# Lattice-Boltzmann simulations of electrowetting phenomena

## TL;DR

This paper introduces a lattice-Boltzmann simulation method that models electrowetting phenomena by integrating electrostatics and hydrodynamics, validated against theoretical and experimental benchmarks.

## Contribution

The authors develop a hybrid lattice-Boltzmann approach that directly incorporates electrostatic fields, enabling accurate simulation of electrowetting effects without hybrid methods.

## Key findings

- Reproduces static droplet configurations and contact angle dependence on voltage.
- Demonstrates contact angle saturation at high voltages due to electric-capillary balance.
- Shows good agreement with lubrication theory for dielectric film stability.

## Abstract

We present a lattice-Boltzmann method that can simulate the coupled hydrodynamics and electrostatics equations of motion of a two-phase fluid as a means to model electrowetting phenomena. Our method has the advantage of modelling the electrostatic fields within the lattice-Boltzmann algorithm itself, eliminating the need for a hybrid method. We validate our method by reproducing the static equilibrium configuration of a droplet subject to an applied voltage and show that the apparent contact angle of the drop depends on the voltage following the Young-Lippmann equation up to contact angles of $\approx 50^\circ$. At higher voltages, we observe a saturation of the contact angle caused by the competition between electric and capillary stresses. We also study the stability of a dielectric film trapped between a conducting fluid and a solid electrode and find a good agreement with analytical predictions based on lubrication theory. Finally, we investigate the film dynamics at long times and report observations of film breakup and entrapment similar to previously reported experimental results.