Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces

Abstract

Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible by creating adverse Marangoni stresses. However, testing this hypothesis is challenging. Careful experiments with purified water already show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. To test the surfactant hypothesis while controlling surfactant concentrations with precision higher than can be achieved experimentally, we perform simulations inclusive of surfactant kinetics. These reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air-water interface (the "plastron") for surfactant concentrations below typical environmental values. These stresses decrease as the stream-wise distance between plastron stagnation points increases. We perform microchannel experiments with SHSs consisting of streamwise parallel gratings, which confirm this numerical prediction, while showing near-plastron velocities significantly slower than standard surfactant-free predictions. In addition, we introduce an unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.superhydrophobic surface | drag reduction | surfactant | Marangoni stress | plastron S uperhydrophobic surfaces (SHSs) combine hydrophobic surface chemistry and micro-or nanoscale patterning to retain a network of air pockets when exposed to a liquid (e.g., reviews in refs. 1-3). Because a large portion of the interface between the solid wall and the liquid is replaced by an air-liquid interface, which can be considered almost as a shear-free surface (known as a "plastron"), SHSs could be used to obtain significant drag reduction in fluid flow applications (4, 5). Microchannel tests have recorded drag reductions of over 20% (e.g., refs. 6-11) and rheometer tests reported slip lengths of up to 185 µm (12). Turbulent flow experiments have reduced drag by up to 75% (13-16). However, a wide range of experiments have provided inconsistent results, with several studies reporting little or no drag reduction (16)(17)(18)(19)(20)(21)(22)(23)(24)(25).A key step toward solving this puzzle has come with the realization that surfactants could induce Marangoni stresses that impair drag reduction. This was first hypothesized to account for experiments that rev...

A theory for the slip and drag of superhydrophobic surfaces with surfactant

“…Similarly, (28) report: u I ≈ 8 × 10 −2 for 5 mm long lanes (see their figure 3b), which is significantly reduced compared with the theoretical (surfactant-free) prediction; and u I ≈ 8 × 10 −3 for 15 mm long lanes ( figure 5), which is practically negligible. The main difficulty in applying our theoretical model, for instance to predict the reduced slip velocities measured experimentally by (27) and (28), is that the surfactant properties and their concentrations are completely unknown in their experiments. Instead, we use our model to predict the concentration of surfactant, for three different possible surfactant types, which could lead to the measured u I reported in (27) and (28).…”

“…[16][17][18][19][20][21], as well as low-Reynolds-number, internal flows, which are the focus of the present paper (e.g. 9,11,[22][23][24][25][26][27][28]. At low Reynolds numbers, the use of SHSs has been proposed to reduce what are otherwise very large pressure differences across microchannels, as is the case in microfluidic devices or in micro-cooling applications (29)(30)(31), as well as to minimize Taylor dispersion in the chemical or biological analysis of species (10).…”

Hydrodynamic response of a surfactant-laden interface to a radial flow

“…As the size of the system decreases, interfacial contributions become increasingly relevant. Microfluidic experiments revealed for instance that traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces [10]. Impurities at the water-air interface have also been shown to affect its viscoelastic response in AFM experiments [11,12].…”

Effective slip lengths for immobilized superhydrophobic surfaces

“…There is now mounting evidence that contamination by surfactants, even in trace amounts (Peaudecerf et al 2017), can immobilize superhydrophobic surfaces, rendering them, essentially, no-slip surfaces. Kim & Hidrovo (2012) performed experiments in a rectangular microchannel with regular sidewall patterning to visualize the location of the air-water interface within the roughness elements.…”

“…Bolognesi et al (2014) suggested surfactants or other surface contaminants as possible causes for this surface immobilization. In a very recent study, Peaudecerf et al (2017) focused on examining the effect of surfactants on hydrodynamic slip in longitudinal flows along unidirectionally patterned surfaces. Careful pressure control was used to maintain flat menisci, with the conclusion that even trace amounts of surfactants can cause a dramatic reduction in the expected slip enhancement properties of the surfaces, again, by causing an immobilization of these surfaces into effective no-slip zones.…”