Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces

Abstract

Superhydrophobic surfaces can retain gas pockets within their microscale textures when submerged in water. This property reduces direct contact between water and solid surfaces and presents opportunities for improving hydrodynamic performance by decreasing viscous drag. In most realistic applications, however, the flow regime is turbulent and retaining the gas pockets is a challenge. In order to overcome this challenge, it is crucial to develop an understanding of physical mechanisms that can lead to the failure of superhydrophobic surfaces in retaining gas pockets when the overlying liquid flow is turbulent. We present a study of the onset of failure in gas retention by analysing direct numerical simulations (DNS) of turbulent flows over superhydrophobic surfaces coupled with the deformation of air–water interfaces that hold the gas pockets. The superhydrophobic surfaces are modelled as periodic textures with patterned slip and no-slip boundary conditions on the overlying water flow. The liquid–gas interface is modelled via a linearized Young–Laplace equation, which is solved coupled with the overlying turbulent flow. A wide range of texture sizes and interfacial Weber numbers are considered in this study. Our analysis identifies flow-induced upstream-travelling capillary waves that are coherent in the spanwise direction as one mechanism for failure in retention of gas pockets. To confirm physical understanding of these waves, a semianalytical inviscid linear analysis is developed; the wave speeds obtained from the space–time correlations in the DNS data were found to match with the predictions of the semianalytical model. The magnitude of the pressure fluctuations due to these waves was found to increase with decreasing surface tension, and increase with a much stronger dependence on the slip velocity, when all numbers are reported in wall units. Based on a fitted scaling, a threshold criterion for the failure of superhydrophobic surfaces is developed that is based on estimates of the onset condition required for the motion of contact lines. The second contribution of this work is the development of boundary maps that identify stable and unstable zones in a parameter space consisting of working parameter and design parameters including texture size and material contact angle. We provide a brief description of previously identified failure modes of superhydrophobic surfaces, namely the stagnation pressure and shear-driven drainage mechanisms. In an overlay map, the stable and unstable zones due to each mechanism are presented. For various input conditions, we provide scaling laws that identify the most critical mechanism limiting the stability of gas retention by superhydrophobic surfaces.

Manipulation of near-wall turbulence by surface slip and permeability

“…Accounting for a non-zero + v and its effect on + ωx allows us to generalise the slip-length theory of Luchini et al [6] and Jiménez [7]. When + y = 0, we observe that a good approximation for conducted to extend the models to surfaces which select certain modes at the interface, such as superhydrophobic posts [17] or deep transverse grooves [25].…”

“…Note that both the simulations of [13] and the linear theory of slip lengths [5,7] assume zero wall-normal velocity fluctuations at the reference plane. However, real surfaces that produce non-zero slips, such as riblets [1], porous substrates [16] or superhydrophobic surfaces [17], induce additionally a non-zero wall-normal velocity at the reference plane. The absence of transpiration in slip-only simulations leads to the saturation of the spanwise slip observed in Figure 2.…”

Comparison between super-hydrophobic, liquid infused and rough surfaces: a direct numerical simulation study

“…In reality the interface is deformable and not slippery as assumed in the present model. García-Cartagena et al (2018) and Seo et al (2018) showed that when the interface deforms the amount of drag reduction is drastically reduced. Though exploring the role of interfacial deflections will be important to understanding many of these slippery surfaces, such an exploration is beyond the scope of this manuscript.…”

Effective slip over partially filled microcavities and its possible failure

“…Despite the discrepancies in the literature, a common technological challenge for the application of superhydrophobic materials is their fragility [8]. Under high pressures or external forces, such as turbulent fluctuation or phase change, the surface texture can be partially or fully impregnated by the outer fluid (Cassie-to-Wenzel transition), causing the system to lose the features it was designed for [9,10,30].…”

“…There are, as yet, surprisingly few fully resolved hydrodynamic simulations able to solve the details of the flow reducing the underlying assumptions. Most prior numerical studies still consider flat/circular menisci with zero subphase viscosity [25][26][27][28][29][30]; however, they extend analytical solutions to more complex surface patterns or the finite-Reynolds-number regime. Flexible bubble shapes were first considered in [31] for a uniform gas mattress, and later for a nonuniform distribution [32].…”