Dynamics of two-dimensional soap froths

Abstract

We have studied experimentally the dynamics of soap froths in two dimensions. We observe two temporal regimes: a transient in which the average bubble area increases in time faster than a power law, and long-term behavior in which the average bubble area increases (over the decade observed) as a power law with exponent \ensuremath{\alpha}${=0.59}_{\mathrm{\ensuremath{-}}0.09}^{+0.11}$. The crossover between these two regimes depends on the initial preparation. In initially disordered systems the rate of area growth increases smoothly and monotonically, whereas in initially ordered systems the rate first overshoots its long-term value and then decreases. The system does not, however, equilibrate during the lifetime of the bubble lattice. We have also verified that Von Neumann's law for the growth rates of bubbles holds statistically. Lewis's hypothesis of a linear relation between a bubble's number of sides and its area fails for few-sided bubbles. Finally we present a simple phenomenological model for the growth of the average area. This model allows us to define a parameter ?(t) quantifying the disorder as a function of time.