Theory of Marangoni spreading
Drop some dishwasher liquid or soapy water over a pool of clean water and it will spread outward over the the pool’s surface. The basic physics behind this daily phenomenon is well-known: Surfactant molecules such as soap gather at the air-water interface and locally alter the surface tension, inducing a flow in the underlying water. This kind of
Marangoni effect has long been studied and is understood in a variety of phenomena, such as in the celebrated tears of wine [1].
It may therefore come as a surprise that
Marangoni spreading, seen daily in the kitchen, has long evaded an exact mathematical description. Some recent progress [2] indicates that surfactant transport can be mapped to a single
complex Burgers equation, which allows to identify a complet set of exact solutions. They reveal that the non-linearity of the spreading problem gives rise to a rich variety of behaviors and that the initial surfactant distribution has a key influence on the subsequent evolution.
The goal of the internship is to investigate, theoretically, Marangoni spreading. Beyond the simplified one-dimensional model situation considered so far, there is a host of situations that await exploration: from two-dimensional spreading to finite-depth pool and Marangoni swimmers that self-propel by releasing surfactant. The student will combine two approaches:
analytical calculations and numerical simulations within the framework of an electrostatic analogy.
The internship is a first step toward a PhD thesis. This topic lies at the confluence of
soft matter, fluid mechanics and statistical physics. Strong background in one of these fields and a taste for theoretical and numerical approaches would be ideal.
Opening toward a PhD: yes (funding with «bourse ministère»).
Contacts:
Francois Detcheverry,
francois.detcheverry@univ-lyon1.fr Team
Liquides et Interfaces, Institut Lumière Matière, Lyon
Thomas Bickel,
thomas.bickel@u-bordeaux.fr Team
Theory of Condensed matter, LOMA, Bordeaux
References:
[1] Capillarity and wetting phenomena: drops, bubbles, pearls, waves, De Gennes et al, (Springer Verlag, 2004).
[2] Exact solutions for viscous Marangoni spreading, Bickel and Detcheverry,
Physical Review E (2022).
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Modifié 1 fois. Dernière modification le 13/10/25 10:21 par François Detcheverry.