Letter abstract
Nature Physics 2, 743 - 748 (2006)
doi:10.1038/nphys432
Subject Category: Fluid dynamics
Phonons in a one-dimensional microfluidic crystal
Tsevi Beatus1, Tsvi Tlusty2 and Roy Bar-Ziv1
The development of a general theoretical framework for describing the behaviour of a crystal driven far from equilibrium has proved difficult1. Microfluidic crystals, formed by the introduction of droplets of immiscible fluid into a liquid-filled channel, provide a convenient means to explore and develop models to describe non-equilibrium dynamics2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Owing to the fact that these systems operate at low Reynolds number (Re), in which viscous dissipation of energy dominates inertial effects, vibrations are expected to be over-damped and contribute little to their dynamics12, 13, 14. Against such expectations, we report the emergence of collective normal vibrational modes (equivalent to acoustic 'phonons') in a one-dimensional microfluidic crystal of water-in-oil droplets at Re
10-4. These phonons propagate at an ultra-low sound velocity of 100 
m s-1 and frequencies of a few hertz, exhibit unusual dispersion relations markedly different to those of harmonic crystals, and give rise to a variety of crystal instabilities that could have implications for the design of commercial microfluidic systems. First-principles theory shows that these phonons are an outcome of the symmetry-breaking flow field that induces long-range inter-droplet interactions, similar in nature to those observed in many other systems including dusty plasma crystals15, 16, vortices in superconductors17, 18, active membranes19 and nucleoprotein filaments20.
- Departments of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel
- Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Correspondence to: Roy Bar-Ziv1 e-mail: barzivr@wisemail.weizmann.ac.il
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