Residence and waiting times of Brownian interface fluctuations

¹  Van 't Hoff Laboratory for Physical and Colloid Chemistry, University of Utrecht - Padualaan 8, 3584 CH Utrecht, The Netherlands
²  Instituut-Lorentz for Theoretical Physics, Leiden University - Niels Bohrweg 2, Leiden, 2333 CA, The Netherlands
³  Physical and Theoretical Chemistry Laboratory, University of Oxford - South Parks Road, Oxford OX1 3QZ, UK

Received: 12 October 2007
Accepted: 22 January 2008

Abstract

We report on the residence times of capillary waves above a given height h and on the typical waiting time in between such fluctuations. The measurements were made on phase-separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval . In experiments, the discrete scanning times are a practical cutoff and we are able to measure the waiting time as a function of this cutoff. The measurement interval dependence of the observed waiting and residence times turns out to be solely determined by the time-dependent height-height correlation function . We find excellent agreement with the theory presented here along with the experiments.