described above and compare the physical quantities of interest (e.g., scaling of bubble volume with time, scaling of heat transfer with bubble density and with other physical parameters) that arise from this calculation with those of the previous ad hoc models.