为了解决这个问题，该团队推导了一个层流模型，在SHS光栅上的三维流动作为几何形状和可溶性表面活性剂性质的函数，它们一起包含10个无量纲基团。团队确定光栅长度g是关键的几何参数，并预测实际滑移与无表面活性剂滑移之比随g2的增大而增大。在他们的模型的指导下，该团队进行了协同数值模拟和微流体实验，发现当该团队改变表面活性剂类型和SHS几何形状时，与理论有很好的一致性。
他们的模型还可以基于速度测量，对微流体系统中固有的表面活性剂的先验未知性质进行估计。对于SHSs，研究人员表明表面活性剂的作用可以通过一个参数来预测，该参数表示光栅长度和界面长度尺度之间的比率，超过这个尺度，流动就会调动空气-水界面。这种长度对表面活性剂的化学性质比对其浓度更敏感，因此即使是微量污染物，如果它们具有高度的表面活性，也可能显著增加阻力。这些发现促进了对现实界面流动的基本理解，并提供了切实可行的策略，以最大限度地减少超疏水阻力。
据悉，最近的实验和计算研究表明，微量表面活性剂(在实践中不可避免)会通过在气-液界面诱导马兰戈尼应力，严重影响超疏水表面(SHSs)的减阻效果。然而，目前还不存在真实SHS几何形状的预测模型，这限制了对这些表面活性剂不利影响的理解和缓解。
附：英文原文
Title: A single parameter can predict surfactant impairment of superhydrophobic drag reduction
Author: Temprano-Coleto, Fernando, Smith, Scott M., Peaudecerf, Franois J., Landel, Julien R., Gibou, Frédéric, Luzzatto-Fegiz, Paolo
Issue&Volume: 2023-1-12
Abstract: Recent experimental and computational investigations have shown that trace amounts of surfactants, unavoidable in practice, can critically impair the drag reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses at the air–liquid interface. However, predictive models for realistic SHS geometries do not yet exist, which has limited the understanding and mitigation of these adverse surfactant effects. To address this issue, we derive a model for laminar, three-dimensional flow over SHS gratings as a function of geometry and soluble surfactant properties, which together encompass 10 dimensionless groups. We establish that the grating length g is the key geometric parameter and predict that the ratio between actual and surfactant-free slip increases with g2. Guided by our model, we perform synergistic numerical simulations and microfluidic experiments, finding good agreement with the theory as we vary surfactant type and SHS geometry. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. For SHSs, we show that surfactant effects can be predicted by a single parameter, representing the ratio between the grating length and the interface length scale beyond which the flow mobilizes the air–water interface. This mobilization length is more sensitive to the surfactant chemistry than to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface active. These findings advance the fundamental understanding of realistic interfacial flows and provide practical strategies to maximize superhydrophobic drag reduction.
DOI: 10.1073/pnas.2211092120
Source: https://www.pnas.org/doi/10.1073/pnas.2211092120