Consider the gravity-driven flow of a thin liquid film down a vertical fibre. A model of two coupled evolution equations for the local film thickness h and the local flow rate q is formulated within the framework of the long-wave and boundary-layer approximations. The model accounts for inertia and streamwise viscous diffusion. Evolution equations obtained by previous authors are recovered in the appropriate limit. Comparisons to experimental results show good agreement in both linear and nonlinear regimes. Viscous diffusion effects are found to have a stabilizing dispersive effect on the linear waves. Time-dependent computations of the spatial evolution of the film reveal a strong influence of streamwise viscous diffusion on the dynamics of the flow and the wave selection process.

考虑一下液体薄膜在垂直纤维下的重力驱动流动。在长波和边界层近似的框架内，建立了两个有关局部膜厚h和局部流速q的耦合演化方程模型。该模型考虑了惯性和沿流的粘性扩散。由以前的作者获得的演化方程式将在适当的范围内恢复。与实验结果的比较表明，在线性和非线性范围内都有很好的一致性。发现粘性扩散效应对线性波具有稳定的扩散效应。膜的空间演化的时变计算揭示了流向粘性扩散对流动动力学和波选择过程的强烈影响。