Abstract

Jackson Pollock is a famous abstract artist who used unconventional painting techniques to create huge non-figurative works. One of his techniques consists in swinging a brush coated in a very viscous paint in front of a vertical canvas. It creates a paint filament that stretches before splashing and coiling on the canvas, creating complex patterns that are impossible to recreate without precise control over the paint’s properties. In this talk, I will present various theoretical and numerical results on rotating filament of viscous fluid and discuss how viscosity, surface tension, gravity, inertia and air resistance affect the splashing pattern. First, I will derive a mathematical model for the shape of the paint filament while it is mid-air, and show how it displays very rich physics from viscous boundary layers to self-similar, friction-dominated spirals. Then, I will focus on the splashing pattern. It sometimes displays curly lines remindful of those of the famous “liquid rope coiling”. I will show how we can actually predict the apparition of coiling even with little understanding of the complex mechanisms at work – which Pollock did not have at the time.