Archive for the ‘Complex Systems’ Category

Foam

November 7, 2008

It is interesting to have a statistical description of foam. In doing so few simple characteristics may come to mind,

Network Properties:

A network can be associated to a foam structure by replacing every cell(bubble) with a node and attach these nodes to their physical neighbors. The statistical properties of this network can be interesting.

Bubble size Distribution:

Various empirical formulae have been proposed by fitting data, including

P(r) \propto {R \over (1+\beta R^2)^4}

P(r) \propto {R^2 e^{-\beta R^2}}

Here r is the radius of the bubble assuming they have spherical shapes and R is the relative size of bubbles to average radius of the population R=r/{\bar {r}}.

Dynamical Aging:

1) Average bubble sizes increase.

2) The probability distribution broadens.

3) Total volume decreases

4) Average life time of a bubble with radius r, we may need to know all the neighbors radii too.

In the case of a single hemispherical bubble at the surface of liquid and gas the bubble burst because of drainage and thinning effect at the top of the buuble. The life time in this case inversely depends on r

\tau \propto {1 \over r}

5) Transition probability of the network after a bubble burst.

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