Curriculum Vitae - APC - Université Paris Diderot-Paris 7

let to sediment from a dilute suspension. As no injection channels will be needed, we will
achieve perfect periodic boundary conditions.
Figure 6. A-Sketch of Quincke rotators rolling coherently along a circular track. B-Car rolling on a circular
road, from [41].
A single particle should undergo a 1D persistent random walk. For Brownian colloids at
equilibrium, this setup is a prototypal realization of single-file diffusion dynamics, as
demonstrated in [24]. What is the collective traffic behavior of the self-propelled rollers? The
particle will interact hydrodynamically and via the electrostatic dipole-dipole repulsion at
short distances, which will result in non-trivial collision rules. If a moving colloid “pushes
electrostatically” one of its neighbor, the induced translation should result in a net rotation
along the same axis as the incoming particle. Therefore coherent motion is expected along the
1D road, in strong contrast with the subdiffusive equilibrium behavior [24]. We will test this
hypothesis and measure both the size and the lifetime of the colloid trains moving coherently.
Somehow related models for coupled molecular motors, suggests that the collective dynamics
should display a strong persistence [25].
By applying an external shear on top of the circular track, we will also explicitly break the
symmetry and enforce coherent clockwise motion. We will use this protocol to reproduce the
macroscopic vehicle traffic experiments shown in Fig. 6B [26]. We will test the emergence of
spontaneous jams without bottleneck. To rationalize our findings, we will characterize and
model the current-density constitutive relation in this elementary 1D geometry. These
experiments will allow us to check the relevance of such microfluidic experiments as analog
simulators of macroscopic traffic flows.
4.5.2.3. Traffic dynamics in ordered and disordered 2D networks.
The first traffic experiments in a non-trivial 2D geometry will be performed in a periodic
channel network, Fig. 7A. The size of the particles will be comparable to the channel width
(typically 5 microns), and the channel length will be chosen larger that the colloid diameter,
thereby making the electrostatic interactions between the particles negligible in the dilute
regimes. As we showed it in [8], in the case of advected particles, the perturbation to the flow
induced by the motion of a single roller will have a dipolar symmetry, whatever the specifics
mechanism responsible for the self-propulsion at the colloidal scale, Fig 7B. This property
will make our observations and our predictions independent on the type of self-propelled
particle at work.
Before investigating the emergence of collective behavior, we will first address a simpler
question: is an ordered traffic flow stable? We will use dilute systems of Quincke rollers
forced to flow in a given direction by applying and external pressure difference to the
microfluidic device. When the pressure difference is set to zero, all the colloids should keep
on rolling along the same direction, Fig. 7A. The resulting dipolar perturbations around the
rollers could in principle destabilize the unidirectional motion, Fig. 7B. A first question is
then: can the dipolar interactions result in the “meting” of the ordered traffic? The
consequences of this “structural” change on the transport properties will be investigated as