Abstract In this paper, effects of non-uniform temperature in the ice nucleus on heterogeneous ice nucleation are investigated via two approaches: changes in Gibbs free energy function and availability function. Analytical expressions for non-uniform temperature distribution inside the ice nucleus and heat transfer from the nucleus to the supercooled wall are obtained in terms of the contact angle and supercooled wall temperature based on the consideration that thermal conductivity resistance of the nucleus, interfacial resistance and thermal resistance due to curvature of ice/water interface are in series. With non-uniform temperature in the nucleus taken into consideration, it is found that the critical radius of the ice nucleation obtained based on availability analysis is slightly larger than those obtained based on Gibbs free energy analysis. Both heterogeneous critical radius and nucleation energy barrier are found to be increasing with surface contact angle. On an ice-phobic surface at small supercooling degrees, the critical radius and the nucleation energy barrier obtained with or without heat transfer taken into consideration differ greatly with the increase of the contact angle. However, at large supercooling degrees and small contact angles, differences in the critical radius and nucleation energy barrier by availability analysis are negligible with or without heat transfer effects. Thus, heterogeneous nucleation behaviors on ice-philic surfaces can be estimated based on the assumption of uniform temperature in the ice nucleus when degree of wall supercooling is large.

中文翻译：

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冰核温度不均对异质冰核形成的影响

摘要 本文通过吉布斯自由能函数和可用性函数的变化两种方法研究了冰核内温度不均匀对异质冰核形成的影响。基于接触角和过冷壁温度，考虑了冰核内部的热导阻、界面电阻和热量，得到了冰核内部温度分布不均匀和从核向过冷壁传热的解析表达式。由冰/水界面弯曲引起的电阻是串联的。考虑到核内温度不均匀，发现基于可用性分析获得的冰核形成临界半径略大于基于吉布斯自由能分析获得的临界半径。发现异质临界半径和成核能垒都随着表面接触角的增加而增加。在小过冷度的疏冰表面上，随着接触角的增加，在考虑传热或不考虑传热的情况下获得的临界半径和成核能垒有很大差异。然而，在大过冷度和小接触角下，通过可用性分析，临界半径和成核能垒的差异可以忽略不计，有或没有传热效应。因此，当壁面过冷度大时，可以基于冰核温度均匀的假设来估计亲冰表面上的异质成核行为。