Different types of Lagrangian coherent structures formed by solid particles in three-dimensional time-periodic flows

Modeling of the experments on formation of coherent structures (also called particle accumulation structures, or PAS) in a three-dimensional time-periodic flow in a finite-size liquid column driven by a combined effect of thermocapillary stress and buoyancy was performed. The exact experimental conditions were studied. We considered particles 1% denser than the fluid. Aiming at reproducing the observed variety of PAS, double-loop (SL-II) and asymmetric single-loop (ASL-I) structures were obtained along with a "conventional" symmetric single-loop PAS (SL-I). The observations are perfectly in line with the experiments. It is shown that the limit trajectory of a particle is not only a matter of the particle's inertia but also of its initial location. We developed a method to calculate the formation time of a structure. The obtained values are very close to those experimentally measured.