Polygonal instability of Marangoni flows

The transport of pepper grains floating at the surface of a bowl of water after the release of a drop of dishwashing liquid is a classical experiment to demonstrate the Marangoni effect, i.e. the flow of a liquid layer induced by interfacial tension gradients at its surface. In this case, the interfacial tension gradient results from a surfactant interfacial concentration gradient. Recently, we showed that continuous injection of an aqueous solution of hydrosoluble surfactants at the surface of a cm-thick pure water layer induced finite-size Marangoni flows surrounded by a region characterized by the presence of several pairs of interfacial vortices arranged along the the vertices of polygons.\footnote{M. Roch\'{e} et al., \textbf{Phys. Rev. Lett.} 112, 208302 (2014)} During this talk, I will show that we can understand the flow structure induced by these Marangoni flows, in particular their tendency to have polygonal shapes. I will describe how flow features such as the number of interfacial vortices or bulk recirculation flows depend on flow geometry. Finally, I will compare these results to a model that explains similar polygonal instabilities in other flows such as the hydraulic jump.\footnote{M. Labousse and J. W. M. Bush, submitted}