Topology of hydrothermal waves in liquid bridges and dissipative structures of transported particles.

High-resolution three-dimensional numerical simulations are carried out for hydrothermal waves in a thermocapillary liquid bridge with Prandtl number Pr=4 and length-to-radius aspect ratio Γ=0.66. The flow topology is analyzed using Poincaré sections in a frame of reference co-rotating with the phase velocity of the wave. We find regions of regular and chaotic motion. The regular regions are shown to be of key importance for dissipative structures of transported particles. Suspended particles which are passively advected in the bulk, but experience dissipation in a thin layer below the free surface, can rapidly form dissipative structures, also called particle accumulation structures. The shape and the formation time of the particulate structures are determined by the location of the invariant tori of the flow field with respect to the sub-surface layer in which the dissipation of the particle motion acts. The results from a hard-wall particle-free-surface interaction model are in good agreement with experimental observations.