The physics of 2D microfluidic droplet ensembles

Tsevi Beatus*, Roy H. Bar-Ziv, Tsvi Tlusty

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

81 Scopus citations


We review non-equilibrium many-body phenomena in ensembles of 2D microfluidic droplets. The system comprises of continuous two-phase flow with disc-shaped droplets driven in a channel, at low Reynolds number of 10 -4-10 -3. The basic physics is that of an effective potential flow, governed by the 2DLaplace equation, with multiple, static and dynamic, boundaries of the droplets and the walls. The motion of the droplets induces dipolar flow fields, which mediate 1/r 2 hydrodynamic interaction between the droplets. Summation of these long-range 2D forces over droplet ensembles converges, in contrast to the divergence of the hydrodynamic forces in 3D. In analogy to electrostatics, the strong effect of boundaries on the equations of motion is calculated by means of image dipoles. We first consider the dynamics of droplets flowing in a 1D crystal, which exhibits unique phonon-like excitations, and a variety of nonlinear instabilities-all stemming from the hydrodynamic interactions. Narrowing the channel results in hydrodynamic screening of the dipolar interactions, which changes salient features of the phonon spectra. Shifting from a 1D ordered crystal to 2D disordered ensemble, the hydrodynamic interactions induce collective density waves and shocks, which are superposed on single-droplet randomized motion and dynamic clustering. These collective modes originate from density-velocity coupling, whose outcome is a 1D Burgers equation. The rich observational phenomenology and the tractable theory render 2D droplet ensembles a suitable table-top system for studying non-equilibrium many-body physics with long-range interactions.

Original languageAmerican English
Pages (from-to)103-145
Number of pages43
JournalPhysics Reports
Issue number3
StatePublished - Jul 2012
Externally publishedYes


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