The Topology of a Bubble in dry Foam

The topological structure of such a bubble requires two necessary conditions. Firstly, Euler’s relation between the numbers of its (surface) areas, its (Plateau) borders, and its nodal points (vertices) must be fulfilled. Secondly, always three borders on its surface meet at each nodal point. These...

Author: Fischer, Fred
Division/Institute:FB 11: Physik
Document types:Reports
Media types:Text
Publication date:2007
Date of publication on miami:05.09.2007
Modification date:13.02.2015
Edition statement:[Electronic ed.]
Subjects:trockener Schaum; Computerprogramme; Bruttoformeln; Graphen von Blasen
DDC Subject:530: Physik
License:InC 1.0
Language:English
Format:PDF document
URN:urn:nbn:de:hbz:6-77579645423
Permalink:http://nbn-resolving.de/urn:nbn:de:hbz:6-77579645423
Digital documents:topology_of_bubbles.pdf

The topological structure of such a bubble requires two necessary conditions. Firstly, Euler’s relation between the numbers of its (surface) areas, its (Plateau) borders, and its nodal points (vertices) must be fulfilled. Secondly, always three borders on its surface meet at each nodal point. These conditions allow certain sets of areas with different numbers of borders. However, only when those areas can form a correct net of borders connected by nodal points at a sphere then a bubble topology for such a set has been realized. With forced T1 and inverse T2 processes and by the use of computer programs real topologies have been obtained for bubbles with area numbers up to 16. Their construction out of the computer data is illustrated. A special classification scheme among bubbles of equal area number as well as the appearance of topological isomers are discussed.