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 VF^-1/3{dV}F$/dt=scrF(F), where F is the number of faces of a bubble of volume ${V}F$, and scrF is an increasing, almost linear function, of F only. This function vanishes for F=${F}₀$, with ${F}₀$ 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 ${V}F^{{{-}}1/3}dVF/dt={κ}[f-(15.8±{}0.1)].