Influence from polydispersity on the morphology of Voronoi and equilibrium foams

Abstract

Stochastic foam models are generated from Voronoi spatial partitioning, using the centers of equi-sized hard spheres in random periodic distributions as seed points. Models with different levels of polydispersity are generated by varying the packing of the spheres. Subsequent relaxation is then performed with the Surface Evolver software which minimizes the surface area for better resemblance with real foam structures. The polydispersity of the Voronoi precursors is conserved when the models are converted into equilibrium models. The relation between the sphere packing fraction and the resulting degree of volumetric polydispersity is examined and the relations between the polydispersity and a number of associated morphology parameters are then investigated for both the Voronoi and the equilibrium models. Comparisons with data from real foams in the literature indicate that the used method is somewhat limited in terms of spread in cell volume but it provides a very controlled way of varying the foam morphology while keeping it periodic and truly stochastic. The study shows several strikingly consistent relations between the spread in cell volume and other geometric parameters, considering the stochastic nature of the models.

Keywords

Cellular structure stochastic seed points sphere packing Surface Evolver

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References

Kraynik

. Foam structure: From soap froth to solid foams. MRS Bull 2003; 28: 275–278.

Köll

Hallström

. Generation of periodic stochastic foam models for numerical analysis. J Cell Plast 2014; 50: 37–54.

Voronoi

. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. deuxième mémoire. recherches sur les parallélloèdres primitifs. Journal für die reine und angewandte Mathematik 1908; 134: 198–287.

Kraynik

Reinelt

van Swol

. Structure of random monodisperse foam. Phys Rev E 2003; 67: 031403–031403.

Redenbach

. Microstructure models for cellular materials. Comput Mater Sci 2009; 44: 1397–1408.

Brakke

. The surface evolver. Exp Math 1992; 1: 141–165.

Kraynik

. The structure of random foam. Adv Eng Mater 2006; 8: 900–906.

Ribeiro-Ayeh S. Finite element modelling of the mechanics of solid foam materials. PhD thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2005.

Jodrey

Tory

. Computer simulation of close random packing of equal spheres. Phys Rev A 1985; 32: 2347–2351.

10.

Thomson

. On the division of space with minimum partitional area. Acta Math 1887; 11: 121–134.

11.

Schlimper R, Rinker M and Schäuble R. Prediction of material behaviour of closed cell rigid foams via mesoscopic modelling. In: Proceedings of ICCM-17, 2009, Edinburgh, UK.

12.

Montminy

Tannenbaum

Macosko

. The 3d structure of real polymer foams. J Colloid Interface Sci 2004; 280: 202–211.

13.

Vecchio

Redenbach

Schalditz

. Angles in laguerre tesselation models for solid foams. Comput Mater Sci 2014; 83: 171–184.

14.

Matzke

. The three-dimensional shape of bubbles in foam – an analysis of the role of surface forces in three-dimensional cell shape determination. Am J Botany 1946; 33: 58–80.