Validity of the “Sharp-Kink Approximation” for Water and Other Fluids

Abstract

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, based on a comparison of predicted and measured contact angles near roomtemperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.

Dependence of quartz wettability on fluid density

“…With the use of the sharp-kink approximation [Dietrich and Napiórkowski, 1991;Merath, 2008] and Young's equation (equation (1)), the following macroscopic equation can be obtained [Garcia et al, 2009;Gatica et al, 2004;Cheng et al, 1991]:…”

“…where I ¼ À∫ ∞ zmin V z ð Þdz is the van der Waals potential integral (I) [Garcia et al, 2009;Gatica et al, 2004], and Δρ = ρ lf À ρ g (ρ g is the gas density and ρ lf is a function of the liquid and gas densities for a specific substrate), [Merath, 2008]. Rearranging equation (2) therefore yields:…”

“…The measurement (or estimation) of the van der Waals forces (term I in equation (3)) is a significant challenge and typically requires substantial effort [Cheng et al, 1991;Gatica et al, 2004;Garcia et al, 2009], and therefore we propose to use the concept presented in equation (3) and plot cos θ w versus ρ g for the measured…”

Are Graphitic Surfaces Hydrophobic?

“…Graphene has potential applications in nanopore sequencing, ion selective filtration, energy storage, and electronics . In these applications, precise control of surface properties, for example, adhesion, friction, and surface energy, is necessary. ,− Water wettability is not only the most important parameter characterizing the surface properties but also directly influences properties such as charge doping and carrier mobility. , As a result, there is significant importance in elucidating the water wettability of graphitic surfaces. In the past 70 years, many water contact angle (WCA) studies have been conducted characterizing the water wettability of graphitic surfaces.…”

Taborek Replies:

“…This has been done for a wide variety of fluid-solid systems [2,[7][8][9][10][11]. The results show that the simple model captures the essential physics and that it is qualitatively but not quantitatively accurate.…”