表面活性剂污染的超疏水通道中的层流减阻
Laminar drag reduction in surfactant-contaminated superhydrophobic channels
AI总结：
本文通过长波理论建立一维模型，系统分析了可溶性表面活性剂对超疏水通道层流减阻的影响，并绘制参数空间图谱以指导优化设计。
摘要：
尽管超疏水表面（SHSs）在减阻应用中展现出前景，但其性能可能因表面活性剂的微量存在而受损，这些表面活性剂会产生马兰戈尼应力从而增加阻力。本文针对三维层流通道流中的可溶性表面活性剂问题进行研究，通道两壁均布置周期性超疏水表面。我们假设扩散足够强，使得跨通道浓度梯度较小。利用一种能够描述快速横向马兰戈尼驱动流动的长波理论，我们推导出一个一维的表面活性剂演化模型，从而能够预测整个参数空间中的减阻效果。该系统表现出多种状态，涉及马兰戈尼效应、体相扩散与界面扩散、平流以及剪切弥散之间的竞争。我们在高维参数空间中划分出渐近区域，推导出每个区域内减阻的近似表达式，并将其与数值模拟进行对比。我们的图谱集为设计含表面活性剂污染的超疏水表面通道提供了全面的解析指南，以在实际应用中最大化减阻效果。
英文摘要：
While superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs on both walls. We assume that diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting a long-wave theory that accounts for a rapid transverse Marangoni-driven flow, we derive a one-dimensional model for surfactant evolution, which allows us to predict the drag reduction across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, advection and shear dispersion. We map out asymptotic regions in the high-dimensional parameter space, deriving approximations of the drag reduction in each region and comparing them to numerical simulations. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.
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