Session M6: Boundary Layer: Superhydrophobic Surfaces II

Marangoni stresses due to surfactant traces can severely limit the drag reduction of superhydrophobic surfaces

Real liquids include traces of surfactants, which can be redistributed unevenly by a nonuniform flow near a gas-liquid interface. The nonuniformities in surface tension will yield Marangoni stresses opposing the motion. Since this effect arises from dynamically-established surfactant gradients (rather than from background levels) it can be almost inevitable. A canonical example is given by the surprisingly slow rise of small bubbles in water. Here we examine the hypothesis that Marangoni stresses can impair drag reduction with superhydrophobic surfaces (SHS). To prescribe surfactant concentration with precision higher than can be achieved experimentally, we perform simulations inclusive of surfactant. These reveal that Marangoni stresses can be significant for concentrations below typical environmental values. We also perform microchannel experiments, which confirm our numerical predictions; in addition, we introduce an unsteady test of surfactant effects. When we remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients. This demonstrates the significance of surfactants in deteriorating drag reduction, and thus the importance of including surfactant stresses in SHS models (Peaudecerf et al., PNAS 2017).   

Low-order models for the drag reduction of surfactant-contaminated superhydrophobic surfaces

In a recent study, Peaudecerf et al. (PNAS 2017) showed that surfactant can decrease the drag-reduction performance of superhydrophobic surfaces (SHS). As SHS could have a large impact in reducing energy utilisation for many internal and external flow applications, it is important to understand and predict how surfactant-Marangoni stresses affect the flow over SHS. We present a semi-analytical model solving Stokes flow over an SHS, coupled with surfactant transport in the bulk and at the interface using modified Frumkin kinetics. We consider both a Poiseuille flow in a two-dimensional channel with a periodic array of plastrons on one side and a two-dimensional shear flow over a flat solid surface with a periodic array of plastrons. We find that at low surfactant concentration this complex nine non-dimensional parameter model can be reduced to eight parameters by combining the Marangoni number and the normalised concentration. At steady state, we obtain a prediction of the Marangoni shear stress due to the concentration gradient of the surfactant adsorb onto the plastron, assuming a uniform shear stress along the plastron. We compare the model with finite-element numerical simulations of the full transport problem. Good agreement is found for a large range of geometries, flow conditions and surfactant properties.   

Visualization of an air-water interface on superhydrophobic surfaces in turbulent channel flows

In the present study, three-dimensional deformation of air-water interface on superhydrophobic surfaces in turbulent channel flows at the Reynolds numbers of Re = 3000 and 10000 is measured with RICM (Reflection Interference Contrast Microscopy) technique. Two different types of roughness feature of circular hole and rectangular grate are considered, whose depth is 20~$\mu$m and diameter (or width) is varied between 20-200 $\mu$m. Since the air-water interface is always at de-pinned state at the considered condition, air-water interface shape and its sagging velocity is maintained to be almost constant as time goes one. In comparison with the previous results under the laminar flow, due to turbulent characteristics of the flow, sagging velocity is much faster. Based on the measured sagging profiles, a modified model to describe the air-water interface dynamics under turbulent flows is suggested.   

Gas diffusion in and out of super-hydrophobic surface in transitional and turbulent boundary layers.

The rate of gas diffusion in and out of a super-hydrophobic surface (SHS) located in boundary layers is investigated at varying Reynolds numbers and ambient pressures. The hierarchical SHS consists of nano-textured, $\approx $100 $\mu $m wide spanwise grooves. The boundary layers over the SHS under the Cassie-Baxter and Wenzel states as well as a smooth wall at same conditions are characterized by particle image velocimetry. The Reynolds number based on momentum thickness of the smooth wall, \textit{Re}$_{\Theta 0}$, ranges from 518 to 2088, covering transitional and turbulent boundary layer regimes. The mass diffusion rate is estimated by using microscopy to measure the time-evolution of plastron shape and volume. The data is used for calculating the Sherwood number based on smooth wall momentum thickness, \textit{Sh}$_{\Theta 0}$. As expected, the diffusion rate increases linearly with the under- or super-saturation level, i.e., \textit{Sh}$_{\Theta 0}$ is independent of ambient pressure. For the turbulent boundary layers, the data collapses onto \textit{Sh}$_{\Theta 0}=$0.47\textit{Re}$_{\Theta 0}^{\mathrm{0.77}}$. For the transitional boundary layer, \textit{Sh}$_{\Theta 0}$ is lower than the turbulent power law. When \textit{Sh}$_{\Theta 0}$ is plotted against the friction Reynolds number (\textit{Re}$_{\tau 0})$, both the transitional and turbulent boundary layer data collapse onto a single power law, \textit{Sh}$_{\Theta 0}=$0.34\textit{Re}$_{\tau 0}^{\mathrm{0.913}}$. Results scaled based on Wenzel state momentum thickness show very similar trends.