Shapes, contact angles, and line tensions of droplets on cylinders

Bauer, C.; Dietrich, S.

doi:10.1103/physreve.62.2428

Cited by 54 publications

(41 citation statements)

References 48 publications

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“…This difference could be because of the topography of the pore walls (SBA-15 is known to have a rougher surface than MCM-41) or a systematic trend with the solid surface curvature, such as described in ref. 46.…”

Section: Discussionmentioning

confidence: 99%

Activated drying in hydrophobic nanopores and the line tension of water

Guillemot

Biben

Galarneau

et al. 2012

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

125

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We study the slow dynamics of water evaporation out of hydrophobic cavities by using model porous silica materials grafted with octylsilanes. The cylindrical pores are monodisperse, with a radius in the range of 1-2 nm. Liquid water penetrates in the nanopores at high pressure and empties the pores when the pressure is lowered. The drying pressure exhibits a logarithmic growth as a function of the driving rate over more than three decades, showing the thermally activated nucleation of vapor bubbles. We find that the slow dynamics and the critical volume of the vapor nucleus are quantitatively described by the classical theory of capillarity without adjustable parameter. However, classical capillarity utterly overestimates the critical bubble energy. We discuss the possible influence of surface heterogeneities, long-range interactions, and high-curvature effects, and we show that a classical theory can describe vapor nucleation provided that a negative line tension is taken into account. The drying pressure then provides a determination of this line tension with much higher precision than currently available methods. We find consistent values of the order of −30 pN in a variety of hydrophobic materials. A remarkable property of water is its ability to form nanosize bubbles, or cavities, on hydrophobic bodies (1). Since their first direct observations through atomic force microscopy about a decade ago (2, 3), surface nanobubbles on hydrophobic surfaces have raised considerable interest, and they are believed to play a major role in surface-driven phenomena, such as boundary slippage of water flows, heat transfer at walls, vaporization and boiling, surface cleaning, etc. (4, 5). In a different context, the evaporation of water in the vicinity of hydrophobic bodies has been studied as a core mechanism for the hydrophobic interaction mediated by water (6-8), which plays a central role in biological matter. The formation of cavities able to bridge hydrophobic units provides a driving force for protein folding and supermolecular aggregation (9). Simulation examples of such drying-induced phenomena include the collapse of a polymer chain, multidomain proteins, and hydrophobic particles (9-13).Despite their direct observation, the easy formation and the high stability of nanobubbles on hydrophobic bodies still raise fundamental questions (5,14,15). Because of significant theoretical work, it is now established that, at the scale of the nanometer, macroscopic concepts apply: hydrophobicity is described by interfacial energies, and the drying transition in hydrophobic confinement is a first-order transition triggered by the nucleation of a critical vapor bubble (1). The energy barrier limiting the kinetics of this transition is a strong signature of nanobubbles properties. Evaporation kinetics has also been pointed out as the most direct measure of the importance of hydrophobic collapse in protein folding (9). However, rate effects in the drying transition have not received much attention. A few numerical studies have addr...

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Section: Discussionmentioning

confidence: 99%

Activated drying in hydrophobic nanopores and the line tension of water

Guillemot

Biben

Galarneau

et al. 2012

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

125

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“…One limitation of the finite element approach and the previous analytical stability arguments in this work is that they rely purely on classical capillary considerations and ignore van der Waals forces and microscopic films that can exist in practice. To overcome these limitations, numerical simulations of wetting on fibers, using for example molecular dynamics as previously applied to wetting on flat surfaces (de Ruijter et al, 1999), or numerical evaluation of free energy functionals (Bauer and Dietrich, 2000), could be used to provide an alternative approach to the assessment of the stability of the conformations and the roll-up process.…”

Section: Surface Free Energy Considerationsmentioning

confidence: 99%

The Shape and Stability of Small Liquid Drops on Fibers

McHale

Newton

Carroll

2001

Oil & Gas Science and Technology - Rev. IFP

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Résumé -Forme et stabilité de gouttelettes de liquide sur des fibres -La forme d'une petite goutte de liquide sur une fibre de petit diamètre peut être décrite soit par une allure en tonneau axé symétrique, soit par une allure en perle (cloche). Les expériences montrent que lorsque le volume réduit, défini par le rapport entre le volume de la goutte et le rayon de la fibre, est grand, la configuration préférée est celle en tonneau. Lorsque le volume réduit est petit, une transition se produit vers la forme en perle. Le volume correspondant à cette transition dépend de l'angle de contact d'équilibre. Dans cet article, nous considérons la solution connue de l'équation de Laplace pour la forme en tonneau. Nous étudions le lien entre le profil, le point d'inflexion dans le profil et la stabilité de la goutte. Dans le cas de la forme en cloche, il n'existe pas de solution connue de l'équation de Laplace. Nous développons ici une approche en éléments finis pour déterminer le profil d'une goutte sur une fibre et présentons des résultats numériques pour la forme en cloche. Les énergies de surface pour ces deux types de goutte sur une fibre sont calculées pour plusieurs volumes de goutte et angles de contact. Les implications correspondantes pour la stabilité de ces gouttes sont alors discutées.Mots-clés : fibre, angle de contact, mouillage, stabilité, forme de goutte. Abstract -The Shape and Stability of Small Liquid Drops on Fibers -The shape of a small liquid drop on a small diameter fiber may be either an axisymmetric barrel shape or it may be a nonaxisymmetric clam-shell shape. Experiments show that when the reduced volume, given by the volume of droplet divided by the fiber radius, is large the barrel shape is the preferred conformation, but that as the volume reduces a transition to a clam-shell (pearl

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“…Geometry can be either local, in the form of rough [1,2] or patterned [3] surfaces, or it can be global, in the form of spheres [4], cylinders/fibers [4][5][6][7][8][9], etc. Of these global geometries, cylinders are of particular importance because fibers are an extremely common material in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Global geometry and the equilibrium shapes of liquid drops on fibers

McHale

Newton

2002

Colloids and Surfaces A: Physicochemical and Engineering Aspect

137

129

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The wetting of a planar surface depends upon both the chemical nature of the surface and the local geometry. On a chemically identical solid surface in the form of a fiber the wetting is significantly different due to the global geometry of the cylindrical shape. A fluid that fully wets a material in the form of a smooth planar surface may not wet the same material when presented as a smooth fiber surface. On a fiber, a vanishing contact angle is not a sufficient condition for the formation of a wetting film; a macroscopic barrel shaped droplet with a vanishing equilibrium contact angle can exist. Moreover, two distinctly different geometric shapes of droplet are possible: a barrel and a clam-shell. In this work, these two shapes are considered using an analytical result for the barrel shape and a finite element calculation for the clam-shell shape. The surface free energies for these two conformations are evaluated for contact angles between 14 o and 70 o and for a wide range of droplet volumes. The results show that when the droplet volume is large or the contact angle is small, an axisymmetric barrel shape is the energetically preferred conformation, but that as the volume reduces or the contact angle increases the clam-shell shape becomes lower in energy. These results are compared to literature data for the roll-up (barrel-toclam-shell) transition and to a previously published criterion for metastability of the barrel shaped droplet. A conjecture on the role of the inflection angle in the barrel-shape droplet profile is also considered. For the contact angle range considered, the finite element results show that all barrelshaped droplets that are lower in energy than clam-shell droplets, are stable according to the metastability condition and also possess an inflection angle.

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Shapes, contact angles, and line tensions of droplets on cylinders

Cited by 54 publications

References 48 publications

Activated drying in hydrophobic nanopores and the line tension of water

Activated drying in hydrophobic nanopores and the line tension of water

The Shape and Stability of Small Liquid Drops on Fibers

Global geometry and the equilibrium shapes of liquid drops on fibers

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