The soap froth has a dynamics that Voronoi diagrams lack.

The two-dimensional network of soap bubbles evolves in time according to the area law
$$\frac{dA}{dt}=k(n-6),\qquad\qquad(*)$$
where $A$ is the area of a cell, $n$ the number of sides it has, and $k$ a coefficient determined by the surface tension of the bubbles. Supplemented by a mechanism by which a cell can change its number of sides (by switching sides with a neighbour or by merging with a small cell), this dynamics introduces an approximately linear correlation between the area and the number of sides known as Lewis's law.

I was fascinated by this dynamics many years ago, see Two-dimensional soap froths and polycrystalline networks: Why are large cells many-sided? The plot below shows the experimentally observed correlation between area and number of sides of cells (plusses and crosses) and two alternative theories (solid and dashed curves).

So to represent the soap froth by a Voronoi diagram one would need to reproduce this area-side number correlation. Is that possible?

Searching the web, I noticed the article Mean-curvature flow of Voronoi diagrams by Elsey and Slepcev (2013), that considers the curvature-driven evolution of Voronoi diagrams. It is unclear to me to what extent this is representative of physical soap film networks.

The area law (*) is due to John von Neumann (1951), and follows directly from the fact that the rate of transfer of mass (or area, for an incompressible gas) across the boundary is proportional to the perimeter $dl$ times the pressure difference $\delta p$, while the pressure difference $\delta p\propto\kappa$ is proportional to the curvature $\kappa$ (Young-Laplace law). Upon integration over the entire perimeter we thus find
$$\frac{dA}{dt}=k\oint \kappa \,dl=k(n-6),$$
according to the Gauss-Bonnet theorem. Remarkably, neither the shape of the bubble nor its edge lengths matter, and it also does not matter if the edges have a constant curvature. So any six-sided cell maintains its area, irrespective of whether it is surrounded by smaller or larger cells.

Notice that this only works in two dimensions, because in three dimensions the pressure difference is proportional to the mean curvature, while the Gauss-Bonnet theorem gives the Gaussian curvature. There is a generalization (due to Avron and Levine, 1992) to a network on a curved surface, such as a dome of radius $R$,
$$ \frac{dA}{dt}=k\left(n-6+3A/\pi R^2\right).$$

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