Effect of line tension on axisymmetric nanoscale capillary bridges at the liquid-vapor equilibrium

TL;DR

This paper theoretically investigates how line tension influences the formation and stability of axisymmetric nanoscale capillary bridges at the liquid-vapor equilibrium on various substrate geometries, highlighting geometric and line tension constraints.

Contribution

It derives a modified Young's equation incorporating line tension effects on curved surfaces, revealing how positive line tension limits capillary bridge formation based on substrate geometry.

Findings

Line tension modifies the equilibrium contact angle on curved surfaces.

Positive line tension restricts the parameter space for capillary bridge existence.

Geometry and line tension interplay limits bridge formation at the nanoscale.

Abstract

The effect of line tension on the axisymmetric nanoscale capillary bridge between two identical substrates with convex, concave and flat geometry at the liquid-vapor equilibrium is theoretically studied. The modified Young's equation for the contact angle, which takes into account the effect of line tension is derived on a general axisymmetric curved surface using the variational method. Even without the effect of line tension, the parameter space where the bridge can exist is limited simply by the geometry of substrates. The modified Young's equation further restricts the space where the bridge can exist when the line tension is positive because the equilibrium contact angle always remain finite and the wetting state near the zero contact angle cannot be realized. It is shown that the interplay of the geometry and the positive line tension restricts the formation of capillary bridge.