# Bubble Dynamics

The second stage of bubble production is the growth stage. In real applications, the conditions under which growth occurs can be complex. The temperature field of the liquid near the heating surface must be nonuniform for heat to be transferred within the liquid. Several types of forces influence bubble growth, including the inertia of the surrounding liquid, shear forces at the interface, surface tension, and the pressure difference between the vapor and the liquid. The energy exchanged includes heat transfer by conduction and convection as well as latent heat of vaporization. The process is by definition transient, the terms in the mass, momentum, and energy equations constantly shifting over time. So we cannot expect that modeling the process of bubble growth will yield simple solutions. Nevertheless, insight can be gained from a process of analysis followed by synthesis. The growth of a bubble can be classified into two groups (both of them will be discussed below): one in which the bubble grows in a quiescent superheated liquid of infinite extent (homogeneous); another in which the bubble is attached and grows on a heated wall (heterogeneous). Finally the dynamics of bubble growth within the superheated liquid droplet will also be is discussed.

## Homogeneous Bubble Growth

Bubble growth within a superheated liquid drop will be considered first. Once a growing vapor bubble’s radius reaches that unstable equilibrium, it grows spontaneously. During the early stage, when the bubble radius is small, the Laplace-Young equation indicates that the pressure differential across the interface is at its maximum value. The resulting high interfacial velocity leads to significant inertia terms in the momentum equation. Meanwhile, the temperature of the interface is close to the superheat temperature of the surrounding liquid, so heat transfer into the vapor bubble experiences the highest driving temperature differential that occurs at any time during the process. As a result, early bubble growth tends to be limited by inertia, or the exchange of momentum between the vapor and liquid phases.

See Main Article Homogeneous Bubble Growth

## Heterogeneous Bubble Growth

For a vapor bubble attached to a heating surface, growth occurs in a nonuniform temperature field. The criteria for initiation and growth of a bubble near a wall were analyzed by Han and Griffith (1965). They assumed that a surface cavity, which serves as a nucleation site, has a hemispherical vapor cap on it. As a result, the bubble can grow only if the thermal layer adjacent to the nucleation site is sufficiently thick. A relation between cavity size and surface temperature elevation was derived on the basis of an assumed relation between the thermal layer thickness and the nucleus size at incipience.

See Main Article Heterogeneous Bubble Growth

## Bubble Growth Within Superheated Liquid Droplets

Two immiscible liquids of different volatility are mixed together such that one liquid is dispersed in the form of droplets within the other, so that the droplets may be heated by direct contact across the liquid/liquid interface. Heat can be supplied by conduction, convection, nucleate boiling, or film boiling.

See Main Article Bubble Growth Within Superheated Liquid Droplets

## References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

Han, Y.Y., and Griffith, P., 1965, “The Mechanism of Heat Transfer in Nucleate Pool Boiling. I – Bubble Initiation, Growth and Departure,” International Journal of Heat Mass Transfer, Vol. 8, pp. 887-904.