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Dynamics and stationary configurations of heterogeneous foams
We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an efficient computational method for this problem. In addition...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6488059/ https://www.ncbi.nlm.nih.gov/pubmed/31034477 http://dx.doi.org/10.1371/journal.pone.0215836 |
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author | Wang, Dong Cherkaev, Andrej Osting, Braxton |
author_facet | Wang, Dong Cherkaev, Andrej Osting, Braxton |
author_sort | Wang, Dong |
collection | PubMed |
description | We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an efficient computational method for this problem. In addition to simulating time dynamics, we also report on stationary states of this flow for ≤ 21 bubbles in two dimensions and ≤ 17 bubbles in three dimensions. For small numbers of bubbles, we recover known analytical results, which we briefly discuss. In two dimensions, we also recover previous numerical results, computed using other methods. Particular attention is given to locally optimal foam configurations and heterogeneous foams, where the volumes of the bubbles are not equal. Configurational transitions are reported for the quasi-stationary flow where the volume of one of the bubbles is varied and, for each volume, the stationary state is computed. The results from these numerical experiments are described and accompanied by many figures and videos. |
format | Online Article Text |
id | pubmed-6488059 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-64880592019-05-17 Dynamics and stationary configurations of heterogeneous foams Wang, Dong Cherkaev, Andrej Osting, Braxton PLoS One Research Article We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an efficient computational method for this problem. In addition to simulating time dynamics, we also report on stationary states of this flow for ≤ 21 bubbles in two dimensions and ≤ 17 bubbles in three dimensions. For small numbers of bubbles, we recover known analytical results, which we briefly discuss. In two dimensions, we also recover previous numerical results, computed using other methods. Particular attention is given to locally optimal foam configurations and heterogeneous foams, where the volumes of the bubbles are not equal. Configurational transitions are reported for the quasi-stationary flow where the volume of one of the bubbles is varied and, for each volume, the stationary state is computed. The results from these numerical experiments are described and accompanied by many figures and videos. Public Library of Science 2019-04-29 /pmc/articles/PMC6488059/ /pubmed/31034477 http://dx.doi.org/10.1371/journal.pone.0215836 Text en © 2019 Wang et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Wang, Dong Cherkaev, Andrej Osting, Braxton Dynamics and stationary configurations of heterogeneous foams |
title | Dynamics and stationary configurations of heterogeneous foams |
title_full | Dynamics and stationary configurations of heterogeneous foams |
title_fullStr | Dynamics and stationary configurations of heterogeneous foams |
title_full_unstemmed | Dynamics and stationary configurations of heterogeneous foams |
title_short | Dynamics and stationary configurations of heterogeneous foams |
title_sort | dynamics and stationary configurations of heterogeneous foams |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6488059/ https://www.ncbi.nlm.nih.gov/pubmed/31034477 http://dx.doi.org/10.1371/journal.pone.0215836 |
work_keys_str_mv | AT wangdong dynamicsandstationaryconfigurationsofheterogeneousfoams AT cherkaevandrej dynamicsandstationaryconfigurationsofheterogeneousfoams AT ostingbraxton dynamicsandstationaryconfigurationsofheterogeneousfoams |