Aqueous foams are packings of gas bubbles in liquid. They exhibit an elastic response due to the surface tension of the interfaces, and plasticity due to bubble rearrangements. Hence a foam’s properties differ substantially from those of its components. Foams have a multitude of applications, from food and drink to soil remediation and fire suppression.
However, foams are unstable. Gas can diffuse through the liquid phase, changing the sizes of the bubbles, and hence their efficacy in applications.
On average, large bubbles grow while small bubbles shrink and subsequently disappear. Thus the length scale of the foam increases, or coarsens. The coarsening process is closely related to grain growth in metals and Ostwald ripening in emulsions.
Coarsening is well characterised in the dry (low) and wet (high) limits of liquid fraction. In the dry limit the gas flow is through the thin films, while in the wet limit there are no thin films and the gas flows through bulk liquid. Growth laws for individual bubbles are known, as is the exponent of time by which the average bubble size evolves in a scaling state. However, these properties have not yet been convincingly established for intermediate liquid fractions, those which are found in most applications.
The growth rate of a bubble is determined by its pressure (relative to that of its neighbours), which is related to the curvature of its liquid/gas interfaces, and also to its surface area in contact with other bubbles. A first approximation is to take these geometric properties as dependent only upon the bubble’s equivalent spherical radius.
I will present mean-field approximations for a bubble’s pressure and contact area at arbitrary liquid fraction which our simulations indicate are a significant improvement. The approximations are combined to give a growth law for coarsening bubbles. This is the basis for a model that predicts the scaling-state bubble size distributions in a coarsening foam, which I will present for various liquid fractions and compare with recent experiments.
