(625b) Simulations of A Vapor Bubble Growth IN Nucleate Boiling

Authors: 
Koplik, J., City College of New York and Graduate Center,City University of New York


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, the problem's inherent complexity has limited the theoretical understanding of the mechanism of nucleate boiling heat transfer enhancement, and its use to predict the rate of heat transfer from a solid to a liquid in contact with it.

In recent years, many numerical simulations of a vapor bubble growth have been based on the micro-layer model, which suggests that the latent heat is involved in vaporizing the micron thick wetting layer that forms beneath a portion of an expanding vapor bubble on a surface that the liquid wets. These simulations are very sensitive to the assumed initial micro-layer thickness and also assumed a uniform, constant metal surface temperature, contrary to the experimental studies. Rarely do these models explicitly recognize the importance of the three-phase contact line at the edge of the vapor bubble on the solid heating surface. Its appearance and the motion of the contact line, we argue from preliminary calculations, is essential to explain the large observed heat enhancement in nucleate boiling; unfortunately, the physics of the contact line and its motion during bubble growth are not well understood. As such, after some preliminary calculations we step down to the molecular scale where forces can be specified accurately and appeal to molecular dynamics to yield the correct physics of the contact line in these situations.

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 media each of finite extent. We define an axisymmetric, cylindrical region with the bubble at its center and implement an axisymmetric boundary integral equation method to numerically solve the quasistatic problem simulation. This formulation assumes small Reynolds, thermal Peclet, Capillary and Bond numbers. We also apply zero heat flux boundary conditions at the radius of the cylindrical cell in order to mimic the effect of bubble-bubble interactions. Furthermore, we couple the solution of the quasi-static problem with three simple, somewhat ad hoc contact line motion models to simulate the growth of an incipient bubble due to conduction until at least one of our assumptions is no longer valid. These models are (1) the contact line is pinned; (2) the contact line maintains its equilibrium contact angle and (3) a kinematic contact line motion that locally evaporates liquid to advance the contact line by virtue of the heat conducted to the contact line region in the current time step. The effects of different parameters such as conductivity ratio of the liquid and solid, wall superheat and bubble density on bubble growth are examined to reveal the fundamental mechanism. 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 literatures reported. 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. Here we first consider the bubble growth when the bubble grows to a size where gravity comes into play, the bubble begins to deform from its spherical shape. If bubble growth nevertheless remains quasi-static, the new shape is still an (equilibrium) solution of Young-Laplace equation for a given bubble volume prescribed by the vaporization during the previous time step and for a contact line position specified by the contact line motion models; in that case, we continue to simulate bubble growth by the above method until it necks.

Since the physics of contact line motion plays an important role in vapor bubble growth and molecular dynamics simulation has the potential to extract the contact line behavior without ad hoc assumptions, with only the molecular interaction physics as an input, we choose this technique 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 atoms interacting with two body forces of two types, a Lennard-Jones potential to provide an impenetrable atomic core and a finitely extensible nonlinear elastic force to link the atoms into chain molecules. The potential functions for the interaction between solid atoms and interaction between molecules and solid are the same LJ form but with different energy scale parameter. The simulation domain we set for the program of interest is a cuboid, which is composed of the solid wall and fluid region. The solid wall lie on the bottom of simulation box and right above it is the fluid region, which is fully occupied by molecules. The upper boundary of the computation domain is an imaginary perfectly adiabatic wall. The collision of an atom with this boundary is purely elastic. The other 4 vertical boundaries of the domain are applied periodic boundary condition. The velocities of the molecules are scaled at every time step so that we can control the desired temperature.

After achieving thermal equilibrium of all the phases in the domain at a uniform temperature T1, we instantaneously increase the temperature at the bottom (i.e., of the three bottom layers) of the solid to T2 and keep it fixed at that boundary. The heat transfers through solid to the liquid and evaporates the liquid from the layer adjacent to the solid. We use a relative low wettability potential on the solid surface to help the vapor to nucleate by adjusting the attraction parameter between the fluid molecules and those of 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. We define the contact angle by azimuthally averaging the 2-dimensional density distribution about the center of the bubble. We track the growth of the bubble and the associated change in its contact line and angle and use this as a model for contact line motion during bubble growth. 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.