Thin film flows appear in many industrial applications such as falling film reactors, wetted-wall absorbers, condensers and vertical evaporators, and transport of oil and gas mixtures in pipelines. Experimental observations show that the presence of waves on the film surface enhances the heat and mass transfer rates substantially across the liquid-gas and liquid-solid interfaces in these processes. A new simplified model is developed for describing the characteristics of free falling wavy liquid films. The model consists of a set of three partial differential equations (in x and t) for the local film thickness h, volumetric flow rate q, and wall shear stress τ. It is shown that the new model is a substantial improvement over all existing simplified models of wavy films such as the Long Wave equation, the Nakaya model (extended third-order Long Wave equation), the Shkadov model, and the Kapitza boundary layer model. These prior models predict non-physical negative wall shear stress when the wave amplitude is large and cannot explain the experimentally observed relationship between the wave amplitude and the Reynolds (Re) and Kapitza (Ka) numbers. In contrast, the present model yields physically meaningful results and quantitative predictions of large amplitude waves. The consistency and accuracy of the model is verified by comparing the linear stability results with the Orr-Sommerfeld studies of the two-dimensional Navier-Stokes equations. Local bifurcation theory is used to analyze the model for small Re, and analytical relations are obtained for predicting the velocity (Ce) and the maximum amplitude of solitary waves.; Experimental studies of free falling viscous films were conducted using water-glycerin solutions and the conductance probe technique. Comparison of the experimental data on wave amplitude and velocity with analytical correlations shows excellent agreement. Numerical simulations of the wave profiles generated from the simplified model also match closely with the experimentally observed wave profiles. Experimental results for two-phase gas-liquid flows under reduced gravity conditions are also presented.
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机译：薄膜流出现在许多工业应用中，例如降膜反应器，湿壁吸收器，冷凝器和垂直蒸发器以及管道中油气混合物的运输。实验观察表明，在这些过程中，膜表面上存在波，从而大大提高了液-气和液-固界面上的传热和传质速率。开发了一种新的简化模型来描述自由下落的波浪状液体薄膜的特性。该模型由一组三个局部微分方程（ x 和 t ）组成，用于局部膜厚度 h ，体积流量 q 和壁面剪应力τ。结果表明，新模型是对所有现有的波浪膜简化模型（例如长波方程，Nakaya模型（扩展的三阶长波方程），Shkadov模型和Kapitza边界层模型）的实质性改进。这些现有模型预测了当波幅较大时非物理性的负壁剪应力，并且无法解释波幅与雷诺数（Re）和Kapitza（Ka）数之间的实验观察关系。相反，本模型产生了物理上有意义的结果以及大振幅波的定量预测。通过将线性稳定性结果与二维Navier-Stokes方程的Orr-Sommerfeld研究进行比较，验证了模型的一致性和准确性。利用局部分叉理论对小Re模型进行了分析，并获得了解析关系来预测速度（ Ce ）和孤立波的最大振幅。使用水-甘油溶液和电导探针技术进行了自由下落的粘性薄膜的实验研究。将波幅和速度的实验数据与解析相关性进行比较，显示出极好的一致性。从简化模型生成的波廓的数值模拟也与实验观察到的波廓紧密匹配。还提出了在重力降低的条件下两相气液流的实验结果。
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