液滴的热辐射迁移问题是一个很有现实意义的问题， 在微重力环境下，给处于均匀母液中的液滴一个均匀辐射，那么液滴在表面不均匀的温度作用下会产生不均匀的表面张力，在不均匀的表面张力的作用下会向辐射方向迁移并最终到达稳定状态。这种迁移问题与温度梯度主导的热毛细迁移问题存在一定的相似处，但也存在很多更加复杂的地方。
       在前人的研究中，理论方面只有零 Re 数，零 Ma 数的解析解和变形解，对于非线性项的影响还缺乏深入的研究，这是因为零 Re 数，零 Ma 数的解析解和变形解过于复杂， 在这种情况下直接引入非线性项会使问题变得更加复杂，这也是目前阻碍这方面理论研究的主要原因。数值方面缺乏对 Ma 数对于液滴迁移的影响和稳态后温度场变化的分析， 而这方面的研究关系到液滴迁移的物理机制，以及在这种情况下对于稳态定义的思考，还有更加复杂的大 Ma 数下的液滴迁移问题，从热毛细迁移的经验来看，大 Ma 数下的迁移会与小 Ma 数中等 Ma 数的情况有着较大的差别，具体情况还需要更加深入的研究。
       本文通过对解析解的截断近似来修正小 Re 数下的迁移问题和变形问题。采用界面追踪方法对轴对称液滴在热辐射作用下的热毛细迁移进行了数值模拟研究。在均匀热辐射条件下，液滴的迁移经过非线性增长最终达到稳态迁移，稳态下液滴迁移速度随着 Ma 数的增加而减小。进一步，分析了温度场在液滴迁移达到稳态后的变化情况，发现了温度场在液滴达到稳态后的迁移过程中与时间近似成二次函数关系的趋势， 其中线性增长占主导作用，同时整个温度场随时间变化的函数关系并非是统一的，而是与所观察点于液滴的相对位置有关，距离液滴越近，温度增长越快，距离液滴越远，温度增长越慢。
       微通道中的热辐射迁移问题在生物和化学领域中非常重要，这方面的研究近年来进展迅速，对于辐射对微通道内液滴的作用的研究也有很多实验在探索，比如辐射对液滴的操控，对液滴的阻碍，对液柱的维持等方面，但在数值方面还缺乏进展。本文通过引入变形和相关修正程序模拟了微通道下液滴的迁移与变形，分析了通道宽窄对于液滴迁移和变形的影响，和 Ma 数对迁移和变形的影响，发现通道越窄，液滴迁移越慢，变形越大； Ma 数越大，达到稳态时间越长，变形越小。
 

      Droplet migration problem in thermal radiation is a problem with great realistic significance, in a microgravity environment, a uniform droplet in mother liquor is uniformly radiated, then the droplet under the effect of uneven surface temperature will produce uneven surface tension, and the action of migration to the radiation direction under the uneven surface tension and eventually reach a steady state. This migration problem has some similarities with the thermal capillary migration caused by temperature gradient, but there are also many more complicated places.
       In previous studies, there are only analytical solutions and deformation solutions of zero Re number, zero Ma number in terms of theory, and there is still a lack of in-depth research on the influence of nonlinear terms. This is because the analytical solutions and deformation solutions of zero Re number and zero Ma number are too complicated. In this case, the direct introduction of nonlinear terms will make the problem more complicated. This is also the main reason that hinders the theoretical research in this field. Numerically, there is a lack of analysis on the influence of Ma number on droplet migration and the change of  temperature field after steady state. However, the research in this aspect is related to the physical mechanism of droplet migration, as well as the thought on the definition of steady state in this case. There are also more complex droplet migration problems under large Ma number. The
migration at large Ma number is quite different from that at small Ma number and medium Ma number, and the specific situation needs further study.
       In this paper, the truncated approximation of the analytic solution is used to correct the migration and deformation problems under small Re numbers. The thermal capillary migration of an axisymmetric droplet under thermal radiation was numerically simulated by using the Front-tracking method. Under the condition of uniform thermal radiation, droplet migration reaches steady-state migration through nonlinear growth, and droplet migration velocity decreases with the increase of Ma
number. Further, the paper analyzes the temperature field changing situation in the change of droplet migration after reaching steady state and found that the temperature field is a approximate quadratic function of time after reaching the steady state with the dominating of linear growth, at the same time, the function of the whole temperature field changing with time is not uniform, but is related to the relative positions of observation point and the droplet. The closer to the droplet, the faster the temperature increases; the farther away from the droplet, the slower the temperature increases.
       Microchannel migration problem in thermal radiation is very important in the field of biology and chemistry, the research progress in recent years, the radiation on the functioning of the droplets in microchannel exploring research also has a lot of experiments, such as the radiation on the manipulation of the droplet, the block of the droplet, the liquid column maintenance, etc., but also the lack of progress in terms of
value. This paper simulates the migration and deformation of the droplet under microchannel by introducing deformation and related revision programs, channel width influence of the droplet migration and deformation are analyzed, and Ma number influence on migration and deformation, found that the narrower the channel, the slower the droplet migration, the greater the deformation; the greater Ma number, the longer time to reach steady state, the smaller deformation.