TY - JOUR
T1 - The physics of 2D microfluidic droplet ensembles
AU - Beatus, Tsevi
AU - Bar-Ziv, Roy H.
AU - Tlusty, Tsvi
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84862759138&partnerID=8YFLogxK
U2 - 10.1016/j.physrep.2012.02.003
DO - 10.1016/j.physrep.2012.02.003
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.systematicreview???
AN - SCOPUS:84862759138
SN - 0370-1573
VL - 516
SP - 103
EP - 145
JO - Physics Reports
JF - Physics Reports
IS - 3
ER -