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

Guriyanova, Svetlana; Semin, Benoît; Rodrigues, Tiago; Butt, Hans‐Jürgen; Bonaccurso, Elmar

doi:10.1007/s10404-009-0498-2

Cited by 43 publications

(78 citation statements)

References 58 publications

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“…We note that similar evaluations could be used for rough or porous surfaces since at large distances from the wall the boundary condition at the rough interface or fluid-porous interface may be approximated by a slip model [38,[43][44][45]. It should be possible to make such an analysis of recent data obtained with grooved surfaces [46], which we suspect will significantly alter the conclusion of these authors. Note that the average eigenvalues of an effective slip length tensor at large (compared to L) separations should coincide with the measured by velocimetry [47] or other far-field methods [48].…”

Section: Final Remarksmentioning

confidence: 99%

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

2011

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We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.

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Section: Final Remarksmentioning

confidence: 99%

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

2011

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“…Recent data (supported by simulations [12]) suggest that the description of flow near rough surfaces has to be corrected, but rather for a separation, not a slip [13,14]. Another suggestion is to combine these two models [15].…”

Section: Introductionmentioning

confidence: 98%

Effective hydrodynamic boundary conditions for microtextured surfaces

et al. 2013

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Understanding the influence of topographic heterogeneities on liquid flows has become an important issue with the development of microfluidic systems, and more generally for the manipulation of liquids at the small scale. Most studies of the boundary flow past such surfaces have concerned poorly wetting liquids for which the topography acts to generate superhydrophobic slip. Here we focus on topographically patterned but chemically homogeneous surfaces, and measure a drag force on a sphere approaching a plane decorated with lyophilic microscopic grooves. A significant decrease in the force compared with predicted even for a superhydrophobic surface is observed. To quantify the force we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between the top and bottom of grooves. We relate its location to a surface topology by a simple, but accurate analytical formula. Since grooves represent the most anisotropic surface, our conclusions are valid for any texture, and suggest rules for the rational design of topographically patterned surfaces to generate desired drag.

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“…Experimental techniques (1-3) to measure slip lengths b-defined as the distance beyond the solid over which a linear extrapolation of the liquid velocity field reaches zero (36)-have reached nanometric resolution. Values of b for small-molecule liquids on the order of tens (1)(2)(3)(37)(38)(39)(40) up to a couple of hundred nanometers (41)(42)(43) are now reported. Polymer melts, containing chain-like molecules which can be highly coupled to one another (13,44,45), may show slip lengths from one up to tens of micrometers (9,10,(46)(47)(48)(49)(50)(51).…”

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confidence: 99%

Slip-mediated dewetting of polymer microdroplets

McGraw

Chan

Maurer

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap-shaped polystyrene microdroplets, with nonequilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy. We find that slip has a strong influence on the droplet evolutions, both on the transient nonspherical shapes and contact line dynamics. The observations are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition.

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

Cited by 43 publications

References 58 publications

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

Effective hydrodynamic boundary conditions for microtextured surfaces

Slip-mediated dewetting of polymer microdroplets

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