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A phase field model for snow crystal growth in three dimensions (三维雪晶生长的相场模型)
发布时间:2017-05-09

A phase field model for snow crystal growth in three dimensions (三维雪晶生长的相场模型)
Gilles Demange, Helena Zapolsky, Renaud Patte & Marc Brunel
npj Computational Materials 3, Article number: 15 (2017)
doi:10.1038/s41524-017-0015-1
Published online:10 April 2017
Abstract| Full Text | PDF OPEN
摘要:
雪花的生长过程为自然界的中自发样式形成提供了一个令人着迷的实例。对这一现象的初步了解,已为各个活跃的科学领域所观察到的非平衡动力学现象,提出了重要见解,涉及从物理系统和化学系统中的图式形成,到生物学中的自组装问题。然而,目前的计算模型极少能成功地再现3D雪花的多样性,也没有建立模型参数与热力学定量之间的函数关系。本研究报告了一种改进的相场模型,能通过各向异性水分子附着、冷凝、表面扩散和各向异性的强表面张力,来描述冰-气相变的微妙,模拟雪花的各向异性、刻面生长和树突状生长。研究证实,该模型可从Nakaya固液相图中再现出最具挑战性的雪花3D形态的生长动力学,发现所再现的雪晶生长动力学与选择理论一致,与以前的实验观察一致。 

Abstract: Snowflake growth provides a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes.We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram.We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations. 

Editorial Summary

Spontaneous patterns: Simulating snowflakes with a softer touch (自发模式:模拟有柔性触感的雪花)

采用通用界面模型计算复杂3D雪花生长为其他树状材料的模拟提供理论依据。当雪晶种子穿过大气不断捕获水分子时,雪晶体通过初始种子向外扩展而使水分子凝固。虽然大多数模拟方法都将这种不断增长的界面视为一个敏感的界限,但法国鲁昂大学的Gilles Demange和同事们报告说,可变换的模拟方法获得非常实用的结果。他们用相场模型技术,将雪花表面表示为冰和水蒸气混合的可移动薄层,用新的表面张力函数来表示各向异性结晶。该方法包括了模拟3D晶面的特殊算法,能使模型准确重现出基本的雪花形态,并可对各种气象条件下云中的冰水含量进行预测。 

A model that reproduces complex 3D snowflake growth using versatile interface descriptors may benefit other dendritic materials. Snow crystals solidify by expanding outward from an initial seed, capturing water molecules as they travel through the atmosphere.While most simulation methods treat this growing interface as a sharp boundary, Gilles Demange and colleagues from the University of Rouen in France report that a less rigid approach yields highly realistic results.Their technique uses a phase field model to represents the snowflake’s surface as a thin moveable layer where ice and vapour mix, and a new surface tension function to explain the anisotropic crystallisation. Including a special algorithm to simulate 3D crystal faceting enabled the model to duplicate essential snowflake morphologies and potentially predict ice water content in clouds under various weather conditions. 

 
 
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