Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

TL;DR

This study models contact angle hysteresis of cylindrical droplets on chemically striped surfaces, deriving a modified Cassie's law and predicting droplet behavior during volume changes, including sudden edge jumps and continuous contact angle variations.

Contribution

It introduces a modified Cassie's law for heterogeneous surfaces and predicts droplet hysteresis behavior on striped substrates using an interface displacement model.

Findings

Droplet edge exhibits sudden jumps with volume changes.

Apparent contact angle varies continuously at stripe boundaries.

Large contact angles dominate during droplet advancement.

Abstract

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.