Experimental analysis of one-dimensional Faraday waves on a liquid layer subjected to horizontal vibrations

Abstract

In this paper, we experimentally show the synchronous (harmonic) nature of the primary surface waves formed on a layer of water (∼1 mm) pinned to a glass substrate and subjected to horizontal (lateral) vibrations. With well-controlled experiments, we attenuated cross-waves and studied the primary standing waves in a one-dimensional wave configuration, with a high precision mechanical vibrator, capable of generating a range of forcing frequencies (100–500 Hz) and amplitudes (1–5 µm). We demonstrate that the emergence of instability (in the form of standing waves) depends upon the forcing amplitude and frequency and the average thickness of the liquid layer. Experiments reveal that the surface remains stable for sufficiently thin and thick layers of the liquid, while instability appears for thicknesses in between the two mentioned lower and upper limits. We show and analyze that, for the average liquid thickness of h = 1.5 mm, asymmetric modes of oscillations appear on the liquid surface; however, with a change in the film thickness and length of the surface profile, symmetric modes may occur as well (h = 2 mm). The problem studied here, i.e., a liquid film with pinned contact lines subjected to horizontal vibrations, shows some of the characteristics of an infinitely extended lateral liquid film, a liquid layer in a container with walls, and a sessile droplet.