Bubble properties and growth rates in coarsening wet foams

Abstract: In an aqueous foam, gas can diffuse through the liquid phase, changing the sizes of the bubbles. On average, large bubbles grow while small bubbles shrink, and subsequently disappear. Thus the average bubble size increases, and the length-scale of the foam coarsens. This reduces the efficacy of foams in applications such as soil remediation and firefighting, and it reduces the shelf-life of foamed foods.

Coarsening is well characterised in the low (dry foam) and high (dilute) limits of liquid fraction ϕ. In the dry limit (ϕ =0) the gas flow is through the thin films separating polyhedral bubbles, while in the dilute limit (ϕ =100%) there are no thin films and the gas flows through bulk liquid between isolated spherical bubbles. 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, which are found in most applications.

The growth rate of a bubble is determined by (i) its pressure relative to that of its neighbours, which is related to the curvature of its liquid/gas interfaces, and (ii) its surface area in contact with other bubbles. I will describe mean-field approximations for a bubble’s pressure and contact area at arbitrary liquid fraction [1], validated against bubble-scale simulations.

These approximations can be combined to give a growth law for a bubble of a given size in a coarsening foam of a given liquid fraction. From this growth law we predict scaling-state bubble size distributions, that is, we find a similarity solution of the continuity equation for the number of bubbles that leaves the distribution of bubble sizes, when scaled by their average, independent of time. I will present results for various liquid fractions [2] and compare them with recent experiments on the International Space Station [3].

References

[1] J. Morgan and S.J. Cox (2024) Effects of liquid fraction and contact angle on structure and coarsening in two-dimensional foams. J. Fluid. Mech., 999: A10.

[2] J. Morgan and S.J. Cox (2026) Mean-field model of bubble size distribution in coarsening wet foams. Soft Matter, 22: 1601-1617.

[3] Galvani, N., et al. (2023). Hierarchical bubble size distributions in coarsening wet liquid foams. Proc. Nat. Acad. Sci, 120: e2306551120.

Mathematicsfluid dynamics

Audience: researchers in the topic

---

Fluids and Structures Seminar @ UEA

---