Shemilt James D, Horsley Alexander, Jensen Oliver E, Thompson Alice B, Whitfield Carl A
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
Division of Immunology, Immunity to Infection and Respiratory Medicine, University of Manchester, Oxford Road M13 9PL, UK.
J Fluid Mech. 2023 Sep 25;971:A24. doi: 10.1017/jfm.2023.588.
To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh-Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation [Shemilt et al., ., 2022, vol. 944, A22] is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.
为了评估肺气道中表面活性剂的存在如何改变导致堵塞形成和气道闭合的黏液流动，我们研究了不溶性表面活性剂对涂覆在圆柱形管内部的黏塑性液体不稳定性的影响。利用薄膜和长波近似推导了包含屈服应力效应、毛细力和马兰戈尼力的层厚度演化方程。通过对薄膜系统进行数值模拟和渐近分析，我们量化了表面活性剂的存在如何减缓瑞利 - 普拉托不稳定性的增长、增加引发不稳定性所需的初始扰动大小并降低层的最终峰值高度。当表面活性剂强度较大时，薄膜动力学与无表面活性剂层的动力学一致，但时间减慢了四倍，且毛细宾汉数（一个与屈服应力成正比的参数）恰好翻倍。通过数值求解长波方程，我们量化了增加表面活性剂强度如何增加堵塞形成时的临界层厚度并延迟堵塞。结果表明，引入表面活性剂会放大先前确定的屈服应力在抑制堵塞形成方面的作用[Shemilt等人，……，2022年，第944卷，A22]。我们讨论了这些结果对于理解表面活性剂缺乏和阻塞性肺病中黏液屈服应力增加的影响的意义。
