Curriculum Vitae - APC - Université Paris Diderot-Paris 7

4.3. State of the art: Why is it new?
We review briefly the state of the art to further stress on the originality and novelty of our
project. The following description is intentionally subjective. The reference list is not
supposed to be comprehensive but rather representative of our perspective on this project.
The transport problems we are interested in are connected to four main classes of studies
performed in very different contexts:
(i) Numerous experiments have been devoted to the filtration of solid particles in artificial
filters. For instance, the typical deep-bed-filtration experiments consist in flowing solid
particles through a random packing of hard spheres of larger diameter. So far, the experiments
have been focused on global and stationary quantities, such as the particle penetration length,
see e.g. [9]. Typically, the outcome of these experiments has been rationalized in the context
of percolation models [9]. The limitation to these experimental works is twofold. First, the
observation of the particle motion through membranes or bead-based filters is extremely
difficult if not impossible for concentrated suspensions. In addition, the geometry of such
random media cannot be controlled and tuned but merely characterized once formed.
Arguably, the microfluidic technologies are very well suited to overcome these limitations.
The lithographic technique are perfectly suited to devise obstacle networks with wellcontrolled
geometries, see eg [8] and Fig. 2a in section IV. In addition, the conventional
microfluidic devices offer perfect imaging conditions.
(ii) Over the last five years, much effort has been devoted to investigate the trafficking
dynamics of droplets in minimal microfluidic geometries, such as a single T-junction or a
single loop [6,7]. Despite the simplicity of the network geometry, these experiments have
revealed complex dynamics: multiple periods, chaos… The non-linearities, which make the
dynamics non-trivial, arise from the hydrodynamic interaction rule at the vertices of the
network. We have recently generalized these approaches to infinite 1D and 2D loop networks
[8]; see the first results in section IV. We are not aware of any other microfluidc traffic
experiments in extended networks.
(iii) From a more fundamental perspective, the traffic dynamics in a random fluidic network
can be considered as a depinning process in the strong disorder limit [10]. So far most of the
experimental investigations have been focused on the weak disorder limit, which
encompasses, the motion of elastic lines and elastic networks in random potentials such as
liquid-solid contact lines, magnetic domain walls. Conversely, the strong disorder limit
remains quite unexplored, even from a theoretical perspective. In the 90s Fisher et al proposed
a minimal model for the transport of particles driven in a strongly disordered network and
interacting dynamically. This model predicts several non-trivial collective behaviours,
including a continuous depinning transition above a finite fluid driving threshold [10]. As the
driving amplitude is increased the system experience a genuine phase transition from a static
state to a steadily flowing state, where the particles flow cooperatively through very sparse
subnetworks. So far, no experimental evidence of such a dynamical transition exists.
(iv) Finally, in a very different context, a surge of theoretical papers devoted to the dynamics
of interacting self-propelled agents has been published over the last ten years, see [11-14] for
extensive reviews. To keep a long and on going story short, two type of agent based models
have been successfully exploited to describe the fluctuations of traffic flows in simple
geometries: the Vicsek model [12], and the so-called exclusion processes (cellular automata)
[13], which are mostly restrained to 1D or quasi 1D systems. Successful condensed matter
and fluid mechanics approaches have also been put forward. However, these works mostly