On the structure of random tissues or froths, and their evolution

Abstract

Von Neumann's law, governing the evolution of two-dimensional soap bubble froths, is shown to be a direct consequence of the structural law of Lewis, and both express mathematically the most probable filling of space. Von Neumann's and Lewis's laws can therefore be generalized to a considerable variety of froths, tissues, metallurgical aggregates, etc., in two and three dimensions. Moreover, a hitherto arbitrary parameter in Lewis's law measures ageing of the structure