Anomalous Scaling for Hydrodynamic Lubrication of Conformal Surfaces

TL;DR

This paper predicts and confirms a universal power-law scaling of friction coefficient with sliding speed for conformal surfaces in hydrodynamic lubrication, revealing a non-trivial exponent different from traditional models.

Contribution

It introduces a new universal power-law scaling law for conformal surface lubrication, supported by experiments and measurements.

Findings

Friction coefficient scales as S^{2/3} for conformal surfaces.

Deviations at thin films are due to regime crossover, not elastohydrodynamics.

Experimental data confirms the predicted scaling law.

Abstract

The hydrodynamic regime of the Stribeck curve giving the friction coefficient $\mu$ as a function of the dimensionless relative sliding speed (the Sommerfeld number, $S$) of two contacting non-conformal surfaces is usually considered trivial, with $\mu \sim S$. We predict that for conformal surfaces contacting over large areas, a combination of independent length scales gives rise to a universal power-law with a non-trivial exponent, $\mu\sim S^{2/3}$, for a thick lubrication film. Deviations as the film thins (decreasing $S$) may superficially resemble the onset of elastohydrodynamic lubrication, but are due to a crossover between hydrodynamic regimes. Our experiments as well as recent measurements of chocolate lubrication confirm these predictions.