Faraday-Wave Contact-Line Shear Gradient Induces Streaming and Tracer Self-Organization: From Vortical to Hedgehoglike Patterns

Abstract

In this Letter, we experimentally demonstrate self-organization of small tracers under the action of longitudinal Faraday waves in a narrow container. We observe a steady current formation dividing the interface in small cells given by Faraday-wave symmetries. These streaming currents rotate in each cell, and their circulation increases with wave amplitude. This streaming flow drives the tracers to form patterns, whose shapes depend on the Faraday-wave amplitude: From low to high amplitudes, we find tracers dispersed on vortices, narrow rotating rings, and a hedgehoglike pattern. We first describe the main pattern features and characterize the wave and tracers' motion. We then show experimentally that the main source of the streaming flow is the spatiotemporal-dependent shear at the wall contact line created by the Faraday wave itself. We end by presenting a 2D compressible advection model that considers the minimal ingredients present in the Faraday experiment, namely, the stationary circulation, the stretching component due to the oscillatory wave, and a steady converging field, which combined produce the observed self-organized patterns.