Tensorial hydrodynamic slip

Bazant, Martin Z.; Vinogradova, Olga I.

doi:10.1017/s002211200800356x

Cited by 179 publications

(211 citation statements)

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“…But complementary results in this direction would provide a fuller analytical description of the so-called slip tensor (Bazant & Vinogradova 2008;Asmolov & Vinogradova 2012) for these surfaces, thereby generalizing the fairly complete analytical description in the dilute limit already available on combining the analytical formulae of Davis &Lauga (2009) andCrowdy (2010).…”

Section: Discussionmentioning

confidence: 94%

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Crowdy

2016

J. Fluid Mech.

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This paper reports new analytical formulae for the longitudinal slip lengths for simple shear over a superhydrophobic surface, or bubble mattress, comprising a periodic array of unidirectional circular menisci, or bubbles, protruding into, or out of, the fluid. The accuracy of the formulae is tested against results from full numerical simulations; they are found to give small relative errors even at large no-shear fractions. In the dilute limit the formulae reduce to an earlier result by Crowdy (Phys. Fluids, vol. 22, 2010, 121703). They also extend analytical results of Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) beyond the limit of a small protrusion angle.

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Section: Discussionmentioning

confidence: 94%

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Crowdy

2016

J. Fluid Mech.

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“…Let then φ 1 and φ 2 = δ/L be the area fractions of the solid and gas phases with φ 1 + φ 2 = 1. Pressure-driven flow past such stripes has been shown to depend on the direction of the flow, and the eigenvalues of the slip-length tensor [20] read [21] …”

Section: Electro-osmotic Velocity In Eigendirectionsmentioning

confidence: 99%

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

Belyaev

Vinogradova

2011

Phys. Rev. Lett.

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Surface conduction in presence of slip is characterized by full Dukhin number, which is given by [1]:where m = 2ε(k B T /ze) 2 /(ηD), and D is the ion diffusivity, which is assumed equal for both types of ions. The first term in (1) is the Dukhin number for the no-slip surface, Du b=0 , while the second one, Du b , is due to hydrodynamic slip. In the Debye-Hückel modelThis restriction (2) allows the simplification:The parameter m ≈ 100/z 2 , and κL ≫ 1 since EDL is thin. Whence Du b=0 ≈ 1/(z 2 κL) ≪ 1 provided the potential is low. For a "slippery part" of Du we evaluate01. Therefore for increasing surface charge (potential) and b/L, the conductivity of the diffuse layer can become comparable to the bulk, and surface condition must be considered. The Péclet number, P e = U L/D , in presence of slip can be evaluated asTypically, electroosmotic velocity is of order is of order micrometers per second for no-slip surfaces [2]. For nanoscale patterns L < 1 µm and typical ion diffusivities D ≈ 10 −6 cm 2 /s this gives P e b=0 < 0.01 ≪ 1. The slip implies a correction factor (1 + bκ) , which suggests that the convective ion transport can safely be neglected only for bκ < 10. Larger values of bκ should relax this standard approximation of small P e. ELECTRO-OSMOTIC VELOCITY IN EIGENDIRECTIONSLongitudinal stripes.-In this configuration only x−velocity component remains, and the Stokes equation takes the formWe expand surface charge density in a Fourier series, and the potential is thenwhere ξ n = κ 2 + λ 2 n , λ n = 2nπ/L , q = q 1 φ 1 + q 2 φ 2 is the mean surface charge, andThe general solution to (6) for u(y, z) has the formwhere U n and U are determined by the slip boundary conditions. Imposing them on (9) in a thin EDL limit yields a dual serieswhich can be solved exactly by using a technique [3] to obtain the thin-EDL electro-osmotic velocity:Transverse stripes.-Although an external pressure gradient is equal to zero, local pressure variations contribute into a non-zero term ∇p in the Stokes equation, so that the flow is essentially two-dimensional. We first introduce a stream function f (x, y)2 which obeys inhomogeneous biharmonic equation:Here u and v are x and y velocity components, correspondingly. The general periodic solution to (14) has the formE t q n κ 2 η + g n y e −λny cos λ n x + + E t ε κ 2 η ∂ψ ∂y (15)Here the potential ψ(x, y) has exactly the form (7) with z replaced by x. The dual series problem in a thin EDL limit can be written aswhere a n = g n + E t q n ηκ 2 (ξ n − λ n ).These dual series can be solved exactly to obtainWe emphasize that a comparison of Eqs. (12) and (18) indicates that the EO flow is generally anisotropic, so that our results do not support an earlier conclusion [4] that the electro-osmotic mobility tensor is isotropic in the thin EDL limit. This inconsistensy [4] (due to an erroneous expression for a transverse electro-osmotic velocity, where factor of 2 was lost) has been corrected for a case b 2 = ∞ in [5]. Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia 3 ITMC and...

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“…Effective boundary conditions are generally tensorial in three-dimensions, [7][8][9][10][11][12][13][14] taking the form of a tensorial Navier slip boundary condition, 12 or similarly, as a "surface mobility tensor" relating slip velocity to applied shear traction. 15 In this letter, we provide a sequence of analytical relations for the surface mobility and related flow features of fluid motion over hydrophobically varying flat surfaces. These results can be used as an expeditious toolset in the design and optimization of surface textures that may otherwise require multiple experiments or continuum simulation.…”

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confidence: 99%

“…15 Specifically, it has been demonstrated 14 that for each λ(x, y) a symmetric mobility tensor M can be found a) Electronic mail: kkamrin@mit.edu. …”

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confidence: 99%

Some exact properties of the effective slip over surfaces with hydrophobic patternings

Six

Kamrin

2013

Physics of Fluids

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Shear flows of viscous fluid layers over nonuniformly hydrophobic surfaces are characterized in the far-field by an effective slip velocity, which relates to the applied stress through some mobility tensor characterizing the surface. Here, we identify two methods to determine the mobility tensor for flat surfaces with arbitrary slip-length variations. A family of “Cross Flow Identities” is then analyzed, which equate mobility components of different unidirectional patternings. We also calculate an analytical mobility solution for a family of continuously varying patterns. We validate the results numerically and discuss implications in various limits.

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Tensorial hydrodynamic slip

Cited by 179 publications

References 26 publications

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

Some exact properties of the effective slip over surfaces with hydrophobic patternings

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