The falling film flows over solid surfaces have been exploited extensively, but the modeling of film dry-out and the dry patches' formation poses a considerable challenge. Here, we presented a simple mathematical model that accounts for the evaporation to predict the evolution of dry patches in a falling film. Besides, we also analyzed the effect of flow rate, spray temperature, and tube diameter on the growth of dry patches. The distribution of liquid film thickness is asymmetrical, and the film thickness decreases firstly and then increases after a central angle of 90°. The liquid film covered the tube initially under the action of gravity, then evaporation thinned liquid film and induced small dry patches. With the increasing flow rate, decreasing spray temperature, or decreasing tube diameter, the dry-out time increases, and the dry patche area decreases. It is more effective to suppress dry patches' appearance by controlling both flow rate and spray temperature rather than tube diameter.

降膜在固体表面上的流动已得到广泛利用，但是膜变干和干燥斑块形成的模型提出了相当大的挑战。在这里，我们提出了一个简单的数学模型，该模型说明了蒸发以预测降膜中干斑的演变。此外，我们还分析了流速，喷雾温度和管径对干斑生长的影响。液膜厚度的分布是不对称的，并且在90°的中心角之后，膜厚度先减小然后增大。液膜最初在重力作用下覆盖管子，然后蒸发变薄的液膜并引起小的干斑。随着流速的增加，喷雾温度的降低或管径的减小，干燥时间增加，干斑面积减少。通过控制流速和喷涂温度而不是管子直径，可以更有效地抑制干燥斑块的出现。