General wetting energy boundary condition in a fully explicit non-ideal fluids solver

TL;DR

This paper introduces a general wetting energy boundary condition for simulating non-ideal multi-phase fluids, improving stability and accuracy in contact line dynamics within an explicit finite difference framework.

Contribution

It proposes a thermodynamically consistent wetting boundary condition that enhances stability and accurately captures contact angles without needing an interface thickness parameter.

Findings

Correctly recovers equilibrium contact angles.

Reduces instability at contact angles near 0 and π.

Aligns contact line dynamics with stress-balanced models.

Abstract

We present an explicit finite difference method to simulate the non-ideal multi-phase fluid flow. The local density and the momentum transport are modeled by the Navier-Stokes (N-S) equations and the pressure is computed by the Van der Waals equation of the state (EOS). The static droplet and the dynamics of liquid-vapor separation simulations are performed as validations of this numerical scheme. In particular, to maintain the thermodynamic consistency, we propose a general wetting energy boundary condition at the contact line between fluids and the solid boundary. We conduct a series of comparisons between the current boundary condition and the constant contact angle boundary condition as well as the stress-balanced boundary condition. This boundary condition alleviates the instability induced by the constant contact angle boundary condition at $\theta \approx0 $ and $\theta \approx \pi$. Using this boundary condition, the equilibrium contact angle is correctly recovered and the contact line dynamics are consistent with the simulation by applying a stress-balanced boundary condition. Nevertheless, unlike the stress-balanced boundary condition for which we need to further introduce the interface thickness parameter, the current boundary condition implicitly incorporates the interface thickness information into the wetting energy.