THE APOLLONIAN DECAY OF BEER FOAM BUBBLE SIZE DISTRIBUTION AND THE LATTICES OF YOUNG DIAGRAMS AND THEIR CORRELATED MIXING FUNCTIONS

• Published in: Discrete Dynamics in Nature and Society Vol. 2006; pp. 1 - 35
• Main Authors: Sauerbrei, S, Hass, E C, Plath, P J
• Format: Journal Article
• Language: English
• Published: Hindawi Limiteds 01.01.2006; Wiley
• ISSN: 1026-0226; 1607-887X
• DOI: 10.1155/DDNS/2006/79717

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)=abtct2.5, 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 D1.3058. 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.