Interpretation of Young's equation for a liquid droplet on a flat and smooth solid surface: Mechanical and thermodynamic routes with a simple Lennard-Jones liquid.

Yasutaka Yamaguchi,Donatas Surblys,Takeshi Omori,Gota Kikugawa,Hiroki Kusudo

doi:10.1063/1.5053881

Yasutaka Yamaguchi, Donatas Surblys + Show 3 more

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https://doi.org/10.1063/1.5053881

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Abstract

In this study, we carried out molecular dynamics simulations of a cylindrical Lennard-Jones droplet on a flat and smooth solid surface and showed that Young's equation as the relation among solid-liquid, solid-vapor, and liquid-vapor interfacial tensions γSL, γSV, and γLV, respectively, was applicable only under a very restricted condition. Using the fluid stress-tensor distribution, we examined the force balance in the surface-lateral direction exerted on a rectangular control volume set around the contact line. As the mechanical route, the fluid stress integrals along the two control surfaces normal to the solid-fluid interface were theoretically connected with γSL and γSV relative to the solid-vacuum interfacial tension γS0 by Bakker's equation extended to solid-related interfaces via a thought experiment, for which the position of the solid-fluid interface plane was defined at the limit that the fluid molecules could reach. On the other hand, the fluid stress integral along the control surface lateral to the solid-fluid interface was connected with γLV by the Young-Laplace equation. Through this connection, we showed that Young's equation was valid for a system in which the net lateral force exerted on the fluid molecules from the solid surface was zero around the contact line. Furthermore, we compared γSL - γS0 and γSV - γS0 obtained by the mechanical route with the solid-liquid and solid-vapor works of adhesion obtained by the dry-surface method as one of the thermodynamic routes and showed that both routes resulted in a good agreement. In addition, the contact angle predicted by Young's equation with these interfacial tensions corresponded well to the apparent droplet contact angle determined by using the previously defined position of the solid-fluid interface plane; however, our theoretical derivation indicated that this correspondence was achieved because the zero-lateral force condition was satisfied in the present system with a flat and smooth solid surface. These results indicated that the contact angle should be predicted not only by the interfacial tensions but also by the pinning force exerted around the contact line.

Highlights

The behavior of the contact line, where a liquid-vapor interface meets a solid surface, has long been a topic of interest in various science and engineering fields because it plays a key role in the wetting properties.1–3 By introducing the concept of interfacial tensions and contact angle θ, Young’s equation4 is given by γSL − γSV + γLV cos θ = 0, (1)where γSL, γSV, and γLV denote solid-liquid, solid-vapor, and liquid-vapor interfacial tensions, respectively
The fluid stress integrals along the two control surfaces normal to the solid-fluid interface were theoretically connected with γSL and γSV relative to the solid-vacuum interfacial tension γS0 by Bakker’s equation extended to solid-related interfaces via a thought experiment, for which the position of the solid-fluid interface plane was defined at the limit that the fluid molecules could reach
The contact angle predicted by Young’s equation with these interfacial tensions corresponded well to the apparent droplet contact angle determined by using the previously defined position of the solid-fluid interface plane; our theoretical derivation indicated that this correspondence was achieved because the zero-lateral force condition was satisfied in the present system with a flat and smooth solid surface

Summary

Introduction

By introducing the concept of interfacial tensions and contact angle θ, Young’s equation is given by γSL − γSV + γLV cos θ = 0, (1). Young’s equation (1) was first proposed based on the horizontal force balance of interfacial tensions exerted on the contact line in 1805 before the establishment of thermodynamics.. It is difficult to experimentally validate these models mainly because measuring the interfacial tensions γSL and γSV, which include the solid phase, is not trivial.. It should be noted that recent micro-structuring techniques can produce a heterogeneous solid surface with a well-defined boundary between areas having different wettability, and it has been shown that this boundary played a key role in the wetting behavior. Young’s equation (1) was first proposed based on the horizontal force balance of interfacial tensions exerted on the contact line in 1805 before the establishment of thermodynamics. Instead of using the concept of force balance, Young’s equation is often re-defined from a thermodynamic point of view. Various models have been further put forward to capture the details of the contact line, such as introducing microscopic contact angle, adding line tension term to Eq (1), and dealing with precursor films. it is difficult to experimentally validate these models mainly because measuring the interfacial tensions γSL and γSV, which include the solid phase, is not trivial. It should be noted that recent micro-structuring techniques can produce a heterogeneous solid surface with a well-defined boundary between areas having different wettability, and it has been shown that this boundary played a key role in the wetting behavior.

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