Abstract
We have given theoretical expressions for the forces exerted on a so-called Wilhelmy plate, which we modeled as a quasi-2D flat and smooth solid plate immersed in a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line, and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. The force expressions were derived by a purely mechanical approach, which is exact and ensures the force balance on the control volumes arbitrarily set in the system, and are valid as long as the solid-liquid (SL) and solid-vapor (SV) interactions can be described by mean-fields. In addition, we revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γSL and γSV, and this was verified through the comparison with the SL and SV works of adhesion obtained by the thermodynamic integration (TI). From these results, it has been confirmed that γSL and γSV as well as the liquid-vapor interfacial tension γLV can be extracted from a single equilibrium MD simulation without the computationally demanding calculation of the local stress distributions and the TI.
Highlights
The behavior of the contact line (CL), where a liquid–vapor interface meets a solid surface, has long been a topic of interest in various scientific and engineering fields because it governs the wetting properties.1–5 By introducing the concept of interfacial tensions and contact angle θ, Young’s equation6 is given by γSL − γSV + γLV cos θ = 0, (1)where γSL, γSV, and γLV denote solid–liquid (SL), solid–vapor (SV), and liquid–vapor (LV) interfacial tensions, respectively
We have given theoretical expressions for the forces exerted on a Wilhelmy plate, which we modeled as a quasi-2D flat and smooth solid plate immersed in a liquid pool of a simple liquid
By a purely mechanical approach, we have derived the expressions for the local forces on the top, the contact line (CL), and the bottom of the plate as well as the total force on the plate
Summary
From a microscopic point of view, Kirkwood and Buff first provided the theoretical framework of surface tension based on the statistical mechanics, and molecular dynamics (MD) and Monte Carlo (MC) simulations have been carried out for the microscopic understanding of wetting through the connection with the interfacial tensions.10–35 Most of these works on a simple flat and smooth solid surface indicated that the apparent contact angle of the meniscus or droplet obtained in the simulations corresponded well to the one predicted by Young’s equation (1). The Wilhelmy method has been applied as one of the most common methods to experimentally measure the LV interfacial tension, e.g., surface tension, or the contact angle.40 In this method, the force on a solid sample vertically immersed in a liquid pool is expressed from the force balance by Ltzotal = lγLV cos θ + mg − ρgV,. As a major outcome of the expressions of the local forces, we will show in this article that all the interfacial tensions involved in the system, γLV, γSL, and γSV, can be measured from a single equilibrium MD simulation without computationally demanding calculations
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