溶质Marangoni效应对降膜流动稳定性的影响

doi:10.11949/0438-1157.20220973

摘要/Abstract

摘要：

降膜流动的稳定性对于提高涂膜质量、保障降膜换热器换热性能和促进药物吸收具有重要作用。基于液膜厚度与活性剂浓度的二维非线性演化方程，研究了含表面活性剂的液膜在倾斜平板上流动的稳定性，提出了包括壁面倾角θ、Marangoni数M、Weber数S和Peclet数Pe在内的临界Reynolds数表达式，分析了溶质Marangoni效应、倾角和扰动波数对线性稳定性的影响，探究了溶质Marangoni效应作用下表面波的时空演化特征。结果表明：初始扰动在溶质Marangoni效应影响下分离出快波与慢波，慢波在演化后期发展为多峰波状结构的表面波。增强溶质Marangoni效应可提高临界Reynolds数，扩大液膜流动稳定区并抑制失稳区的扰动增长，削弱表面波的色散效应。提高S和降低Pe均可抑制慢波的演化，而对快波演化基本无影响。

关键词: 表面活性剂, 稳定性, 流体动力学, 数值模拟

Abstract:

The stability of falling film flows is one of the significant factors in improving coating quality, guaranteeing the heat transfer performance of falling film heat exchangers and promoting drug absorption. Based on the two-dimensional nonlinear evolution equation of liquid film thickness and surfactant concentration, the stability of a falling film flow with an insoluble surfactant on an inclined plane is investigated. The critical Reynolds number is presented, including inclination angle θ, Marangoni number M, Weber number S and Peclet number Pe. The impact of solutal Marangoni effect, inclination angle and perturbation wave number on the linear stability of film flow is examined. The spatial and temporal perturbation characteristics of surface waves are inspected. The results show that the initial small perturbation is separated into fast waves and slow waves under the solutal Marangoni effect and the slow wave develops into a surface wave with multi-peak wave structure in the later stage of evolution. Enhancing solutal Manangoni effect is effectively to raise the critical Reynolds number, which expands the stability region, decreases the perturbation growth of the instability region and reduces the dispersion of the surface waves. Both increasing S and decreasing Pe can suppress the evolution of slow waves, but have little effect on the evolution of fast waves.

Key words: surfactant, stability, hydrodynamics, numerical simulation

中图分类号:

O 363.2

刘成治, 李春曦, 周静宜, 叶学民. 溶质Marangoni效应对降膜流动稳定性的影响[J]. 化工学报, 2022, 73(12): 5405-5413.

Chengzhi LIU, Chunxi LI, Jingyi ZHOU, Xuemin YE. Influence of solutal Marangoni effect on the stability of falling film flows[J]. CIESC Journal, 2022, 73(12): 5405-5413.

图/表 10

图1 含不溶性活性剂薄液膜沿斜面下降流动示意图

Fig.1 Schematic diagram of a liquid film flow over an inclined plane in the presence of an insoluble surfactant

图2 最大扰动增长率ωr,m随M和θ 的变化（“”表示临界状态）

Fig.2 Variation in the maximum perturbation growth rate ωr,m with M and θ (“” indicates a critical state)

图3 最危险波数km随M和θ 的变化（“”表示临界状态）

Fig.3 Variation in the most dangerous wave number km with M and θ (“” indicates a critical state)

图4 扰动增长率ωr+和相速度ci 随M的变化

Fig.4 Variation in perturbation growth rate ωr+ and phase speed ci with M

图5 不同参数下的中性稳定曲线（“”表示临界状态）

Fig.5 Neutral stability under different parameters (“” indicates a critical state)

图6 本文结果与文献[20]结果的对比（“”表示临界状态）

Fig.6 Comparison of the results of this paper with that of Ref.[20](“” indicates a critical state)

图7 溶质Marangoni效应对表面波演化的影响（实线箭头表示慢波，虚线箭头表示快波）

Fig.7 Influence of solutal Marangoni effect on surface waves evolution(solid arrow represents slow waves, and dashed arrow represents fast waves)

图8 溶质Marangoni效应对活性剂浓度分布的影响

Fig.8 Influence of solutal Marangoni effect on the distribution of surfactant concentration

图9 Peclet数对表面波演化的影响（实线箭头表示慢波，虚线箭头表示快波）

Fig.9 Influence of Peclet number on surface waves evolution (solid arrow represents slow waves, and dashed arrow represents fast waves)

图10 Weber数对表面波演化的影响（实线箭头表示慢波，虚线箭头表示快波）

Fig.10 Influence of Weber number on surface waves evolution (solid arrow represents slow waves, and dashed arrow represents fast waves)

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