We study the dynamics of an ultra-thin reactive liquid film flowing down a heated vertical fiber under the influence of gravity. A key focus is on the impact of the van der Waals attraction, which is proportional to , where denotes the film thickness. Linear stability analysis of the film flow reveals that the van der Waals attractions and the Marangoni effect enhance the instability. Furthermore, instability is reduced by exothermic chemical reactions, while it is strengthened in the case of endothermic chemical reactions. Moreover, the weakly nonlinear stability of the film flow is studied. The results indicate the possibility of both subcritical and supercritical stability in the system. Lastly, direct numerical simulations of the evolution equation are conducted for various flow parameters. These results enhance our understanding of the intricate interplay of chemical reactions, thermal effects, and intermolecular forces influencing the liquid film dynamics in complex systems.

中文翻译：

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模拟沿着加热纤维流动的反应膜


我们研究了在重力影响下沿着加热的垂直纤维流动的超薄反应液膜的动力学。重点关注范德华吸引力的影响，它与 成正比，其中表示薄膜厚度。薄膜流的线性稳定性分析表明，范德华引力和马兰戈尼效应增强了不稳定性。此外，放热化学反应会降低不稳定性，而吸热化学反应则会增强不稳定性。此外，还研究了膜流的弱非线性稳定性。结果表明系统具有亚临界和超临界稳定性的可能性。最后，对各种流动参数的演化方程进行直接数值模拟。这些结果增强了我们对影响复杂系统中液膜动力学的化学反应、热效应和分子间力的复杂相互作用的理解。