Space-time-resolved measurements of the effect of pinned contact line on the dispersion relation of water waves

Abstract

We report on an experimental investigation of the propagation of gravity-capillary waves in a narrow channel with a pinned contact line. By using Fourier transform profilometry we measure the static curved meniscus as well as the surface perturbation. By varying the channel width, between 7 and 15 times the capillary length, we show how edge constraints modify the surface curvature and therefore the dispersion relation. From the space-time-resolved field, we obtain a decomposition of the linear mode onto transverse modes satisfying the condition of pinned contact line. This approach, in which we complement the theoretical model with experimental analysis, allows computations of wave numbers and natural frequencies with a robust statistics. We verify experimentally the convergence of the model and the pertinence of the linear approximation. In addition, we analyze the relative contribution of the experimentally measured static meniscus. An excellent agreement between the computed natural frequencies and the forcing frequency confirms the contribution of the actual space-time-resolved measured surface. These experimental results are an accurate estimation of the influence of the additional restoring force exerted by the pinned contact line on the deformed surface which increases the wave celerity. The local character of this effect is evidenced by the decrease of the shift of the dispersion relation as a function of the channel width.