Probing the Nanohydrodynamics at Liquid-Solid Interfaces Using Thermal Motion

Joly, L.; Ybert, Christophe; Bocquet, Lydéric

doi:10.1103/physrevlett.96.046101

Cited by 167 publications

(187 citation statements)

References 32 publications

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“…Since the EO flow amplification scales as (1 + bκ), and b can be of the order of tens of nanometers [9,10,11,12], for typically nanometric Debye length an order of magnitude enhancement might be expected.…”

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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Section: Electro-osmotic Velocity In Eigendirectionsmentioning

confidence: 99%

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

Belyaev

Vinogradova

2011

Phys. Rev. Lett.

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“…This length being typically nanometric in standard aqueous electrolytes, one can anticipate that the dynamics of charged systems should probe hydrodynamics in the nanometric vicinity of charged solid surfaces. One can in particular expect an interesting coupling with nanometric slippage, as predicted theoretically for neutral surfaces [2] and evidenced experimentally [5,8]. Furthermore, hydrophilic and hydrophobic surfaces exhibit different electric properties [12], and the coupling between pure wetting effects and "charge-mediated" effects is a priori subtle and remains to be clarified.…”

Section: Introductionmentioning

confidence: 99%

“…[2,5,6,8,9]). Moreover, it has been shown that this violation of the usual no-slip BC is controlled by the wetting properties of the fluid on the solid surface: while the no-slip BC is fulfilled on hydrophilic surfaces, a finite velocity slip is measured on hydrophobic surfaces [2,5,8], originating in a low friction of the liquid at the wall.…”

Section: Introductionmentioning

confidence: 99%

Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

Joly

Ybert

Trizac

et al. 2006

The Journal of Chemical Physics

209

229

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Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using Molecular Dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the non-trivial effect of surface charge is discussed. This work allows to reconsider existing experimental data, concerning ζ potentials of hydrophobic surfaces and suggest the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.

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“…As a guide, the dotted line shows the theoretical prediction for bZ100 nm slip length, illustrating the method sensitivity. Graph is taken from Joly et al (2006). than 1 mm) makes such a measurement rather challenging.…”

Section: Micro-and Nanovelocimetrymentioning

confidence: 99%

“…The results for different wetting properties of the solid substrates lead to measurable differences in the diffusion coefficient, allowing us to deduce the corresponding surface slippage. Details of the set-up are reported by Joly et al (2006). Below, we discuss only the most pertinent features of the experimental procedure.…”

Section: Thermal Motion Of Confined Colloidsmentioning

confidence: 99%

Using surface force apparatus, diffusion and velocimetry to measure slip lengths

Bouzigues

Bocquet

Charlaix

et al. 2007

Phil. Trans. R. Soc. A.

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Determining the slip lengths for liquids flowing close to smooth walls is challenging. The reason lies in the fact that the scales that must be addressed range between a few and hundreds of nanometres. Several techniques have been used over the last few years. Here, we consider three of them based on surface force apparatus, diffusion and velocimetry, respectively. The descriptions offered here incorporate recent instrumental progress made in the field.

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Probing the Nanohydrodynamics at Liquid-Solid Interfaces Using Thermal Motion

Cited by 167 publications

References 32 publications

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

Electro-osmosis on Anisotropic Superhydrophobic Surfaces

Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

Using surface force apparatus, diffusion and velocimetry to measure slip lengths

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