A generalized Young’s equation for contact angles of droplets on homogeneous and rough substrates

Wang, Xiaosong; Cui, Shuwen; Zhou, Long; Xu, Shenghua; Sun, Zhigang; Zhu, Rui

doi:10.1080/01694243.2013.833401

Cited by 19 publications

(4 citation statements)

References 21 publications

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“…The liquid-vapor surface tension is denoted by σ, and the intrinsic line tension is denoted by τ . Since, we consider a nonvolatile liquid droplet, we use Helmholtz free energy instead of the Gibbs or grand potential free energy [22,[24][25][26]. Therefore, the problem of dividing surface of liquid-vapor interface [3,22,25] and the Kondo equation [24,25] for the Laplace pressure will not be considered explicitly.…”

Section: A Generalized Yount's Equationmentioning

confidence: 99%

“…By decomposing the free energy of a droplet on a solid substrate into volume, interfacial, and line contributions, we can theoretically determine the intrinsic line tension. Since the liquid-vapor surface is curved and interfacial zone is diffuse, there is a conceptual problem of dividing surface [3,22,[24][25][26]. Therefore, instead of directly analyzing a cap-shaped droplet with a finite base radius and a spherical meniscus, a liquid wedge with a flat meniscus, which corresponds to the limit of infinite base radius, is usually considered.…”

Section: Introductionmentioning

confidence: 99%

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A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

Iwamatsu

2018

Preprint

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A generalized Young's equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid-vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman's formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of µN so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretical calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.

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Section: A Generalized Yount's Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

Iwamatsu

2018

Preprint

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“…With the contact surface assumed absolutely smooth, stiff, homogenous and inert (i.e., an ideal surface), the relation between contact angle and interfacial tension of a droplet was firstly described by Young's equation [14,15]. Further, whilst the Wenzel equation determined the contact angles on a rough surface for homogeneous wetting regime [16], the Cassie-Baxter equation developed the theories for heterogeneous wetting regime (e.g., porous contact surface) [17].…”

Section: Introductionmentioning

confidence: 99%

Determination of contact angle of droplet on convex and concave spherical surfaces

Wang

et al. 2015

Chemical Physics

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“…Now, Equation (1.1) is called the Young's equation. The Young's equation Equation (1.1) is widely applied to macroscopic capillary phenomena (Pfleging & Proella, 2014;Xiao-Song et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Derivation of Generalized Young’s Equation for Wetting of Cylindrical Droplets on Rough Solid Surface

Wang¹

2015

MER

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The surface tension depends on the radius of curvature of the liquid-vapor interface. For nano-scale wetting phenomena of cylindrical droplets, we should consider the curvature effects of the surface tension and the line tension. However, previous works have not analyzed the influence of the curvature effects of the surface tension. In this paper, we discuss the influence of the curvature effects of the surface tension on the contact angles based the Kim-Lee-Han-Park equation. The hydrophilic wetting of cylindrical droplets on rough and chemically homogeneous non-deformable substrates were studied by methods of thermodynamics. A generalized Young's equation for wetting of cylindrical droplets on chemically homogeneous and rough non-deformable substrates was derived based on the thermodynamic equilibrium conditions. This equation reduces to the Wenzel equation if we ignore the influence of line tension. For contact angles of cylindrical droplets with sufficiently large radii, a generalized Young's equations were derived considering the curvature effects of the surface tension.

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A generalized Young’s equation for contact angles of droplets on homogeneous and rough substrates

Cited by 19 publications

References 21 publications

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

Determination of contact angle of droplet on convex and concave spherical surfaces

Derivation of Generalized Young’s Equation for Wetting of Cylindrical Droplets on Rough Solid Surface

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