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.

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The accumulation of small mono-disperse heavy particles in thermocapillary liquid bridges is investigated experimentally and numerically. We consider particle accumulation near the center of the toroidal vortex, the so-called toroidal core of particles (COP), and the particle-depletion zone near the axis of the liquid bridge. Based on the acceleration and deceleration of the tangential flow along the thermocapillary free surface it is argued that the interaction of the particles with the free surface is of key importance for the fast particle accumulation within a few characteristic momentum diffusion times. The experimentally determined particle-accumulation times are compared with time-scale estimates for accumulation due to either particle free-surface interaction or due to inertia of particles which are heavier than the liquid. We show that the experimental accumulation times are compatible with the accumulation times predicted by the particle-free-surface interaction (PSI) while the time-scale estimates based on the inertia of the particles are too large to explain the fast de-mixing observed in experiments. The shape of the COP resembles certain KAM tori of the incompressible flow of a hydrothermal wave. Two scenarios are proposed to explain the structure and the dynamics of the COP depending on the existence or non-existence of suitable KAM structures. The shape of the experimental particle-depletion zone agrees well with the release surface which is defined by the particle-free-surface interaction process. The favorable comparison of the dynamics and structure of experimental and numerical accumulation patterns provides strong evidence

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