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A balance of surface science and aerodynamic knowledge is brought to bear to elucidate the fundamental parameters determining the incipient motion (runback) for a drop exposed to shearing airflow. It was found that wetting parameters such as contact angle are very influential in determining the minimum required air velocity for drop shedding. On the basis of experimental results for drops of water and hexadecane (0.5-100 microL) on PMMA, Teflon, and a superhydrophobic aluminum surface, an exponential function is proposed that relates the critical air velocity for shedding to the ratio of drop base length to projected area. The results for all of the water systems can be collapsed to self-similar curves by normalization. Results from other researchers also conform to the exponential self-similar functional form proposed. It was shown that the data for hexadecane drops can be matched relatively well to those for water drops by means of a corrective factor based on fluid properties and contact angles. Also, the critical air velocity for shedding from the superhydrophobic surface is seen to be more constant over a range of volumes than for the other surfaces. Finally, contact angle measurements from airflow shedding experiments are compared to measurements made by tilted plate and quasi-static advancing and receding tests. The observed differences between contact angles from different measurement methods show that the transfer of contact angle data among various applications must be done with care.

We demonstrate a reduction in the measured inner wall shear stress in moderately turbulent Taylor-Couette flows by depositing sprayable superhydrophobic microstructures on the inner rotor surface. The magnitude of reduction becomes progressively larger as the Reynolds number increases up to a value of 22% at Re ¼ 8.0 × 10 4 . We show that the mean skin friction coefficient C f in the presence of the superhydrophobic coating can be fitted to a modified Prandtl-von Kármán-type relationship of the form ðC f =2Þ1=2 from which we extract an effective slip length of b ≈ 19 μm. The dimensionless effective slip length b þ ¼ b=δ ν , where δ ν is the viscous length scale, is the key parameter that governs the drag reduction and is shown to scale as b þ ∼ Re 1=2 in the limit of high Re. DOI: 10.1103/PhysRevLett.114.014501 PACS numbers: 47.85.lb, 47.27.N-, 68.08.Bc, 83.50.Rp It is well known that superhydrophobic (SH) surfaces can reduce drag in laminar flows by presenting an effective wall slip boundary condition due to stable pockets of vapor within the asperities of the textured substrate [1,2]. The trapped vapor layer adjacent to the solid wall lubricates the fluid flow by introducing an effective slip boundary condition along portions of the wall, and consequently reduces the overall drag [3]. The magnitude of the effective slip length b in viscous laminar flows is governed by the surface feature length scale and the wetted solid fraction [4][5][6]. Measurements in various microchannel flows [7][8][9][10][11] yield values of b that are typically in the range of 10-30 μm.There is less consensus on the extent to which microscopic effective slip can influence macroscopic skin friction in turbulent flows [12,13]. Numerical simulations of turbulent channel flows indicate that the shear-free liquid-vapor interface can reduce skin friction by introducing an effective slip velocity in the viscous sublayer [14,15], and by the suppression of turbulent flow structures in the near-wall region [16]. While recent experimental studies report varying amounts of drag reduction in turbulent flows using SH surfaces [17][18][19], there are inconsistencies in the magnitude of observed drag reduction across studies, and its dependence on the slip length, surface characteristics, and Reynolds number in turbulent flow remain unclear.In this Letter, we demonstrate sustained reduction in frictional drag in turbulent Taylor-Couette (TC) flows by applying a polymeric SH coating to the inner rotor. The extent of drag reduction DR ¼ 100 × ðT flat − T SH Þ=T flat based on the inner rotor torque T , steadily increases with Re up to 22% at Re ¼ 80 000. The reduction in friction arises from finite slip effects at the moving rotor. The two key results we describe in our Letter are (i) the magnitude of drag reduction is directly related to a dimensionless slip length b þ ≡ b=δ ν , which couples the effective slip length b to the viscous length scale δ ν ¼ ν=u τ ¼ ν ffiffiffiffiffiffiffiffi ffi ρ=τ i p of the turbulent flow (where ν is the kinematic v...

Despite the practical need, no models exist to predict contact angles or wetting mode of surfactant solutions on rough hydrophobic or superhydrophobic surfaces. Using Gibbs' adsorption equation and a literature isotherm, a new model is constructed based on the Wenzel and Cassie equations. Experimental data for aqueous solutions of sodium dodecyl sulfate (SDS) contact angles on smooth Teflon surfaces are fit to estimate values for the adsorption coefficients in the model. Using these coefficients, model predictions for contact angles as a function of topological f (Cassie) and r (Wenzel) factors and SDS concentration are made for different intrinsic contact angles. The model is also used to design/tune surface responses. It is found that: (1) predictions compare favorably to data for SDS solutions on five superhydrophobic surfaces. Further, the model predictions can determine which wetting mode (Wenzel or Cassie) occurred in each experiment. The unpenetrated or partially penetrated Cassie mode was the most common, suggesting that surfactants inhibit the penetration of liquids into rough hydrophobic surfaces. (2) The Wenzel roughness factor, r, amplifies the effect of surfactant adsorption, leading to larger changes in contact angles and promoting total wetting. (3) The Cassie solid area fraction, f, attenuates the lowering of contact angles on rough surfaces. (4) The amplification/attenuation is understood to be due to increased/decreased solid-liquid contact-area.

This paper resolves questions in the literature regarding the autophilic effect (i.e., movement of surfactant past the advancing contact line-leading to an increase in drop radius beyond that due to the advance) and its importance to quasi-static sessile drop wetting. Various systems (SDS, HTAB, and MEGA 10 surfactant solutions at three concentrations each and pure water and ethylene glycol on hydrophobic Teflon and OTS-coated silicon) are probed to determine the existence, time constant, and magnitude of the autophilic effect, using quasi-static advancing and receding sessile drops. From spreading results and advancing contact angle measurements, it is inferred that the autophilic effect does not occur for our systems (in contradiction of some literature) for the following reasons. First, no relation exists between the time constant for spreading and surfactant concentration, meaning the spreading seen is likely inertial in cause and not due to surfactants. Second, advancing contact angle decreases between tests on clean surfaces and those pre-exposed to surfactant, ruling out the possibility that the autophilic effect is faster than the advance. Third, spreading is seen after the end of the advance over both clean and pre-exposed surfaces, ruling out the possibility that the autophilic effect is slower than the advance. Finally, the pure liquids spread in a similar fashion to surfactant solutions on Teflon and similar contact angle measurements are seen for surfactant solutions and pure liquids of similar surface tension.