A Kelvin–Clapeyron Adsorption Model for Spreading on a Heated Plate

Reyes, R.; Wayner, Peter

doi:10.1115/1.2822576

Cited by 14 publications

(8 citation statements)

References 27 publications

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“…These values suggest A may decrease weakly with increasing T w , but that to a first approximation, A is constant. This conclusion is consistent with the dependence of A on T w inferred by Reyes & Wayner (1996, figure 2) from an empirical relation between A and surface energies. By contrast, Kim varies A to fit the computed and measured film profiles, and since T w varies between experiments, he finds A as a function of T w .…”

Section: Comparison With Existing Experimentssupporting

confidence: 92%

Contact angles for evaporating liquids predicted and compared with existing experiments

Morris

2001

J. Fluid Mech.

100

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The stationary meniscus of an evaporating, perfectly wetting system exhibits an apparent contact angle Θ which vanishes with the applied temperature difference ΔT, and is maintained for ΔT > 0 by a small-scale flow driven by evaporation. Existing theory predicts Θ and the heat flow q∗ from the contact region as the solution of a free-boundary problem. Though that theory admits the possibility that Θ and q∗ are determined at the same scale, we show that, in practice, a separation of scales gives the theory an inner and outer structure; Θ is determined within an inner region contributing a negligible fraction of the total evaporation, but q∗ is determined at larger scales by conduction across an outer liquid wedge subtending an angle Θ. The existence of a contact angle can thus be assumed for computing the heat flow; the problems for Θ and q∗ decouple. We analyse the inner problem to derive a formula for Θ as a function of ΔT and material properties; the formula agrees closely with numerical solutions of the existing theory. Though microphysics must be included in the model of the inner region to resolve a singularity in the hydrodynamic equations, Θ is insensitive to microphysical detail because the singularity is weak. Our analysis shows that Θ is determined chiefly by the capillary number Ca = μlVl/σ based on surface tension σ, liquid viscosity μl and a velocity scale Vl set by evaporation kinetics. To illustrate this result of our asymptotic analysis, we show that computed angles lie close to the curve Θ = 2.2Ca1/4; a small scatter of ±15% about that curve is the only hint that Θ depends on microphysics. To test our scaling relation, we use film profiles measured by Kim (1994) to determine experimental values of Θ and Ca; these are the first such values to be published for the evaporating meniscus. Agreement between theory and experiment is adequate; the difference is less than ±40% for 9 of 15 points, while the scatter within experimental values is ±25%.

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Section: Comparison With Existing Experimentssupporting

confidence: 92%

Contact angles for evaporating liquids predicted and compared with existing experiments

Morris

2001

J. Fluid Mech.

100

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“…It means that J(x) changes sign and condensation occurs in an extremely small vicinity of the CL. A similar effect exists for the complete wetting case [13].…”

supporting

confidence: 66%

Contact line singularity at partial wetting during evaporation driven by substrate heating

Janecek¹,

Nikolayev²

2012

EPL

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We present a theoretical investigation of the evaporation of a liquid on a solid substrate into the atmosphere of its pure vapor. The evaporation is provoked by the overheating of the substrate above the saturation temperature. At partial wetting, the liquid forms a wedge ending at the triple liquid-vapor-solid contact line (CL). The wedge region is extremely important in all evaporation geometries (bubble, drop, meniscus in a capillary) for two reasons. First, in this region a significant part of the evaporative heat flux is spent to compensate the latent heat. Second, a strong meniscus curvature that occurs in this region leads to the apparent contact angle larger than its actual microscopic value. We show that unlike the conventional diffusive evaporation models, the evaporation rate at the CL is bounded and is defined by the CL velocity. In particular the evaporation rate vanishes at the CL when it is immobile. This means that the slip length is not essential for the contact line singularity relaxation. The pressure boundary conditions at the CL are also derived. An analytic expression for the apparent contact angle (valid in the asymptotic limit of vanishing overheating) is derived. It is compared to numerical results.

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“…We also suggest that phase change can remove the singularity usually associated with the ''no slip'' boundary condition on an ''iso-Ž thermal'' or nonisothermal substrate in spreading Wayner, . 1994a,b;Reyes and Wayner, 1996 . However, this is usually neglected in current studies on spreading where slip and surface diffusion mechanisms are used to relieve the infinite Ž .…”

confidence: 98%

Intermolecular forces in phase‐change heat transfer: 1998 Kern award review

Wayner

1999

AIChE Journal

132

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A Kelvin–Clapeyron Adsorption Model for Spreading on a Heated Plate

Cited by 14 publications

References 27 publications

Contact angles for evaporating liquids predicted and compared with existing experiments

Contact angles for evaporating liquids predicted and compared with existing experiments

Contact line singularity at partial wetting during evaporation driven by substrate heating

Intermolecular forces in phase‐change heat transfer: 1998 Kern award review

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