Computing sessile droplet shapes on arbitrary surfaces with a new pairwise force smoothed particle hydrodynamics model

TL;DR

This paper introduces a new pairwise force profile for smoothed particle hydrodynamics to accurately simulate droplet shapes on complex, heterogeneous surfaces, validated through static and dynamic tests.

Contribution

A novel polynomial pairwise force profile for PF-SPH that improves modeling of droplet shapes on arbitrary surfaces, validated with static and dynamic simulations.

Findings

Successfully validated the new PF-SPH model in static and dynamic tests.

Demonstrated capability to simulate droplets on structured, heterogeneous surfaces.

Model shows potential for extension to dynamic droplet behaviors like spreading and impact.

Abstract

The study of the shape of droplets on surfaces is an important problem in the physics of fluids and has applications in multiple industries, from agrichemical spraying to microfluidic devices. Motivated by these real-world applications, computational predictions for droplet shapes on complex substrates -- rough and chemically heterogeneous surfaces -- are desired. Grid-based discretisations in axisymmetric coordinates form the basis of well-established numerical solution methods in this area, but when the problem is not axisymmetric, the shape of the contact line and the distribution of the contact angle around it are unknown. Recently, particle methods, such as pairwise force smoothed particle hydrodynamics (PF-SPH), have been used to conveniently forego explicit enforcement of the contact angle. The pairwise force model, however, is far from mature, and there is no consensus in the literature on the choice of pairwise force profile. We propose a new pair of polynomial force profiles with a simple motivation and validate the PF-SPH model in both static and dynamic tests. We demonstrate its capabilities by computing droplet shapes on a physically structured surface, a surface with a hydrophilic stripe, and a virtual wheat leaf with both micro-scale roughness and variable wettability. We anticipate that this model can be extended to dynamic scenarios, such as droplet spreading or impaction, in the future.