Laminar drag reduction in surfactant-contaminated superhydrophobic channels
Laminar drag reduction in surfactant-contaminated superhydrophobic channels
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DOI：
10.1017/jfm.2023.264
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发表时间：
2022-09
影响因子：
3.7
通讯作者：
Samuel D. Tomlinson;F. Gibou;P. Luzzatto‐Fegiz;Fernando Temprano-Coleto;O. Jensen;J. Landel
中科院分区：
文献类型：
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作者：
Samuel D. Tomlinson;F. Gibou;P. Luzzatto‐Fegiz;Fernando Temprano-Coleto;O. Jensen;J. Landel
摘要虽然超疏水表面（SHS）显示出减阻应用的前景，但它们的性能可能会受到痕量表面活性剂的影响，表面活性剂会产生Marangoni应力，增加阻力。解决这个问题的可溶性表面活性剂在三维层流通道流，与周期性的SHS长的有限长度的纵向槽位于两个墙壁上。我们假设，体扩散是足够强的跨通道的浓度梯度是小的。利用长波理论和占快速横向和较慢的纵向Marangoni流之间的差异，我们推导出一个一维模型的表面活性剂传输从全三维传输方程。我们的一维模型使我们能够预测整个参数空间的减阻和表面活性剂分布。该系统表现出多个制度，涉及Marangoni效应之间的竞争，体和界面扩散，体和界面平流，剪切分散和表面活性剂之间的交换体和界面。我们映射出的高维参数空间中的渐近区域，并推导出显式的封闭形式的近似减阻，没有任何拟合或经验参数。通过对均匀和非均匀应力分布的速度场和表面活性剂浓度的分析，讨论了表面活性剂减阻效果和负面影响的物理基础。我们的理论预测的阻力减少比较以及从文献数值求解全三维运输问题的结果。我们的地图集提供了一个全面的分析指导，设计表面污染的渠道与SHS，以最大限度地减少阻力的应用。
Abstract Although 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 made of long finite-length longitudinal grooves located on both walls. We assume that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting long-wave theory and accounting for the difference between the rapid transverse and slower longitudinal Marangoni flows, we derive a one-dimensional model for surfactant transport from the full three-dimensional transport equations. Our one-dimensional model allows us to predict the drag reduction and surfactant distribution across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, bulk and interfacial advection, shear dispersion and surfactant exchange between the bulk and the interface. We map out asymptotic regions in the high-dimensional parameter space, and derive explicit closed-form approximations of the drag reduction, without any fitting or empirical parameters. The physics underpinning the drag reduction effect and the negative effect of surfactant is discussed through analysis of the velocity field and surfactant concentrations, which show both uniform and non-uniform stress distributions. Our theoretical predictions of the drag reduction compare well with results from the literature solving numerically the full three-dimensional transport problem. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.