title: Hamiltonian traffic dynamics in microfluidic-loop networks.
abstract: Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain poorly understood. In this Letter, we focus on the transport of a finite number of particles in one-dimensional loop networks. By combining numerical, theoretical, and experimental efforts, we evidence that this collective process offers a unique example of Hamiltonian dynamics for hydrodynamically interacting particles. In addition, we show that the asymptotic trajectories are necessarily reciprocal despite the microscopic traffic rules explicitly break the time-reversal symmetry. We exploit these two remarkable properties to account for the salient features of the effective three-particle interaction induced by the exploration of fluidic loops.
authors.affiliation: PMMH ESPCI-ParisTech, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin 75231 Paris cedex 05 France.
authors.forename: Raphaël
authors.initials: R
authors.lastname: Jeanneret
authors.forename: Julien-Piera
authors.initials: JP
authors.lastname: Vest
authors.forename: Denis
authors.initials: D
authors.lastname: Bartolo