Apparent Contact Angle and Contact Angle Hysteresis on Liquid Infused Surfaces

TL;DR

This paper provides a theoretical analysis of the apparent contact angle and hysteresis on liquid infused surfaces, revealing their dependence on droplet size, surface features, and fluid tensions, with derived formulas for practical prediction.

Contribution

It introduces a new theoretical framework for understanding contact angles and hysteresis on liquid infused surfaces, including formulas accounting for droplet size and surface roughness effects.

Findings

Apparent contact angle depends on droplet size and wetting ridge.

Derived a closed-form expression for contact angle with vanishing wetting ridge.

Predicted contact angle hysteresis due to surface corrugations.

Abstract

We theoretically investigate the apparent contact angle and contact angle hysteresis of a droplet placed on a liquid infused surface. We show that the apparent contact angle is not uniquely defined by material parameters, but also has a strong dependence on the relative size between the droplet and its surrounding wetting ridge formed by the infusing liquid. We derive a closed form expression for the contact angle in the limit of vanishing wetting ridge, and compute the correction for small but finite ridge, which corresponds to an effective line tension term. We also predict contact angle hysteresis on liquid infused surfaces generated by the pinning of the contact lines by the surface corrugations. Our analytical expressions for both the apparent contact angle and contact angle hysteresis can be interpreted as `weighted sums' between the contact angles of the infusing liquid relative to the droplet and surrounding gas phases, where the weighting coefficients are given by ratios of the fluid surface tensions.