The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions (Q2491486)

Summary: We present different methods to characterise the decay of beer foam by measuring the foam heights and recording foam images as a function of time. It turns out that the foam decay does not follow a simple exponential law but a higher-order equation \(V(t)=a - bt - ct^{2.5}\), which can be explained as a superposition of two processes, that is, drainage and bubble rearrangement. The reorganisation of bubbles leads to the structure of an Apollonian gasket with a fractal dimension of \(D\approx 1.3058\). Starting from foam images, we study the temporal development of bubble size distributions and give a model for the evolution towards the equilibrium state based upon the idea of Ernst Ruch to describe irreversible processes by lattices of Young diagrams. These lattices generally involve a partial order, but one can force a total order by mapping the diagrams onto the interval \([0,1]\) using ordering functions such as the Shannon entropy. Several entropy-like and nonentropy-like mixing functions are discussed in comparison with the Young order, each of them giving a special prejudice for understanding the process of structure formation during beer foam decay.