Curriculum Vitae - APC - Université Paris Diderot-Paris 7

definitely convinced us that the trapping time could exceed the typical exit time of an isolated
droplet by several orders of magnitude.
These questions are in principle, connected to optimization problems. As a matter of fact, for
droplets advected in a pipe network, we know that at a vertex, a droplet follows the direction
where the elongation rate is maximal. Therefore, it can be shown that these trajectories
correspond to the path followed by a particle, which would explore a tilted random potential
according to the steepest descent algorithm. The corresponding random potential is linearly
related to the local conductivity (or permeability) field of the fluidic network in a nonlocal
manner. We expect this analogy will give us access to new tools to investigate the statistics of
the trajectories in disordered networks.
4.5.1.2. Strong clogging: Clogging/Unclogging transition.
We propose to study the clogging/unclogging transition in networks filled with deformable
particles in the strong clogging regime. For an isolated droplet, the exact resolution of the
hydrodynamic problem is complex. However, it is conceptually simple at a qualitative level,
see Fig. 4. As the particle density is increased, the problem becomes highly non-trivial as it
involves a large number of hydrodynamically coupled particles in a strongly disordered
environment. Firstly, we purpose to measure how the mean droplet current at the outlet varies
as we increase the imposed driving pressure, and the particle density. It is very likely to
observe a continuous “depinning” transition from a creep to a stationary flow regime. In [10]
Watson and Fisher considered theoretical model close to the proposed set-up. They uncovered
a continuous “second order” transition from static to stationary flows through the network.
Interestingly, close to the onset of the network congestion, the flow was shown to take place
along very sparse sub-networks of flowing channels.
We will analyze the typical size and the shape of the mobile regions close to the unclogging
transition, by measuring the displacement-displacement two-point correlation functions. We
will study the variations of the corresponding correlation length close to the unclogging
transition. Another quantity, which will be simply accessible in our experiments, is the
lifetime of the flowing regions, which should diverge at the onset of the network unclogging
if the transition is indeed a genuine dynamic critical phenomena. Our first experiments will be
performed in wide microfluidic Hele-Shaw cells including random (but controlled)
distributions obstacles (posts).
4.5.2 Traffic flows of self-propelled particles in simple and disordered geometries.
As mentioned above, we have already exploited the Quincke effect to devise a new
experimental set-up intended to manipulate and to observe artificial active colloids. We are
currently investigating the individual dynamics of these particles, which is a necessary first
step prior to any traffic experiment. We are currently characterizing the statistics of the
persistent random walks performed by colloidal rollers: e.g. the variations of the velocity and
of the persistence length with the applied field and the size of the colloid. Once this first set of
results will be obtained, we will proceed to the collective dynamics of Quincke rollers.
4.5.2.1. Motile colloids in homogeneous media: emergence and stability of colloidal
swarms.