Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator

TL;DR

This study directly measures the renormalized disorder correlator of a contact line's height fluctuations at depinning, confirming predictions from Functional RG theory and exploring deviations for physical insights.

Contribution

First direct experimental measurement of the renormalized disorder correlator Delta(u) for contact lines at depinning, validating Functional RG predictions.

Findings

Measured Delta(u) consistent with Functional RG predictions including a linear cusp.

Observed small deviations from theory that could reveal underlying physical processes.

Compared avalanche-size distributions with theoretical predictions, finding qualitative agreement.

Abstract

We have measured the center-of-mass fluctuations of the height of a contact line at depinning for two different systems: liquid hydrogen on a rough cesium substrate and isopropanol on a silicon wafer grafted with silanized patches. The contact line is subject to a confining quadratic well, provided by gravity. From the second cumulant of the height fluctuations, we measure the renormalized disorder correlator Delta(u), predicted by the Functional RG theory to attain a fixed point, as soon as the capillary length is large compared to the Larkin length set by the microscopic disorder. The experiments are consistent with the asymptotic form for Delta(u) predicted by Functional RG, including a linear cusp at u=0. The observed small deviations could be used as a probe of the underlying physical processes. The third moment, as well as avalanche-size distributions are measured and compared to predictions from Functional RG.