Droplet solidification is governed by classical Stefan problems which have been commonly treated as a single-phase problem by the majority of the studies in the literature. This approach, however, is unable to capture the initial temperature and the start of freezing time correctly. The treatment of two-phase Stefan problem in spherical coordinates is limited. No known exact solution exists, albeit numerical solutions and asymptotics have proven to be useful. We present a singular perturbation solution in the limit of low Stefan number and arbitrary Biot number for the two-phase Stefan problem in a finite spherical domain. An asymptotic solution is developed for a droplet at a non-freezing initial temperature subjected to a convective boundary condition at the surface. The solution is developed for both long-time and short-time scales. The results from asymptotic expansion method are validated with the experimental results in the literature and are further verified by a numerical model of a freezing droplet using enthalpy–porosity method. The sensitivity of the asymptotic solution to the droplet initial temperature, Biot number, and Stefan number has also been studied. The results indicate that the solution from perturbation series and enthalpy–porosity method agrees to within 1%–10% for temperature profile and overall freezing times over a wide range of practical values for initial temperature, Stefan and Biot numbers for the application of spray freezing. Our perturbation series solution is also able to capture the effect of initial temperature on the overall freezing time of the droplet.

液滴凝固受经典的Stefan问题控制，经典的Stefan问题在文献中的大多数研究中通常将其视为单相问题。但是，这种方法无法正确捕获初始温度和冻结时间的开始。球坐标系中两相Stefan问题的处理受到限制。没有已知的精确解，尽管数值解和渐近线已被证明是有用的。对于有限球域中的两相Stefan问题，我们在低Stefan数和任意Biot数的极限中提出奇异摄动解。针对在表面处于对流边界条件的非冻结初始温度下的液滴，开发了一种渐近解。该解决方案针对长期和短期尺度而开发。渐进膨胀法的结果已被文献中的实验结果验证，并通过使用焓-孔隙率法的冻结液滴数值模型进一步验证。还研究了渐近溶液对液滴初始温度，比奥数和斯特凡数的敏感性。结果表明，在一系列初始喷雾温度，Stefan和Biot值的实用值范围内，摄动序列和焓-孔隙率方法的解在温度分布图和总冻结时间上均在1％-10％之内。我们的扰动系列解决方案还能够捕获初始温度对液滴总体冻结时间的影响。