Reliable Determination of Contact Angle from the Height and Volume of Sessile Drops

TL;DR

This paper introduces a numerical method to determine the contact angle of sessile drops using height and volume constraints, providing consistent and accurate measurements compared to traditional profile curve methods.

Contribution

The novel approach uses differential equations and numerical integration to accurately compute contact angles from drop measurements, avoiding profile curve drawbacks.

Findings

Computed contact angles are consistent across different drop sizes.

Results agree with literature values for water on Teflon and Lucite.

Method provides a reliable alternative to direct profile measurements.

Abstract

Contact angle is an important parameter in characterizing the wetting properties of fluids. The most common methods for measuring the contact angle is to measure it directly from the profile curve of a sessile drop, a method with certain inherent drawbacks. Here we describe an alternative method that uses the height and volume of a sessile drop as constraints to construct its profile by numerical integration of its two governing differential equations. The integration yields, self consistently, the average value of the contact angle along the entire contact line as well as the footprint radius of the drop and its crown radius of curvature. As a test case, the new method is used to obtain the contact angle of pure water on two different substrates, Teflon and Lucite. For each substrate, four drops ranging in volume from 10 {\mu}l to 40 {\mu}l are used. The computed contact angles are consistent across the four different drop sizes for each substrate and are in agreement with typical literature values.