On the statistical mechanics of fluids adsorbed in chemically non-symmetric linear wedges

Henderson, J. R.

doi:10.1080/00268970500093936

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…2 and shall not explicitly discuss the geometries with grooves and pillars: the sharp edges present in these cases lead to the further complication of an additional line tension τ e associated with each edge. This line tension is an excess contribution to the free energies of the homogeneous liquid and vapor phases exposed to such geometries [46], and should not be confused with the line tension associated with a three-phase vapor-liquidsurface contact line. We only focus on conditions of partial wetting of the vapor phase, both for the planar surface and the sinusoidally corrugated surface; we are neither concerned with the wetting or drying transitions, nor with the possibility that filling of wedges or partial filling of the grooves formed by the sinusoidal corrugation occurs [47].…”

Section: Introductionmentioning

confidence: 99%

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

Egorov,

Binder

2020

Preprint

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The contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor rw), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form z wall (y) = ∆ cos(2πy/λ) , for a potential of short range σw acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be computed exactly, and corrections to Wenzel's equation are typically of order σw∆/λ 2 . For fixed rw and fixed σw the approach to Wenzel's result with increasing λ may be nonmonotonic and this limit often is only reached for λ/σw > 30. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases both for planar and corrugated walls, as well as the corresponding surface tensions. Again, deviations from Wenzel's results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret corresponding simulation results along similar lines. Wenzel's approach is found to generally hold when λ/σw 1, ∆/λ < 1, and conditions avoiding proximity of wetting or filling transitions.

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Section: Introductionmentioning

confidence: 99%

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

Egorov,

Binder

2020

Preprint

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When does Wenzel’s extension of Young’s equation for the contact angle of droplets apply? A density functional study

Егоров

Binder

2020

The Journal of Chemical Physics

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The contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel’s relation attributes this difference simply to the geometric magnification of the surface area (by a factor rw), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form zwall(y) = Δ cos(2πy/λ), for a potential of short range σw acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change in the wall-vapor surface tension can be computed exactly, and corrections to Wenzel’s equation are typically of the order σwΔ/λ2. For fixed rw and fixed σw, the approach to Wenzel’s result with increasing λ may be nonmonotonic and this limit often is only reached for λ/σw > 30. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases for planar and corrugated walls as well as the corresponding surface tensions. Again, deviations from Wenzel’s results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret the corresponding simulation results along similar lines. Wenzel’s approach is found to generally hold when λ/σw ≫ 1 and Δ/λ < 1 and under conditions avoiding proximity of wetting or filling transitions.

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Statistical mechanics of the disjoining pressure of a planar film

Henderson

2005

Phys. Rev. E

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The physics of wetting transitions (stability of fluid films adsorbed at planar substrates) is reassessed in the context of the original theory of wetting known as Frumkin-Derjaguin theory [A. Frumkin, Zh. Fiz. Khim. 12, 337 (1938)]. In particular, the Russian School classify wetting phenomena in terms of the mean-field disjoining pressure. The integral of the mean-field disjoining pressure, with respect to film thickness, defines the interface potential accessible from density-functional theory (DFT). For wall-fluid models (substrate defined as an external field), the exact disjoining pressure of an adsorbed film can be expressed as a one-body sum rule. One of the aims of this work is to verify the internal consistency of the statistical thermodynamics of Frumkin-Derjaguin theory, by direct evaluation of the disjoining pressure sum rule, using DFT. For short-range models, the form of the interface potential (and hence disjoining pressure) is directly obtainable from liquid-state asymptotics. The second aim of this work is to verify from DFT that for standard short-range models there are three qualitatively different regimes, arising from competition between the correlation lengths predicted by asymptotic theory. A variety of related issues are also considered, including (i) crossover between the various regimes, (ii) incorporation of capillary-wave fluctuations (beyond mean-field), and (iii) qualitative changes induced by power-law dispersion interactions and the related prediction of two-stage wetting.

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On the statistical mechanics of fluids adsorbed in chemically non-symmetric linear wedges

Cited by 3 publications

References 28 publications

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

When does Wenzel’s extension of Young’s equation for the contact angle of droplets apply? A density functional study

Statistical mechanics of the disjoining pressure of a planar film

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