Marangoni-driven patterns, ridges and hills in surfactant-covered parametric surface waves
Author(s)
Type
Journal Article
Abstract
Parametric oscillations of an interface separating two fluid phases create nonlinear surface
waves, called Faraday waves, which organise into simple patterns, such as 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 control parameter,
B, that assesses the relative importance of Marangoni stresses as compared with 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 bidirectional Marangoni stresses
at the neck of the ridges. The mechanisms underlying the pattern transitions and the
formation of exotic ridges and hills are discussed.
waves, called Faraday waves, which organise into simple patterns, such as 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 control parameter,
B, that assesses the relative importance of Marangoni stresses as compared with 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 bidirectional Marangoni stresses
at the neck of the ridges. The mechanisms underlying the pattern transitions and the
formation of exotic ridges and hills are discussed.
Date Issued
2025-04-10
Date Acceptance
2025-02-21
Citation
Journal of Fluid Mechanics, 2025, 1008
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Journal / Book Title
Journal of Fluid Mechanics
Volume
1008
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Identifier
10.1017/jfm.2025.245
Subjects
parametric instability
pattern formation
Faraday waves
Publication Status
Published
Article Number
R4
Date Publish Online
2025-04-10