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標題: 從力的觀點模擬肥皂泡之結構
Simulation of bubble structure – from the viewpoint of force
作者: 劉芝辰
Liu, Chih-Chen
關鍵字: 泡沫;bubble cluster;類凡得瓦力;數值模擬;van der Waals-like force;numerical simulation
出版社: 生物物理學研究所
引用: [1] J.-M. Chomaz. The dynamics of a viscous soap film with soluble surfactant. Journal of Fluid Mechanics 442 (2001) 387 [2] J. K. Ferri and K. J. Stebe. Which surfactants reduce surface tension faster? A scaling argument for diffusion-controlled adsorption. Advances in Colloid and Interface Science 85 (2000) 61 [3] D. Stamenović. A model of foam elasticity based upon the laws of Plateau. Journal of Colloid and Interface Science 145 (1991) 255 [4] J. E. Taylor. The structure of singularities in soap-bubble-like and soap-film-like minimal surface. Annals of Mathematics 103 (1976) 489 [5] M. F. Vaz, S. J. Cox and M. D. Alonso. Minimum energy configurations of small bidisperse bubble clusters. Journal of Physics: Condensed Matter 16 (2004) 4165 [6] Roman Ďurikovič. Computer animation: animation of soap bubble dynamics, cluster formation and collision. Journal of the Applied Mathematics, Statistics and Informatics 1 (2005) 21
肥皂泡膜是常見的膜的結構,雖然簡單但卻符合一定的規則,前人從實驗觀察中得出這些規則,並提出一些理論,解釋了多顆泡泡接觸在一起的結構。我們以泡泡粒子作為膜分子的等效粒子,用來描述泡泡的幾何結構,這些粒子會受到類似van der Waals'' force的力以及壓力的作用。我們電腦計算泡泡粒子的受力、速度以及位移,模擬泡泡的動態過程,得到平衡時的形狀及多顆泡泡聚集時的結構,並將所得到的幾何結構和已知實驗結果比較,同時以前人所提出的理論檢視我們的模型。

A soap bubble is a thin membrane of soapy water enclosing air that forms a spherical surface. The structure of a bubble cluster (called foam) is stable due to a balance between surface tension and air pressure. Here we consider a bubble consists of a finite number of effective particles and simulate its formation under an effective van der Waals-like force between particles and the air pressure within the bubble. We test our model by simulating the coalescing process of two bubbles. We also check the structure of foam generated by our model with various existing related theorems. We find our model is qualitatively satisfied and can be used for further study of foam.
其他識別: U0005-0207201216425800
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