Aqueous foams are systems out of equilibrium. If you produce foam with uniform bubble size and liquid content in an enclosed container, the foam will evolve to a non-uniform profile in bubble size and liquid fraction. Essentially, the top of the foam will be dry with large bubbles and the bottom of the foam will be wet with small bubbles. This is due to the drainage of liquid and the coarsening of gas from small to large bubbles.
Drainage and coarsening
The study of foam drainage has a long history that culminates in a non-linear partial differential "drainage equation" for the change of liquid fraction with time and position. The drainage equation is ultimately a continuity equation expressing the conservation of liquid in foams. But drainage is not the only phenomena present in aqueous foams. Gas diffusion is equally important (Vera and Durian, PRL, 2002) and has a major impact enhancing drainage in freely evolving foams. We investigate steady state foams in the light of the connection between drainage and coarsening.
Steady state foams
We generate a column of foam and maintain it in steady state by continuously bubbling gas in the bottom of the column. In this regime, the bubbles move upwards at a fixed velocity and the bubble size and liquid fraction profiles do not change with time. We study the capillary and viscous drag contributions to the liquid fraction profile and the effect of coarsening on the net transport of gas in the system.
Formation of a Bi-disperse distribution in steady state foams
As we studied steady-state foams, we observed the very unusual formation of a bi-disperse distribution of bubbles sizes. The foam column starts out with a layer of almost identical bubbles. This relatively mono-disperse distribution develops into a bi-disperse distribution characterized by a number of big bubbles surrounded by tiny bubbles. Eventually, the small bubbles shrink down and evaporates while the foam becomes poly-disperse (see figure above). The phenomena e is controlled by gas diffusion alone, since no bubble rupture and vertical bubble rearrangements are present.
Electrical conductivity of foams
Aqueous foams are non-equilibrium systems made of a continuous liquid phase and dispersed gaseous phase. One of the fundamental questions in aqueous foams concerns the content of liquid under various conditions. To the experimentalist, the ability of measuring the liquid content in a foam provides valuable information which will help to build up an understanding of the dynamical properties of the foam. One way to access this information in aqueous foams is by measuring the conductivity of the foam. If the foam is wet, the liquid content is high and the foam conducts well. If the foam is dry, the conductivity is poor. In our investigation of conductivity in foams, we propose a empirical formula to determine the liquid fraction of foams and dispersion that gives the liquid fraction in terms of the relative conductivity of foam to the liquid.
(To learn more about electrical conductivity in foams, check this article on "Electrical conductivity of dispersions: from dry foams to dilute suspensions".)