Study of the stability of a thermo-capillary boundary layer with a deformable free surface

During uranium enrichment, convective movements of the liquid metal are generated by floatability forces and, above all, by thermo-capillary forces. In some circumstances, a movement of the surface occurs which drives the fluid by viscosity. This thermo-capillary effect is called Marangoni effect. This research thesis notably aims at distinguishing the different regimes and structures of a thermo-capillary boundary layer. In a first part, the author gives an overview of the situation of researches on instability by addressing some specific instabilities (of boundary layer, thermo-capillary) and their mechanisms (case of plane flow, inclined flow). The second part addresses the linear stability of a thermo-capillary boundary layer: base flow (physical model, equations and boundary conditions, search for affine solutions, flow analysis), analytical study (study of the linear stability, resolution of stability equations), stability of a thermo-capillary boundary layer (not deformable free surface, deformable free surface, comparisons). The last part reports an energy approach to physical mechanisms through an analytical study of both types of free surface (deformable or not), and of instability mechanisms for a thermo-capillary boundary layer (analysis and distribution of energy transfers)