The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions
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−ct2.5, which can be explained as a superp...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/79717 |
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| author | S. Sauerbrei E. C. Haß P. J. Plath |
| author_facet | S. Sauerbrei E. C. Haß P. J. Plath |
| author_sort | S. Sauerbrei |
| collection | DOAJ |
| description | 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−ct2.5, 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≈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. |
| format | Article |
| id | doaj-art-d8531d5dcacf497ea78b03295af843e5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d8531d5dcacf497ea78b03295af843e52025-08-20T03:24:15ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/7971779717The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functionsS. Sauerbrei0E. C. Haß1P. J. Plath2Institut für Angewandte und Physikalische Chemie–Arbeitsgruppe Chemische Synergetik, Universität Bremen, Bibliothekstraße NW 2, Bremen 28359, GermanyInstitut für Angewandte und Physikalische Chemie–Arbeitsgruppe Chemische Synergetik, Universität Bremen, Bibliothekstraße NW 2, Bremen 28359, GermanyInstitut für Angewandte und Physikalische Chemie–Arbeitsgruppe Chemische Synergetik, Universität Bremen, Bibliothekstraße NW 2, Bremen 28359, GermanyWe 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−ct2.5, 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≈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.http://dx.doi.org/10.1155/DDNS/2006/79717 |
| spellingShingle | S. Sauerbrei E. C. Haß P. J. Plath The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions Discrete Dynamics in Nature and Society |
| title | The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| title_full | The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| title_fullStr | The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| title_full_unstemmed | The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| title_short | The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| title_sort | apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions |
| url | http://dx.doi.org/10.1155/DDNS/2006/79717 |
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