Lewis' law versus Feltham's law in soap froth

Abstract

The scaling of area and perimeter of n-sided cells versus n in a two-dimensional cellular pattern are investigated. Lewis' law states that 〈< A( n)〉 is linear in n while Feltham's law states that the perimeter 〈 E( n)〉 is linear in n. We have tested these two different predictions on soap froth for large samples, starting with approximately 5000 cells, at different times and different gap thicknesses. We conclude that Feltham's law has a smaller statistical error than Lewis' law. We also compared the results with several two-dimensional Voronoi constructions of random points and perturbed triangular lattice. We found that the error bars of the Lewis's law and Feltham's law are comparable in the Voronoi constructions. Using geometric constraints, we argue and verified by experimental data that there is a universal law obeyed by the slopes and intercepts of these laws, on all samples.