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

¹  CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75005 Paris, France, EU
²  Laboratoire de Physique Statistique, (ENS, CNRS, Universités Paris 6 et Paris 7) - 24 rue Lhomond, 75005 Paris, France, EU
³  Laboratoire Jean Perrin (CNRS, Université Paris 6) - 24 rue Lhomond, 75005 Paris, France, EU

Corresponding authors: ledou@lpt.ens.fr wiese@lpt.ens.fr moulinet@lps.ens.fr etienne.rolley@lps.ens.fr

Received: 29 April 2009
Accepted: 18 August 2009

Abstract

We measure 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 , predicted by Functional RG 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 predicted by Functional RG, including a linear cusp at . 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.