Butter on a hot pan: self-regulating dynamics of melt-lubricated sliding

TL;DR

This study investigates the self-regulating dynamics of melt-lubricated sliding, combining experiments with ice and wax and a theoretical model to understand the complex heat transfer and phase change processes involved.

Contribution

The paper introduces a parameter-free theoretical model that accurately predicts melt-lubricated sliding behavior across various conditions, validated by extensive experiments.

Findings

Experimental velocities range from 0.01 m/s to 2 m/s.

The model captures the feedback between melt-layer thickness and heat transfer.

Validation across wide parameter ranges confirms the model's predictive power.

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.