Abstract
Modelling the profile of a liquid droplet has been a mainstream technique for researchers to study the physical properties of a liquid. This study proposes a facile modelling approach using an elliptic model to generate the profile of sessile droplets, with MATLAB as the simulation environment. The concept of the elliptic method is simple and easy to use. Only three specific points on the droplet are needed to generate the complete theoretical droplet profile along with its critical parameters such as volume, surface area, height, and contact radius. In addition, we introduced fitting coefficients to accurately determine the contact angle and surface tension of a droplet. Droplet volumes ranging from 1 to 300 µL were chosen for this investigation, with contact angles ranging from 90° to 180°. Our proposed method was also applied to images of actual water droplets with good results. This study demonstrates that the elliptic method is in excellent agreement with the Young–Laplace equation and can be used for rapid and accurate approximation of liquid droplet profiles to determine the surface tension and contact angle.
Highlights
The behaviour and properties of a liquid droplet have long been an attractive research topic
Throughout the past two centuries, researchers have focused on studying droplet shapes as a critical parameter [1,2,3]
The two most commonly used methods to study droplet shapes are (i) the sessile drop method, where a droplet rests on a horizontal solid substrate, and (ii) the pendant drop method, where a droplet is suspended from the tip of a needle
Summary
The behaviour and properties of a liquid droplet have long been an attractive research topic. The scope of measurements is wider for the sessile drop method where the surface tension, contact angle, and surface free energy of the solid surface are generated from the analysis due to interactions between the droplet and solid substrate. This study proposes an elliptic model to generate sessile droplet profiles which provide measurable parameters such as contact angles and surface tensions. This model divides the droplet into two elliptic curves which can be uniquely defined using an analytical method. Our elliptic model generates all these critical parameters without iteration which eliminates the need for complex algorithm optimisation
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