Shape of a droplet on a surface in the presence of an external field and its critical disruption condition

TL;DR

This paper models and analyzes the equilibrium shape of a droplet under an electric field, combining theoretical, numerical, and empirical methods to understand deformation and critical disruption conditions.

Contribution

It introduces a comprehensive theoretical model and computational approach to determine droplet shapes influenced by electric fields, including a universal critical disruption condition.

Findings

Successfully obtained droplet shapes considering electrostatic, surface tension, and gravitational energies.

Derived an empirical critical disruption condition with a universal 1/2 scaling exponent.

Master curve aligns well with experimental and numerical data.

Abstract

Due to the potential application of regulating droplet shape by external fields in microfluidic technology and micro devices, it becomes increasingly important to understand the shape formation of a droplet in the presence of an electric field. How to understand and determine such a deformable boundary shape at equilibrium has been a long-term physical and mathematical challenge. Here, based on the theoretical model we propose, and combining the finite element method and the gradient descent algorithm, we successfully obtain the droplet shape by considering the contributions made by electrostatic energy, surface tension energy, and gravitational potential energy. We also carry out scaling analyses and obtain an empirical critical disruption condition with a universal scaling exponent 1/2 for the contact angle in terms of normalized volume. The master curve fits both the experimental and the numerical results very well.