Effective exponents for the diffusive coarsening of wet foams and analogous materials

It is a long-standing puzzle why experimentally measured exponents for power law growth of the average bubble radius cross over from 1/2 in the dry limit to 1/3 near the jamming transition, rather than in the very wet limit of dilute bubbles. Here, this is explained by calculation of the diffuse gas exchange rate between nearly kissing spherical bubbles. The result is only logarithmically faster than a 1/3 power law, a difference too small to be seen in existing data. The same approach is generalized to jammed foams, where bubbles are modeled as truncated spheres with circular soap films of average radii fR where R is the average bubble radius. The result is a growth law that is not a power law that can, nevertheless, be characterized with an effective exponent that varies from 1/2 toward 1/3 as f decreases to 0 at the jamming transition. This exponent prediction is compared with existing data sets in terms of a system-specific connection of f to liquid content.