扩散区液滴非等温凝结非定常问题的自相似解
Self-similar solution of a nonsteady problem of nonisothermal vapour condensation on a droplet growing in diffusion regime
摘要：
本文提出了一个数学上精确的自相似解的联合非定常问题的蒸汽扩散到一个液滴增长的蒸汽-气体介质和移除的热量释放的液滴进入蒸汽-气体介质在蒸汽冷凝。得到了液滴温度的方程;只有在该温度下才存在自相似解。该方程要求液滴温度恒定，甚至在整个液滴生长期间明确定义它。在强烈显示热效应的情况下，当液滴生长速率显著降低时，液滴温度的方程被解析地求解。它示出，所获得的温度完全一致的一个，同时解决其扩散制度的增长在液滴。在所获得的温度的液滴的相关的非稳态蒸汽浓度和温度分布的蒸汽-气体介质周围的液滴表示在初始（之前的液滴的成核）参数的蒸汽-气体介质。使用相同的参数来制定液滴在扩散状态下生长所依据的定律，并且还定义在液滴成核之后直到液滴生长的扩散状态稳定所经过的时间，此时液滴的平方半径变得与时间成比例。为了完整起见，研究了热效应弱显示的情况。
英文摘要：
This paper presents a mathematically exact self-similar solution to the joint nonsteady problems of vapour diffusion towards a droplet growing in a vapour-gas medium and of removal of heat released by a droplet into a vapour-gas medium during vapour condensation. An equation for the temperature of the droplet is obtained; and it is only at that temperature that the self-similar solution exists. This equation requires the constancy of the droplet temperature and even defines it unambiguously throughout the whole period of the droplet growth. In the case of strong display of heat effects, when the droplet growth rate decreases significantly, the equation for the temperature of the droplet is solved analytically. It is shown that the obtained temperature fully coincides with the one that settles in the droplet simultaneously with the settlement of its diffusion regime of growth. At the obtained temperature of the droplet the interrelated nonsteady vapour concentration and temperature profiles of the vapour-gas medium around the droplet are expressed in terms of initial (prior to the nucleation of the droplet) parameters of the vapour-gas medium. The same parameters are used to formulate the law in accordance with which the droplet is growing in diffusion regime, and also to define the time that passes after the nucleation of the droplet till the settlement of diffusion regime of droplet growth, when the squared radius of the droplet becomes proportionate to time. For the sake of completeness the case of weak display of heat effects is been studied.
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