Coherent structures formed by small particles in traveling-wave flows

We experimentally verify the "phase locking model,"which describes the formation of one-dimensional coherent structures by low-Stokes-number particles as proposed by Pushkin et al. [Phys. Rev. Lett. 106, 234501 (2011)0031-900710.1103/PhysRevLett.106.234501] in thermocapillary liquid bridges: When the particles form the coherent structures in time-periodic flows, the synchronous coupling of the toroidal vortex and the azimuthally traveling wave is achieved for a range of azimuthal wave number m. We further propose coherent structures of rational wave numbers in the azimuthal direction and unveil those experimentally.