General criteria for the estimation of effective slip length over corrugated surfaces

AbstractWe investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl’s second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i.e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.

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Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: the small-solid-fraction singularity

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.224 ◽

2017 ◽

Vol 820 ◽

pp. 580-603 ◽

Cited By ~ 11

Author(s):

Ory Schnitzer

Keyword(s):

Shear Flow ◽

Asymptotic Analysis ◽

Solid Fraction ◽

Asymptotic Expansions ◽

Slip Length ◽

Longitudinal Shear ◽

Unidirectional Flow ◽

Effective Slip Length ◽

Effective Slip ◽

Scaling Arguments

We study the effective slip length for unidirectional flow over a superhydrophobic mattress of bubbles in the small-solid-fraction limit $\unicode[STIX]{x1D716}\ll 1$. Using scaling arguments and utilising an ideal-flow analogy we elucidate the singularity of the slip length as $\unicode[STIX]{x1D716}\rightarrow 0$: relative to the periodicity it scales as $\log (1/\unicode[STIX]{x1D716})$ for protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}<\unicode[STIX]{x03C0}/2$ and as $\unicode[STIX]{x1D716}^{-1/2}$ for $0<\unicode[STIX]{x03C0}/2-\unicode[STIX]{x1D6FC}=O(\unicode[STIX]{x1D716}^{1/2})$. We continue with a detailed asymptotic analysis using the method of matched asymptotic expansions, where ‘inner’ solutions valid close to the solid segments are matched with ‘outer’ solutions valid on the scale of the periodicity, where the bubbles protruding from the solid grooves appear to touch. The analysis yields asymptotic expansions for the effective slip length in each of the protrusion-angle regimes. These expansions overlap for intermediate protrusion angles, which allows us to form a uniformly valid approximation for arbitrary protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}\leqslant \unicode[STIX]{x03C0}/2$. We thereby explicitly describe the transition with increasing protrusion angle from a logarithmic to an algebraic small-solid-fraction slip-length singularity.

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Liquid Slippage in Confined Flows: Effect of Periodic Micropatterns of Arbitrary Pitch and Amplitude

Volume 1: Micro/Nanofluidics and Lab-on-a-Chip; Nanofluids; Micro/Nanoscale Interfacial Transport Phenomena; Micro/Nanoscale Boiling and Condensation Heat Transfer; Micro/Nanoscale Thermal Radiation; Micro/Nanoscale Energy Devices and Systems ◽

10.1115/mnhmt2016-6491 ◽

2016 ◽

Cited By ~ 1

Author(s):

Avinash Kumar ◽

Subhra Datta ◽

Dinesh Kalyanasundaram

Keyword(s):

Slip Length ◽

Fluid Dynamic ◽

Low Cost ◽

Slip Boundary Condition ◽

Friction Reduction ◽

Fourier Decomposition ◽

Slip Boundary ◽

Local Degree ◽

Effective Slip Length ◽

Effective Slip

The recently confirmed violation of the no-slip boundary condition in the flow of small-molecule liquids through microchannels and nanochannels has technological implications such as friction reduction. However, for significant friction reduction at low cost, the microchannel wall needs to be chemically inhomogeneous. The direct fluid dynamic consequence of this requirement is a spatial variation in the local degree of liquid slippage. In this work, the pressure-driven flow in a channel with periodically patterned slippage on the channel walls is studied using a spectrally accurate semi-analytical approach based on Fourier decomposition. The method puts no restrictions on the pitch (or wavelength) and amplitude of the pattern. The predicted effective slip length in the limits of small pattern amplitude and thick channels is found to be consistent with previously published results. The effective degree of slippage decreases with the patterning amplitude. Finer microchannels and longer pattern wavelengths promote slippage.

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Effective slip-length tensor for a flow over weakly slipping stripes

Physical Review E ◽

10.1103/physreve.88.023004 ◽

2013 ◽

Vol 88 (2) ◽

Cited By ~ 24

Author(s):

Evgeny S. Asmolov ◽

Jiajia Zhou ◽

Friederike Schmid ◽

Olga I. Vinogradova

Keyword(s):

Slip Length ◽

Effective Slip Length ◽

Effective Slip

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Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.647 ◽

2014 ◽

Vol 740 ◽

pp. 168-195 ◽

Cited By ~ 61

Author(s):

Clarissa Schönecker ◽

Tobias Baier ◽

Steffen Hardt

Keyword(s):

Flow Field ◽

Slip Length ◽

Two Fluids ◽

Cassie State ◽

Effective Slip Length ◽

Primary Fluid ◽

Effective Slip ◽

Local Slip ◽

Analytical Expressions ◽

Secondary Fluid

AbstractAnalytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of the two fluids is reflected in a locally varying slip distribution along the fluid–fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the viscosities of the two fluids as well as the magnitude of the local slip, which is a function of the surface geometry. They agree well with results from numerical computations of the full geometry. The analytical expressions allow an investigation of the influence of the viscous stresses inside the secondary fluid for arbitrary geometries of the rectangular grooves. For classic superhydrophobic surfaces, the deviations in the effective slip length compared to the case of inviscid gas flow are pointed out. Another important finding with respect to an accurate modelling of flow over microstructured surfaces is that not only the effective slip length, but also the local slip length of a grooved surface, is anisotropic.

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EFFECTIVE SLIP LENGTH: SOME ANALYTICAL AND NUMERICAL RESULTS

The ANZIAM Journal ◽

10.1017/s1446181115000127 ◽

2015 ◽

Vol 57 (1) ◽

pp. 79-88

Author(s):

XINGYOU (PHILIP) ZHANG ◽

NAT J. LUND ◽

SHAUN C. HENDY

Keyword(s):

Stokes Flow ◽

Traditional Method ◽

Slip Length ◽

Slip Boundary Condition ◽

Numerical Results ◽

Micro Scale ◽

Slip Boundary ◽

Effective Slip Length ◽

Homogenization Approach ◽

Effective Slip

More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results.

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Stokes Flow Through a Periodically Grooved Tube

Journal of Fluids Engineering ◽

10.1115/1.4002654 ◽

2010 ◽

Vol 132 (10) ◽

Cited By ~ 9

Author(s):

Chiu-On Ng ◽

C. Y. Wang

Keyword(s):

Stokes Flow ◽

Slip Length ◽

Geometrical Parameters ◽

Slip Boundary ◽

Effective Slip Length ◽

Effective Slip ◽

Flow Through ◽

Transverse Grooves ◽

Shear Area ◽

Fluid Penetration

This is an analytical study on Stokes flow through a tube of which the wall is patterned with periodic transverse grooves filled with an inviscid gas. In one period of the pattern, the fluid flows through an annular groove and an annular rib subject to no-shear and no-slip boundary conditions, respectively. The fluid may penetrate the groove to a certain depth, so there is an abrupt change in the cross section of flow through the two regions. The problem is solved by the method of domain decomposition and eigenfunction expansions, where the coefficients of the expansion series are determined by matching velocities, stress, and pressure on the domain interface. The effective slip length and pressure distributions are examined as functions of the geometrical parameters (tube radius, depth of fluid penetration into grooves, and no-shear area fraction of the wall). Particular attention is paid to the limiting case of flow through annular fins on a no-shear wall. Results are generated for the streamlines, resistance, and pressure drop due to the fins. It is found that the wall condition, whether no-shear or no-slip, will be immaterial when the fin interval is smaller than a certain threshold depending on the orifice ratio.

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