Marangoni-driven pattern transitions in surfactant-covered Faraday waves*

Parametric vibration of an interface results in the formation of standing waves of frequency half of the vibration, called Faraday waves. Owing to the capillary-gravity dispersion relation, these standing waves select a wavenumber at a certain vibrating frequency. Depending on the direction and number of unstable wave modes, N-fold symmetric patterns are usually formed, of which stripes (N=1) and squares (N=2), are the simplest. Complexities such as contact-line dissipation, viscosity, and surface contamination are well known to affect even the simplest patterns like squares. In the previous studies, surfactant-like surface contaminants are studied to elucidate the damping mechanism, wavelength selection, and the Marangoni stresses on the structure of the surface waves. However, these studies are limited to linearised, one- or two- dimensional, some of which carried out in lubrication limit [1], with a dearth of fully three-dimensional study of Marangoni stresses on the pattern formation in the strongly nonlinear regime. In this work, we report the three-dimensional spatio-temporal evolution and pattern transitions induced by Marangoni-driven surface flows. We introduce a characteristic parameter B, a ratio of Marangoni and inertial time scales, to rationalise the pivotal point of pattern transition in surfactant-covered Faraday waves. Beyond B = 1, square patterns transition to asymmetric squares, weakly wavy stripes, and beaded-squares with oscillon-like physical features, which we call bulbous structures.   These newly observed structures are a consequence of the heterogenous Marangoni-driven surface backflow on the beaded stripes. With the advantage of high-fidelity direct numerical simulations, we uncover the physics of the formation of these structures and their spatio-temporal evolution.

References:

[1] Kumar, S., & Matar, O. K. (2004). On the Faraday instability in a surfactant-covered liquid. Physics of Fluids, 16(1), 39-46.