Marangoni-driven patterns, ridges, and hills in surfactant-covered parametric surface waves

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, like squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday wave patterns. We use a quantity $B$, that assesses the relative importance of Marangoni stresses as compared to the the surface wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$. For a surfactant-free interface, a square wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes, and ultimately to ridges and hills. These hills are a consequence of the bi-directional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.