Evolution of soap froth from an initial bubble crystal state to the scaling state

Abstract

Soap froth evolution from an initial state consisting of mainly hexagons, to a scaling state with a time invariant distribution of cells is reported. Analysis of the two-dimensional cellular pattern as a function of time is performed using information entropy associated with the probability density function of the number of sides of the cell. We observe a period of self-organization in the cellular pattern, when the entropy is decreasing with time. To a good approximation, we also observed that the fractional entropy occupied by hexagons is time independent over the entire period of measurement, from transient, to self-organizing and the quasi-static scaling regime at long time. The universal curve relating the Aboav’s parameter and the second moment of the probability density of number of edges is obeyed during the entire period of evolution. The resemblance of the pattern formation of soap froth to the evolution of bacteria culture is discussed.