Single phase limit for melting nanoparticles
Single phase limit for melting nanoparticles
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DOI：
10.1016/j.apm.2008.07.009
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发表时间：
2009-05
影响因子：
5
通讯作者：
Bisheng Wu;S. McCue;P. Tillman;J. M. Hill
中科院分区：
文献类型：
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作者：
Bisheng Wu;S. McCue;P. Tillman;J. M. Hill
通过吉布斯-汤姆逊条件纳入表面张力的影响，将球形或圆柱形纳米颗粒的熔化建模为 Stefan 问题。从固相慢传导奇异极限下的一般两相公式导出一相移动边界问题，并在小时间和大Stefan数的极限下对所得方程进行了解析研究。通过应用积分公式和迭代方案，可以找到温度分布和固熔界面位置的进一步解析近似。所有这些分析结果都与使用前固定方法获得的数值解进行了比较，并且表明在各种情况下都提供了良好的近似值。表面张力的加入可以在颗粒熔化时降低熔化温度，从而加速熔化过程。与没有表面张力的经典单相 Stefan 问题不同，固体-熔体界面在颗粒的某些临界半径（对于金属而言为几纳米量级）处表现出爆炸，这种现象已通过实验观察到。该模型的一个有趣特征是预测在爆炸发生之前表面张力会导致固体颗粒过热。
The melting of a spherical or cylindrical nanoparticle is modelled as a Stefan problem by including the effects of surface tension through the Gibbs–Thomson condition. A one-phase moving boundary problem is derived from the general two-phase formulation in the singular limit of slow conduction in the solid phase, and the resulting equations are studied analytically in the limit of small time and large Stefan number. Further analytical approximations for the temperature distribution and the position of the solid–melt interface are found by applying an integral formulation together with an iterative scheme. All these analytical results are compared with numerical solutions obtained using a front-fixing method, and are shown to provide good approximations in various regimes. The inclusion of surface tension, which acts to decrease the melting temperature as the particle melts, is shown to accelerate the melting process. Unlike the classical one-phase Stefan problem without surface tension, the solid–melt interface exhibits blow-up at some critical radius of the particle (which for metals is of the order of a few nanometres), a phenomenon that has been observed experimentally. An interesting feature of the model is the prediction that surface tension drives superheating in the solid particle before blow-up occurs.