Direct 2D simulation of small gas bubble clusters: From the expansion step to the equilibrium state

International Journal for Numerical Methods in Fluids

Volumn 54, Issue 1, 2007, Pages 73-101

  Bruchon, J ^a   Fortin, A ^a   Bousmina, M ^a   Benmoussa, K ^a  

^a UNIVERSITÉ LAVAL   (Canada)

Author keywords

Gas bubble cluster expansion; Laplace's rule; Level set method; Liquid gas coupling; Mesh adaptation method; Plateau's rule

Indexed keywords

FLOW INTERACTIONS; FLOW VELOCITY; MESH GENERATION; NEWTONIAN LIQUIDS; PHASE EQUILIBRIA; TWO DIMENSIONAL;

GAS BUBBLE CLUSTER EXPANSION; LEVEL SET METHOD; LIQUID-GAS COUPLING; MESH ADAPTATION METHOD;

BUBBLES (IN FLUIDS);

BUBBLES (IN FLUIDS); FLOW INTERACTIONS; FLOW VELOCITY; MESH GENERATION; NEWTONIAN LIQUIDS; PHASE EQUILIBRIA; TWO DIMENSIONAL;

EID: 34247466535     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1394     Document Type: Article

References (21)

1. Almgren FJ, Taylor JE. The geometry of soap films and soap bubbles. Scientific American 1976; 235:82-93.
2. Weaire D, Hutzler S. The Physics of Foams. Oxford: New York, 1999.
3. Weaire D, Cox SJ, Graner F. Uniqueness, stability and Hessian eigenvalues for two-dimensional bubble clusters. European Physical Journal E 2002; 7:123-127.
4. Cox SJ, Vaz MF, Weaire D. Topological changes in a two-dimensional foam cluster. European Physical Journal E 2003; 11:29-35.
5. Vaz MF, Cox SJ, Alonso MD. Minimum energy configurations of small bidisperse bubble clusters. Journal of Physics: Condensed Matter 2004; 16:4165-4175.
6. Graner F. Morphology of Condensed Matter - Physics and Geometry of Spatially Complex Systems. Springer: Berlin, 2002.
7. Brakke K. The surface evolver. Experimental Mathematics 1992; 1(2):141-165.
8. Bruchon J. Etude de la formation d' une structure de mousse par simulation directe de l' expansion de bulles dans une matrice liquide polymère. Ph.D. Thesis, Ecole Nationale Supérieure des Mines de Paris, 2004.
9. Fortin A, Benmoussa K. Numerical simulation of the interaction between fluid drops in multi-phase flows. Journal of Computational Physics 2006, submitted for publication.
10. Fortin A, Benmoussa K. An adaptive remeshing strategy for free-surface fluid flow problems. Part I: The axisymmetric case. Journal of Polymer Engineering 2006; 26(1):21-58.
11. Everitt SL, Harlen OG, Wilson HJ, Read DL. Bubble dynamics in viscoelastic fluids with application to reacting and non-reacting polymer foams. Journal of Non-Newtonian Fluid Mechanics 2003; 114:83-107.
12. Kern N, Weaire D, Martin A, Hutzler S, Cox SJ. Two-dimensional viscous froth model for foam dynamics. Physical Review E 2004; 70.
13. Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. Journal of Computational Physics 2005; 203(2):626-649.
14. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. Journal of Computational Physics 1992; 100:335-383.
15. Béliveau A, Fortin A, Demay Y. A two-dimensional numerical method for the deformation of drops with surface tension. International Journal of Computational Fluid Dynamics 1998; 10:225-240.
16. Sethian JA. Level Sets Methods and Fast Marching Methods. Cambridge Monograph on Applied and Computational Mathematics, vol. 3. 1986.
17. Brooks AN, Hughes TJR. Streamline upwind/Petrov - Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
18. Sussman M, Fatemi E. An efficient interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow. SIAM Journal on Scientific Computing 1999; 20(4):1165-1191.
19. Belhamadia Y, Fortin A, Chamberland A. Three-dimensional anisotropic mesh adaptation for phase change problems. Journal of Computational Physics 2004; 201(2):753-770.
20. Belhamadia Y, Fortin A, Chamberland E. Mesh adaptation for the solution of the Stefan problem. Journal of Computational Physics 2004; 194(1):233-255.
21. Cox SJ, Weaire D, Vaz MF. The transition from two-dimensional to three-dimensional foam structures. European Physical Journal E 2002; 7:311-315.