Interface Roughening Dynamics: Temporal Width Fluctuations and the Correlation Length

In this work we study experimentally and numerically the temporal width fluctuations obtained in kinetic roughening of single interfaces. This fluctuative behavior, which results from competing mechanisms in the interface growth process, is shown to contain information on the growth process of the specific interface. We define a measure of the temporal interface width fluctuations in order to extract the correlation length of the interface from the fluctuating data. We study numerically the quenched Kardar-Parisi-Zhang (QKPZ) equation for single interfaces in order to assess the role of the different mechanisms, such as normal growth and surface tension, on the fluctuations. We analyze experimental data of mercury droplets spreading on various metal films (silver and gold) in various thicknesses, as well as data of water spreading on paper (imbibition), in order to demonstrate the validity of our method in a wide range of growing interfaces.