A theory for the slip and drag of superhydrophobic surfaces with surfactant
A theory for the slip and drag of superhydrophobic surfaces with surfactant
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DOI：
10.1017/jfm.2019.857
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发表时间：
2020-01-25
影响因子：
3.7
通讯作者：
Luzzatto-Fegiz, Paolo
中科院分区：
文献类型：
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作者：
Landel, Julien R.;Peaudecerf, Francois J.;Luzzatto-Fegiz, Paolo
超疏水表面（SHS）具有减少固体边界阻力的潜力。然而，多项独立研究最近表明，环境中自然存在的少量表面活性剂可以诱发马兰戈尼力，从而增加阻力，至少在层流状态下是如此。为了获得准确的阻力预测，必须求解质量、动量、本体表面活性剂和界面表面活性剂守恒方程。这需要昂贵的模拟，从而阻碍了表面活性剂在 SHS 研究中被广泛考虑。为了解决这个问题，我们提出了一种在具有可溶性表面活性剂的周期性 SHS 通道中稳定、压力驱动、层流、二维流动的理论。在小浓度的假设下，我们线性化流动和表面活性剂之间的耦合，找到局部滑移长度的缩放预测。为了获得减阻和界面剪切，我们通过假设整体斯托克斯流和均匀界面剪切找到了速度场的级数解。我们发现滑移和阻力如何取决于九个无量纲组，这些组共同表征了 SHS 附近的表面活性剂传输、气体分数和归一化界面长度。我们的模型与每个无量纲组中跨数量级的数值模拟一致。模拟还提供了缩放理论中的常数。相对于不含表面活性剂的模型，我们的模型显着改进了预测，否则可能会高估滑移并低估阻力几个数量级。我们的滑移长度模型可以提供其他模拟中的边界条件，从而无需解决整个问题即可考虑表面活性剂的影响。
Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearize the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.