Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-dkqnh Total loading time: 0.13 Render date: 2021-10-20T00:43:51.786Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes

Published online by Cambridge University Press:  20 August 2015

Yongsam Kim*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Yunchang Seol*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Ming-Chih Lai*
Affiliation:
Department of Applied Mathematics, Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
Charles S. Peskin*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 USA
*
Get access

Abstract

We extend the immersed boundary (IB) method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble network. In the article [Y. Kim, M.-C. Lai, and C. S. Peskin, J. Comput. Phys. 229:5194-5207,2010], we implemented an IB method for the foam problem in the two-dimensional case, and tested it by verifying the von Neumann relation which governs the coarsening of a two-dimensional dry foam. However, the method implemented in that article had an important limitation; we did not allow for the resolution of quadruple or higher order junctions into triple junctions. A total shrinkage of a bubble with more than four edges generates a quadruple or higher order junction. In reality, a higher order junction is unstable and resolves itself into triple junctions. We here extend the methodology previously introduced by allowing topological changes, and we illustrate the significance of such topological changes by comparing the behaviors of foams in which topological changes are allowed to those in which they are not.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Glazier, J.A., Gross, S.P., and Stavans, J., Dynamics of two-dimensional soap froths. Phys. Rev. A, 36(1), 1987.Google Scholar
[2]Hilgenfeldt, S., Kraynik, A.M., Koehler, S.A., and Stone, H.A., An accurate von Neumann’s law for three-dimensional foams, Phys. Rev. Lett. 86(12):26852688, 2001.CrossRefGoogle ScholarPubMed
[3]Kermode, J.P. and Weaire, D., 2D-Froth: a program for the investigation of 2-dimensional froths. Computer Physics Communications 60, 75109, 1990.CrossRefGoogle Scholar
[4]Kim, Y. and Peskin, C.S.. 2-D parachute simulation by the Immersed Boundary Method. SIAM J.Sci.Comput. 28(6), 2006.Google Scholar
[5]Kim, Y., Lai, M.-C., and Peskin, C.S., Numerical simulations of two-dimensional foam by the immersed boundary method. J. Comput. Phys. 229:51945207, 2010.CrossRefGoogle Scholar
[6]Layton, A.T., Modeling water transport across elastic boundaries using an explicit jump method. SIAM J. Sci. Comput. 28(6):21892207,2006.CrossRefGoogle Scholar
[7]MacPherson, R.D. and Srolovitz, D.J., The von Neumann relation generalized to coarsening of three-dimensional microstructures, Nature, 446(26):10531055, 2007.CrossRefGoogle Scholar
[8]Mullins, W.W., in Metal Surfaces: Structure, Energetics, and Kinetics. (eds. Robertson, W.D. and Gjostein, N.A.) 1766(American Society for Metals, Metals Park, Ohio, 1963).Google Scholar
[9]J., von Neumann in Metal Interfaces (ed. Herring, C.) 108110(American Society for Metals, Cleveland, 1951).Google Scholar
[10]Peskin, C.S., The immersed boundary method. Acta Numerica, 11:479517, 2002.CrossRefGoogle Scholar
[11]Stokie, J.M., Modelling and simulation of porous immersed boundaries. Computers Structures 87(11-12): 701709, 2009.CrossRefGoogle Scholar
[12]Weaire, D. and Hutzler, S., The Physics of Foams. Oxford University Press, 1999.Google Scholar
[13]Weaire, D. and Kermode, J.P., Computer simulation of a two-dimensional soap froth I. Method and motivation. Phil. Mag. B. 48(3), 245259, 1983.CrossRefGoogle Scholar
[14]Weaire, D. and Kermode, J.P., Computer simulation of a two-dimensional soap froth II. Analysis of results. Phil. Mag. B. 50(3), 379395, 1984.CrossRefGoogle Scholar
10
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *