Butter on a hot pan: self-regulating dynamics of melt-lubricated sliding
Abstract
When solids melt while sliding down heated inclines, their motion is governed by a complex coupling between heat transfer, phase change, gravity and viscous dissipation. Despite relevance across a variety of domains, like kitchen physics, geophysics, tribology, and manufacturing, this coupled problem lacks understanding and quantitative experimental validation. Here we report experiments with ice and paraffin wax on a temperature-controlled ramp that achieve terminal velocities from 0.01 m/s to 2 m/s across wide parameter ranges. We develop a theoretical model that captures the self-regulating feedback between melt-layer thickness, sliding velocity, and heat transfer. Without any adjustable parameters, our model collapses all measurements, validating the fundamental mechanism and enabling predictions for analogous systems.
Cite
@article{arxiv.2603.09494,
title = {Butter on a hot pan: self-regulating dynamics of melt-lubricated sliding},
author = {Edoardo Bellincioni and Simon Biermann and Jacco H. Snoeijer and Leen van Wijngaarden and Sander G. Huisman},
journal= {arXiv preprint arXiv:2603.09494},
year = {2026}
}