A theory to describe the morphological transition that occurs in a compressible foam when its volume is increased is constructed. The foam is observed to separate into two bubble populations or 'phases', one consisting of a large number of small bubbles, the 'liquid' phase, the other consisting of a small number of large bubbles, the 'gaseous' phase. First, working along lines similar to the van der Waals theory for a fluid system, approximate forms of the equation of state of the foam are derived and explored. These work well in the weakly compressible range. hut fail to capture the nature of the transition. Taking a clue from the phenomenology, a theory of the 'phase separated' regime is then formulated working with the approximation that the two phases into which the foam separates are each relatively homogeneous. The successful single-phase formulae are applied to each phase, introducing an additional 'order parameter' which gives the ratio of the average size of bubbles in the two phases. Approximate expressions are written for the Helmholtz free energy and the equi libria of the foam derived from these. All results are compared to numerical simulations using Surface Evolver with very satisfying results. Due to the negligible size of t hermal fluctuations, the morphological transition from a uniform to a nonuniform configuration as the system volume is expanded, is not spontaneous but consists of avalanches of reconnections with smooth evolution between them.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
TAM R 951
2000-6026
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112660
Sponsor(s)/Grant Number(s)
NASA Microgravity Fluid Physics Program
Copyright and License Information
Copyright 2000 Board of Trustees of the University of Illinois
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.
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