Investigating Foam Drainage

1
Investigating Foam Drainage
Simon Cox, Stefan Hutzler and Denis Weaire
Motivation
The Belgian scientist Joseph Plateau described
definitively the rules governing the
equili- brium structure of a foam.
Dry Foam
In a dry foam, long thin liquid- carrying
channels, known as Plateau borders, meet with
four-fold symmetry at junctions.
It turns our that the nature of the liquid flow
through these tetrahedrally-symmetric junctions
is important to the macroscopic properties of a
foam. This is particularly true of wet foams,
where the borders are relatively short. We model
this flow using the CFD package Fluent.
Wet Foam
Photograph courtesy of J. Cilliers (UMIST)
Bubbly liquid
We are also trying to understand the role of the
junctions by using wire frames, just as Plateau
did.
The Foam Drainage Equation describes the liquid
fraction (a) in terms of (dimensionless) position
(?) and time (t), where Q is the liquid flow
rate. It is based upon Poiseuille flow (non-slip
boundary condition) down the Plateau borders.
In a tetrahedral frame there are six soap films,
four Plateau borders and a single junction. By
adding liquid we can see how a single junction
moves.
The easiest experiment to perform is that of Free
Drainage, where a foam is made and left to drain
under gravity. The foam never disappears
completely instead it leaves an equilibrium
profile, where gravity balances the pressure
gradient.
When liquid is added to the top of a dry foam,
it descends as a solitary wave. This is also
found as a solution of the FDE. The wave
velocity scales with Q1/2.
The solitary wave experiment can be genera- lised
to double waves, where a second wave follows the
first with a higher velocity. We can also track
the position of a pulse of fluid that descends
through the foam, and when more pulses are added
the dynamics become extremely complicated
although they show power-law scaling behaviour.
The FDE can be further generalised to allow for
a variation in the number of bubbles throughout
the foam, so that we can model more realistic
foams.
However, this solitary-wave scaling changes in
the USA! Why? Because Fairy Liquid has different
properties to Dawn (for which the velocity scales
with Q1/3).
But at high flow-rates (and thus wet foams) an
instability occurs in the solitary wave
experiment, when the foam itself moves. This
leads to considerations of rheology.
Metallic foams are now being fabricated. They are
extremely useful in applications such as car
manufacture, where their strength and lightness
is desirable. Achieving uniform structure in a
metallic foam is easiest under microgravity
another of our projects which involves the
International Space Station.
So to understand wet foams we want to utilise
microgravity. We shall use the International
Space Station, with funding from the European
Space Agency.
Picture courtesy of J. Banhart, reproduced from
Duarte Banhart (2000) Acta Mater.
Artists impression courtesy of ESA.