Thin-Film Smoothed Particle Hydrodynamics Fluid

Mengdi Wang1, Yitong Deng1, Xiangxin Kong1, Aditya H. Prasad1, Shiying Xiong1, and Bo Zhu1
1Dartmouth College
webpage paper code

Several thin-film phenomena simulated using the thin-film SPH method. Counting from left to right: (1) surface flow on a oscillating soap bubble, (2) pinched-off droplets between two circular rims pulling away from one another, (3) a soap bubble bursting into tiny droplets and filaments after being poked from the right, (4) the vibrant, opal-like color pattern caused by Rayleigh-Taylor instability on a large-deforming, wet thin-film surface.

Abstract

This particle-based method simulates thin-film fluid with aggressive surface deformation and vigorous tangential flows. The dynamics model is built from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory, together with a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) and customized for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in this application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. This enables two-way coupling of the surface deformation with the in-plane flows in a physically based manner. The method simulates complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton’s interference fringes, and the Marangoni effect on liberally deforming surfaces, demonstrated through realistic visual results and numerical validations. The particle-based nature of the system also enables it to handle topology changes and codimension transitions, connecting thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Video

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