Self-assembly of inertial particles in time-periodic flows
Dmitri O. Pushkin
MRC, University of Brussels, Belgium
Abstract:
We show that small, heavier than the surrounding fluid, macroscopic particles may spontaneously organize in ordered structures in time-periodic incompressible flows [1]. Unlike particle accumulation/segregation patterns studied in the past, these structures are dynamic and can not be understood as asymptotic locations of individual particles. Instead, we show that the coherent structures arise due to synchronization of motion of individual particles, which takes place in time-periodic flows. The proposed synchronization mechanism hinges on the nonlinear phenomenon of phase-locking or frequency-locking.
This novel mechanism of particle ordering explains the surprising assembly of particles into rotating spirals that was discovered experimentally in thermocapillary flows more than a decade ago [2]. Although the phenomenon has been extensively studied on the ground and on board of the International Space Station, its comprehensive explanation has been lacking.
In our exposition we introduce a simple model of fluid-particle interaction, which can be reduced to the circle map. This theoretical approach allows establishing a correspondence between the geometrical shapes of the ordered particulate spirals, which have been observed in experiments and our numerical simulations, and the phase-locked regions of the circle map known as Arnold tongues. We discuss further parallels between dynamical behaviour of the circle map and features of particle ordering observed in experiments and numerical simulations, such as intermittent rise and fall of the coherent particulate structures.
We find that synchronization of motion of small particles in time-periodic flows is a generic effect. Therefore, it may cause localization and ordering of particles in large-scale periodic flows that abound in nature and technological applications.
[1] D.O. Pushkin, D.E. Melnikov and V.M. Shevtsova, ``Particle self-ordering in periodic flows: stadium wave in a drop'', 2010 (submitted).
[2] D. Schwabe et al., ``New features of thermocapillary convection in floating zones revealed by tracer particle accumulation structures (PAS)'', Microgravity Sci. Technol. 9, 163 (1996).