Line tension from dual-geometry sessile droplet measurements: Combining contact-angle size-dependence data for axisymmetric and cylindrical droplets to determine the line tension

TL;DR

This paper introduces a thermodynamic analysis and a new technique combining measurements from axisymmetric and cylindrical droplets to accurately determine line tension from contact-angle size dependence.

Contribution

It presents a method to isolate the line tension contribution by combining contact-angle data from different droplet geometries under identical conditions.

Findings

A new thermodynamic framework for contact-angle size dependence.

A technique to extract line tension from combined droplet measurements.

Clarification of the contributions of interface adsorptions and line tension.

Abstract

We perform a thermodynamic analysis of various contributions to the size dependence of the contact-angle cosine for both axisymmetric and cylindrical sessile droplets. This shows that a commonly used method to determine the line tension from the slope of the contact-angle cosine dependence on the three-phase contact-line curvature (for axisymmetric droplets) provides a certain combination of the line tension, the adsorptions at the three interfaces, and the macroscopic contact angle. To extract the contribution related to the contact line in the leading order and determine the line tension, we propose a simple technique using droplet-size dependences of the contact angle for axisymmetric and cylindrical droplets under the same conditions.