Stationary solid particle attractors in standing waves

The present analysis extends earlier theories on patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow by considering the case in which the particle carrier flow has the typical features of a "standing wave." For the first time an explanation for this phenomenon is elaborated through arguments based on the interplay between vorticity and wave-interference dynamics (following a deductive approach after the so-called phase-locking or "resonance" model originally introduced by Pushkin et al. [Phys. Rev. Lett. 106, 234501 (2011)] and later variants developed by Lappa [Phys. Fluids 25(1), 012101 (2013) and Chaos 23(1), 013105 (2013)]). The results of dedicated numerical simulations are used in synergy with available experimental work. An interesting analogy is proposed with the famous Chladni's series of experiments on patterns formed by sand on vibrating plates.