The fraction of a volume occupied by a particular component, here subcritical bubbles.Volume fraction is a dimensionless quantity that expresses how much of a given volume is occupied by a specific component. In physics, it is often denoted by the Greek letter φ (phi) and ranges from 0 (component absent) to 1 (component fills the entire volume). For example, in a mixture of two fluids, the volume fraction of one fluid tells you its share of the total space, independent of the other component's properties. In the context of subcritical bubbles—transient fluctuations in a metastable state—the volume fraction measures how much of the system is momentarily occupied by these bubbles, which is crucial for understanding phase transitions and nucleation rates.
The concept of volume fraction has roots in classical mixture theory, dating back to the 19th century in the study of porous media and alloys. Its specific application to nucleation and bubble dynamics emerged in the mid-20th century with the development of kinetic theories of phase transitions.
To compute a volume fraction, you divide the volume occupied by the component of interest by the total volume of the system. In practice, this can be done by integrating the local density of that component over space and normalizing by the total volume. For subcritical bubbles, which are small and short-lived, the volume fraction is typically tiny and fluctuates with time; it is often estimated from statistical mechanics models that track bubble formation and collapse.
Volume fraction is used in materials science to design composites (e.g., fiber volume fraction in carbon-fiber composites) and in chemical engineering to characterize multiphase flows, such as oil-water mixtures in pipelines.
In a foam, the volume fraction of liquid can be as low as 0.01, meaning 99% of the volume is gas, yet the foam still behaves like a solid due to surface tension.
| f(mix) | variable | Free energy of mixing per lattice site — free energy density joule per cubic metre |
| component A | variable | Volume fraction of component A — volume fraction |
| component B | variable | Volume fraction of component B — volume fraction |
| N_A | variable | Degree of polymerization of component A — degree of polymerization |
| N_B | variable | Degree of polymerization of component B — degree of polymerization |
| interaction term | variable | Interaction contribution (typically χ φ_A φ_B) |
| ln | operator | Computes the natural logarithm of the argument — natural logarithm |





