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.229:5194-5207,2...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.展开更多
We investigate the statistical behaviors of two-dimensional dry foam using numerical simulations based on the immersed boundary(IB)method.We model the liquid phase of a foam as a thin elastic boundary with surface ten...We investigate the statistical behaviors of two-dimensional dry foam using numerical simulations based on the immersed boundary(IB)method.We model the liquid phase of a foam as a thin elastic boundary with surface tension and the gas phase as a viscous incompressible fluid which can go through the liquid boundary.We present evidence of the existence of a limiting scaling state of the dry foam dynamics in which the asymptotic value ofμ_(2),the second moment of the distribution of the numbers of cell sides,lies in the range of 1.3±0.3.We also numerically ver-ify some well-known formulas derived in the dynamics of two-dimensional dry foam such as von Neumann relation,Lewis law,and Aboav-Weaire law.Our simulation re-sults are comparable to those of soap froth experiments and Potts model simulations.Furthermore,we investigate the statistical behaviors of two-dimensional dry foam in an oscillatory shear flow to show the applicability of our method to more general flow conditions.展开更多
基金supported by National Research Foundation of Korea Grant funded by the Korean Government(2010-0006165)The second author was supported by the Chung-Ang University Research Scholarship Grant in 2010The third author is supported in part by National Science Council of Taiwan under research grant NSC-97-2628-M-009-007-MY3,NSC-98-2115-M-009-014-MY3,and the support of NCTS in Taiwan.
文摘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.
基金supported by a National Research Foundation of Korea grant funded by the Korean government(Grant No.2017R1E1A1A03070636).
文摘We investigate the statistical behaviors of two-dimensional dry foam using numerical simulations based on the immersed boundary(IB)method.We model the liquid phase of a foam as a thin elastic boundary with surface tension and the gas phase as a viscous incompressible fluid which can go through the liquid boundary.We present evidence of the existence of a limiting scaling state of the dry foam dynamics in which the asymptotic value ofμ_(2),the second moment of the distribution of the numbers of cell sides,lies in the range of 1.3±0.3.We also numerically ver-ify some well-known formulas derived in the dynamics of two-dimensional dry foam such as von Neumann relation,Lewis law,and Aboav-Weaire law.Our simulation re-sults are comparable to those of soap froth experiments and Potts model simulations.Furthermore,we investigate the statistical behaviors of two-dimensional dry foam in an oscillatory shear flow to show the applicability of our method to more general flow conditions.
