Finite-size Lagrangian coherent structures in thermocapillary liquid bridges

Abstract

The rapid accumulation of small, finite-size rigid particles along closed rotating threads in high-Prandtl-number thermocapillary liquid bridges is investigated numerically when the flow arises as a traveling hydrothermal wave. For a dilute suspension, different motion models are investigated which could provide the dissipation mechanisms leading to the experimentally observed particle-motion attractors. Making use of a phenomenological particle-boundary interaction model, it is shown that the particle size effect, which becomes important when the particle moves near the thermocapillary free surface, provides the relevant source of dissipation for the remarkably fast particle accumulation. Furthermore, the accumulation phenomenon is tightly correlated with the Kolmogorov-Arnold-Moser (KAM) tori of the flow in the absence of particles. Therefore, KAM tori in the rotating frame of reference, in which the flow field is steady, can be considered templates for the accumulation structures. The numerical results obtained are compared with experimental data for the so-called spiral loop 1 and spiral loop 2 particle accumulation structures. In addition, other accumulation structures are numerically predicted which yet await experimental confirmation.