Bubble size–topology correlations in two-dimensional foams derived from surface energy minimization

We obtain the number fractions x_i, the average areas {A}_i and the average perimeters {P}_i of i-sided bubbles in a two-dimensional foam by minimizing the total surface energy and assuming a simple relation between {P}_i and {√A}_i. Calculations for linear and Weibull distributions of the square root of the bubble area yield large deviations, particularly at small i, from Lewis's and Desch's laws, which linearly relate {A}_i and {P}_i, respectively, to i. Nevertheless, we find good agreement with experimental results for x_i, {P}_i and {A}_i in foams.