Foams
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What is a foam?
The foam is a binary system formed by two immiscible phases,
called dispersed and continuous phase. (One possible definition.)
The dispersed phase takes up regions of the space, the bubbles, which are enclosed by the continuous phase.
The volume fraction of the continuous phase is much smaller than the dispersed one.
Around the bubbles, the continuous phase forms a skeleton of communicating tubes.
A foam can be regarded either as a discrete aggregate of bubbles or as connected network of films.
The two points of view are complementary and, depending on the considered problems, one of the two views it used.
In my work I always considered foams as a discrete aggreate of bubbles.
The existence of foams is due to the fact that when two immiscible fluids are in contact, the contribution of this contact to the system energy is proportional to the area of the contact surface (surface energy). The proportionality factor is called surface tension. If some energy is furnished to the system, the exceeding energy can be trapped in form of surface energy, increasing in this way the contact surface between the two phases.
From the point of view of thermodynamics, foams are metastable systems and evolve spontaneously toward their destruction,
coming back in a state where there is only a single surface of contact between the phases. Since foams are characterized by
great surface energy, they evolve naturally toward state of lower energy, reducing in this way the contact surface and
dissipating the exceeding energy as thermal energy.
The disappearance of foams occurs by three fundamental phenomena: Coarsening (diffusion of the gas through the bubbles), Coalescence (films rupture)
and Drainage (drainage of the liquid and havier phase by gravity).
Although foams are unstable and they are inevitably destined to disappear, their life time can be considerably increased by adding some surface--active agents to the continuous phase. These substances, called surfactants, reduce the surface tension of the interfaces between the two phases. In this way the energetic gap between the "foam state" and "non--foam state" is reduced too and the foam is more stable. More importantly, the surfactants stabilise the thin films against rupture.
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Dry liquid foams
A foam is said liquid when the continuous phase is a liquid and the dispersed phase is a gas.
A liquid foam is called dry when it has very little liquid (smaller than 10% of the foam volume).
Almost all the foam volume is taken by gas cells and the bubbles have a polyhedral shape.
The thickness of the films is so small, with respect to the linear size of the bubble, that it can be neglected.
So, the liquid contained in the films is approximately zero and all the liquid is present only in the interstitial
regions between the bubbles where the films meet (Plateau borders and nodes).
Ideal foams
When the foam is very dry (the liquid fraction tends to zero),
the Plateau border can be considered as lines and the nodes where they meet as points. This limit is only a theoretical model
of real foams which makes the problem easier to study: the assumption of zero liquid gives rise to some properties which
are observed, with a good approximation, also when little liquid is present.
Dry foams equilibrium
When foams are created, by increasing the surface energy of the immiscible gas-liquid system, they achieve very quickly the mechanical equilibrium,
which is a relative minimum of the surface energy . In reality the equilibrium is not even reached because the foam
continually evolves according to the coarsening process. As typical coarsening time-scale is shorter than equilibration time scale,
diffusion and equilibration are often considered as decoupled processes and equilibration as a instantaneous process.
At equilibrium, the foam has some important properties which characterize this state.
These properties, known as Plateau's laws, were observed experimentally by J. Plateau, the mathematical proof was given by J.Taylor.
Supposing that the surface tension is constant and equal for all the films, Plateau's laws for very dry foams are:
- The pressure drop across a film, composed by two liquid/gas interfaces, is proportional to the mean curvature of the film H: , where the mean curvature of a surface is the mean value between the maximal and the minimal sectional curvature of the surface.
- The films can intersect only three at a time on a Plateau border, and must do so at 120°.
- At the vetices, or nodes, no more than four borders may meet, and this tetrahedral vertex is perfectly symmetric.