Waiting and Residence Times of Brownian Interface Fluctuations

TL;DR

This study investigates the residence and waiting times of capillary wave fluctuations at interfaces in colloid-polymer systems, revealing how these times depend on measurement intervals and correlating well with theoretical predictions.

Contribution

It provides a detailed analysis of the stochastic behavior of Brownian interface fluctuations and introduces a method to relate measurement interval effects to the height-height correlation function.

Findings

Excellent agreement between theory and experiments

Waiting times depend on measurement interval and correlation function

Method applicable to other Brownian interface systems

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 $\Delta t$. 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 $g(t)$. We find excellent agreement with the theory presented here along with the experiments.