Flow past superhydrophobic surfaces with cosine variation in local slip length (original) (raw)

The local slip length and flow fields over nanostructured superhydrophobic surfaces

International Journal of Multiphase Flow, 2020

The local slip behavior and flow fields near the gas-liquid interface (GLI) of a Newtonian liquid flowing past a superhydrophobic surface with periodic rectangular grooves are investigated using molecular dynamics (MD) simulations. The saturated vapor of the liquid fills the groove to form the GLI. A flat GLI is introduced by carefully adjusting the channel height to make the liquid bulk pressure equal to the coexistence pressure. The setup with the flat GLI allows for an accurate determination of the local slip velocity, shear rate and slip length. We find that the local slip velocity and shear rate at the GLI are well described by the elliptical and exponential functions, respectively. By directly computing the local slip length from the local flow fields, we propose a novel distribution function for the slip length along the GLI for both transverse and longitudinal flows. Moreover, we demonstrate that the relationship between the local and the effective slip lengths in the transverse and longitudinal cases deviates from the continuum assumptions as the groove width is reduced to the nanoscale dimensions. The functional form for the local slip length can be potentially used as a boundary condition in the continuum analysis without considering the explicitly gas flow in the grooves of superhydrophobic surfaces.

Effective slippage on superhydrophobic trapezoidal grooves

The Journal of Chemical Physics, 2013

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova, J. Fluid Mech. 706, 108 ] that relates the eigenvalues of the effective slip-length tensor for one-dimensional textures. Second, we propose theoretical estimates for the effective slip length and calculate it numerically by solving the Stokes equation based on a collocation method. The comparison between the two approaches shows that they are in excellent agreement. Our results demonstrate that the effective slippage depends strongly on the area-averaged slip, the amplitude of the roughness, and on the fraction of solid in contact with the liquid. To interpret these results, we analyze flow singularities near slipping heterogeneities, and demonstrate that they inhibit the effective slip and enhance the anisotropy of the flow. Finally, we propose some guidelines to design optimal one-dimensional superhydrophobic surfaces, motivated by potential applications in microfluidics.

Effective slip on textured superhydrophobic surfaces

Physics of Fluids, 2005

We study fluid flow in the vicinity of textured and superhydrophobically coated surfaces with characteristic texture sizes on the order of 10 m. Both for droplets moving down an inclined surface and for an external flow near the surface ͑hydrofoil͒, there is evidence of appreciable drag reduction in the presence of surface texture combined with superhydrophobic coating. On textured inclined surfaces, the drops roll faster than on a coated untextured surface at the same angle. The highest drop velocities are achieved on surfaces with irregular textures with characteristic feature size ϳ8 m. Application of the same texture and coating to the surface of a hydrofoil in a water tunnel results in drag reduction on the order of 10% or higher. This behavior is explained by the reduction of the contact area between the surface and the fluid, which can be interpreted in terms of changing the macroscopic boundary condition to allow nonzero slip velocity.

Microgroove geometry dictates slippery hydrodynamics on superhydrophobic substrates

Physics of Fluids, 2018

We report the detailed hydrodynamics over micro-grooved substrates in a confined hydrophobic microfluidic environment. In sharp contrast to the traditional premises, the liquid-air interface shape or interfacial slip velocity is not presumed a priori. We compare our results with the reported analytical solutions of the low Reynolds number flow with the Navier slip boundary condition considering a predefined flat interface. Discrepancies between such simplified solutions and the comprehensive solutions reported here clearly suggest the critical implications of the microgroove geometry and Reynolds number toward altering the flow physics. Our results reveal that the slip velocity at the interface and the slip length is directly proportional to the microgroove width, whereas the slip length increases with the increasing width and decreases with the increase in the Reynolds number. These results may open up new possibilities of tuning the micro-grooved geometry toward obtaining desired flow characteristics in superhydrophobic microchannels, for which simplified models based on pre-defined interfacial topology may not reliably work.

Large Slip of Aqueous Liquid Flow over a Nanoengineered Superhydrophobic Surface

Physical Review Letters, 2006

While many recent studies have confirmed the existence of liquid slip over certain solid surfaces, there has not been a deliberate effort to design and fabricate a surface that would maximize the slip under practical conditions. Here, we have engineered a nanostructured superhydrophobic surface that minimizes the liquid-solid contact area so that the liquid flows predominantly over a layer of air. Measured through a cone-and-plate rheometer system, the surface has demonstrated dramatic slip effects: a slip length of 20 m for water flow and 50 m for 30 wt % glycerin. The essential geometrical characteristics lie with the nanoposts populated on the surface: tall and slender (i.e., needlelike) profile and submicron periodicity (i.e., pitch).

Drag Reduction on a Patterned Superhydrophobic Surface

Physical Review Letters, 2006

We present an experimental study of a low-Reynolds number shear flow between two surfaces, one of which has a regular grooved texture augmented with a superhydrophobic coating. The combination reduces the effective fluid-surface contact area, thereby appreciably decreasing the drag on the surface and effectively changing the macroscopic boundary condition on the surface from no slip to limited slip. We measure the force on the surface and the velocity field in the immediate vicinity on the surface (and thus the wall shear) simultaneously. The latter facilitates a direct assessment of the effective slip length associated with the drag reduction.

Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries

Physics of Fluids, 2007

We investigate the hydrodynamic friction properties of superhydrophobic surfaces and quantify their superlubricating potential. On such surfaces, the contact of the liquid with the solid roughness is minimal, while most of the interface is a liquid-gas one, resulting in strongly reduced friction. We obtain scaling laws for the effective slip length at the surface in terms of the generic surface characteristics ͑roughness length scale, depth, solid fraction of the interface, etc.͒. These predictions are successfully compared to numerical results in various geometries ͑grooves, posts or holes͒. This approach provides a versatile framework for the description of slip on these composite surfaces. Slip lengths up to 100 m are predicted for an optimized patterned surface.

Experimental evidence of slippage breakdown for a superhydrophobic surface in a microfluidic device

A full characterization of the water flow past a silicon superhydrophobic surface with longitudinal micro-grooves enclosed in a microfluidic device is presented. Fluorescence microscopy images of the flow seeded with fluorescent passive tracers were digitally processed to measure both the velocity field and the position and shape of the liquid-air interfaces at the superhydrophobic surface. The simultaneous access to the meniscus and velocity profiles allows us to put under a strict test the no-shear boundary condition at the liquid-air interface. Surprisingly, our measurements show that air pockets in the surface cavities can sustain non-zero interfacial shear stresses, thereby hampering the friction reduction capabilities of the surface. The effects of the meniscus position and shape as well as of the liquid-air interfacial friction on the surface performances are separately assessed and quantified.

A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces

Physics of Fluids, 2007

A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effects of this surface deformation are studied in this paper. The corrections to the effective slip length produced by the curvature are analyzed theoretically and a comparison with available data and related mathematical models is presented.

Measurement of slip length on superhydrophobic surfaces

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012

In this paper, a review of different techniques used to measure the slip length on superhydrophobic surfaces with large slip length is presented. First, we present the theoretical models used to calculate the effective slip length on superhydrophobic surfaces in different configurations of liquid flow. Then, we present the different techniques used to measure the slip past these superhydrophobic surfaces: rheometry, particle image velocimetry, pressure drop, surface force apparatus and atomic force microscopy.