The influence of droplet size on line tension

TL;DR

This paper investigates how droplet size affects line tension on chemically inhomogeneous substrates using an effective interfacial Hamiltonian, revealing temperature-dependent decay behaviors and geometric contact angle implications.

Contribution

It provides a detailed analysis of line tension dependence on droplet size and temperature, including finite width effects and a geometric contact angle construction.

Findings

Line tension varies with droplet width and temperature.

Decay of line tension shifts from exponential to algebraic at the stripe wetting temperature.

Geometric contact angle analysis offers new insights into droplet morphology.

Abstract

Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with cylinder-shaped droplets sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension - which includes the inhomogeneity finite width effects - are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature T_W1: for T<T_W1 they decay exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric construction of the corresponding contact angle is carried out and its implications are discussed.