Growth laws for 3D soap bubbles

Von Neumann’s law for 2D soap froth states that the growth rate of a bubble with n sides is proportional to n-6, and does not depend on other details of its shape. I have generalized this relation to 3D by means of an approximate geometrical model invoking maximal entropy considerations. The resulting generalized growth law is ${\mathit{V}}_{\mathit{F}}^{\mathrm{-}1/3}$ ${\mathit{dV}}_{\mathit{F}}$/dt=scrF(F), where F is the number of faces of a bubble of volume ${\mathit{V}}_{\mathit{F}}$, and scrF is an increasing, almost linear function, of F only. This function vanishes for F=${\mathit{F}}_0$, with ${\mathit{F}}_0$ in the range 15.7–16.1, depending on the degree of sophistication of the model. The theory reproduces fairly well a recent numerical result which indicates ${\mathit{V}}_{\mathit{F}}^{\mathrm{-}1/3}$ ${\mathit{dV}}_{\mathit{F}}$/dt=κ[f-(15.8±0.1)].