Dynamics and stationary configurations of heterogeneous foams

• Published in: PloS one Vol. 14; no. 4; p. e0215836
• Main Authors: Wang, Dong, Cherkaev, Andrej, Osting, Braxton
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 29.04.2019; Public Library of Science (PLoS)
• Subjects: Algorithms; Applied mathematics; Bubbles; Computational physics; Computer applications; Computer simulation; Configurations; Control theory; Euclidean space; Fluid dynamics; Foams; Foams (Chemistry); Mathematical models; Mechanical properties; Methods; Models, Theoretical; Numerical Analysis, Computer-Assisted; Numerical experiments; Phase transitions; Steady flow; Structure; Thermodynamics; United States > US
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0215836

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.