Nanohydrodynamics:  The Intrinsic Flow Boundary Condition on Smooth Surfaces

Cottin-Bizonne, Cécile; Steinberger, Audrey; Cross, Benjamin; Raccurt, Olivier; Charlaix, Élisabeth

doi:10.1021/la7024044

Cited by 110 publications

(103 citation statements)

References 32 publications

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“…Nearly all of the first reports, and a few of the recent ones, suggested that if slip occurred it was only on nonwetted surfaces (Churaev et al 1984;Blake 1990;Baudry et al 2001;Tretheway and Meinhart 2002;Cottin-Bizonne et al 2008;Maali et al 2008). However, the occurrence of slip was also shown for partially or totally wettable surfaces (Pit et al 2000;Craig et al 2001;Bonaccurso et al 2002;Sun et al 2002;Zhu and Granick 2004;Joseph and Tabeling 2005;Tallon 2007, 2008).…”

Section: Introductionmentioning

confidence: 97%

“…It is accepted that surface wettability (Pit et al 2000;Bonaccurso et al 2002;Choi et al 2003;Qian et al 2005;Cottin-Bizonne et al 2008;Maali et al 2008), surface roughness (Zhu and Granick 2002;Bonaccurso et al 2003;Truesdell et al 2006;Vinogradova and Yakubov 2006), and super hydrophobicity (Bhushan et al 2009) influence the interaction between liquid and solid at the interface. Thus, the boundary condition necessary for describing the flow of liquid on a solid must be adapted to such situations.…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

Guriyanova

Semin

Rodrigues

et al. 2009

Microfluid Nanofluid

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We measured the hydrodynamic drainage force of an aqueous, Newtonian liquid squeezed between two hydrophobic or two hydrophilic surfaces by means of the colloidal probe technique. We controlled the wettability, the roughness, the topology, and also the approaching velocity of the surfaces. We found that asperities on the surfaces caused an artificial decrease of the measured drainage force that must be considered by the interpretation of the force curves. Even considering the effect of asperities, our experimental results could be interpreted only with the aid of a partial slip model. Or else, interpreted assuming that the viscosity close to the surfaces is different from bulk. On patterned hydrophilic surfaces, we demonstrated that the drainage force depends not only on the overall surface roughness or micro structuring but also on the specific length scale of the surface nanostructures.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

Guriyanova

Semin

Rodrigues

et al. 2009

Microfluid Nanofluid

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“…For glycerin displacing silicone oil in capillary tubes, Fermigier and Jenffer 11 estimated l s to be less than 10 nm, consistent with newer and more accurate measurements. 12 This means that a diffuse-interface simulation, in order to achieve the sharp-interface limit, would have to use a comparable ⑀ value. To capture the interfacial profile and hence the interfacial tension accurately, the grid size needs to be at least as small as ⑀.…”

Section: Introductionmentioning

confidence: 99%

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

2011

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The Cahn–Hilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the near-wall layer by the relaxation of a wall energy. The first part of the paper elucidates the role of the wall relaxation in a flowing system, with two main results. First, we show that wall energy relaxation produces a dynamic contact angle that deviates from the static one, and derive an analytical formula for the deviation. Second, we demonstrate that wall relaxation competes with Cahn–Hilliard diffusion in defining the apparent contact angle, the former tending to “rotate” the interface at the contact line while the latter to “bend” it in the bulk. Thus, varying the two in coordination may compensate each other to produce the same macroscopic solution that is insensitive to the microscopic dynamics of the contact line. The second part of the paper exploits this competition to develop a computational strategy for simulating realistic flows with microscopic slip length at a reduced cost. This consists in computing a moving contact line with a diffusion length larger than the real slip length, but using the wall relaxation to correct the solution to that corresponding to the small slip length. We derive an analytical criterion for the required amount of wall relaxation, and validate it by numerical results on dynamic wetting in capillary tubes and drop spreading.

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“…1). All the typical length scales (particle radius, wall pattern length, and particle-wall gap) considered here are on the order of micrometers, sufficiently large to describe the fluid as a continuum obeying the Navier-Stokes equations [8,9,10,11,12] with no slippage at the solid wall [13,14,15,16,17,18,19]. Our model corresponds to the real case of sufficiently deep grooves where it can be safely assumed perfect-slip at the liquid-gas interface, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Mobility tensor of a sphere moving on a superhydrophobic wall: application to particle separation

Pimponi

Chinappi

Gualtieri

et al. 2013

Microfluid Nanofluid

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The paper addresses the hydrodynamic behavior of a sphere close to a micro-patterned superhydrophobic surface described in terms of alternated no-slip and perfect-slip stripes. Physically, the perfect-slip stripes model the parallel grooves where a large gas cushion forms between fluid and solid wall, giving rise to slippage at the gas-liquid interface. The potential of the boundary element method (BEM) in dealing with mixed no-slip/perfect-slip boundary conditions is exploited to systematically calculate the mobility tensor for different particle-to-wall relative positions and for different particle radii. The particle hydrodynamics is characterized by a non trivial mobility field which presents a distinct near wall behavior where the wall patterning directly affects the particle motion. In the far field, the effects of the wall pattern can be accurately represented via an effective description in terms of a homogeneous wall with a suitably defined apparent slippage. The trajectory of the sphere under the action of an external force is also described in some detail. A "resonant" regime is found when the frequency of the transversal component of the force matches a characteristic crossing frequency imposed by the wall pattern. It is found that, under resonance, the particle undergoes a mean transversal drift. Since the resonance condition depends on the particle radius the effect can in principle be used to conceive devices for particle sorting based on superhydrophobic surfaces.

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Nanohydrodynamics: The Intrinsic Flow Boundary Condition on Smooth Surfaces

Cited by 110 publications

References 32 publications

Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

Hydrodynamic drainage force in a highly confined geometry: role of surface roughness on different length scales

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

Mobility tensor of a sphere moving on a superhydrophobic wall: application to particle separation

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