A new conjecture extends the GM law for percolation thresholds to dynamical situations

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q_2 of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.Comment: 8 pages, latex, 3 figures include

Dense bubble flow in a silo: an unusual flow of a dispersed medium

The dense flow of air bubbles in a two-dimensional silo (through an aperture D) filled with a liquid is studied experimentally. A particle tracking technique has been used to bring out the main properties of the flow: displacements of the bubbles, transverse and axial velocities. The behavior of the air bubbles is observed to present similarities with non-deformable solid grains in a granular flow. Nevertheless, a correlation between the bubble velocities and their deformations has been evidenced. Moreover, a new discharge law (Beverloo-like) must be considered for such a system, where the flow rate is observed to vary as D^{1/2} and depends on the deformability of the particles.Comment: 5 pages, 6 figure

Magnetocapillary self-assemblies: locomotion and micromanipulation along a liquid interface

This paper presents an overview and discussion of magnetocapillary self-assemblies. New results are presented, in particular concerning the possible development of future applications. These self-organizing structures possess the notable ability to move along an interface when powered by an oscillatory, uniform magnetic field. The system is constructed as follows. Soft magnetic particles are placed on a liquid interface, and submitted to a magnetic induction field. An attractive force due to the curvature of the interface around the particles competes with an interaction between magnetic dipoles. Ordered structures can spontaneously emerge from these conditions. Furthermore, time-dependent magnetic fields can produce a wide range of dynamic behaviours, including non-time-reversible deformation sequences that produce translational motion at low Reynolds number. In other words, due to a spontaneous breaking of time-reversal symmetry, the assembly can turn into a surface microswimmer. Trajectories have been shown to be precisely controllable. As a consequence, this system offers a way to produce microrobots able to perform different tasks. This is illustrated in this paper by the capture, transport and release of a floating cargo, and the controlled mixing of fluids at low Reynolds number.Comment: 10 pages, 8 figures review pape

Compound droplet manipulations on fiber arrays

Recent works demonstrated that fiber arrays may constitue the basis of an open digital microfluidics. Various processes, such as droplet motion, fragmentation, trapping, release, mixing and encapsulation, may be achieved on fiber arrays. However, handling a large number of tiny droplets resulting from the mixing of several liquid components is still a challenge for developing microreactors, smart sensors or microemulsifying drugs. Here, we show that the manipulation of tiny droplets onto fiber networks allows for creating compound droplets with a high complexity level. Moreover, this cost-effective and flexible method may also be implemented with optical fibers in order to develop fluorescence-based biosensor

Waveguides for walking droplets

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce without coalescing. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d confinement is optimal for narrow channels of width of $D \simeq 1.5 \lambda_F$. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.Comment: 8 pages, 6 figure

Statics and dynamics of magnetocapillary bonds

When ferromagnetic particles are suspended at an interface under magnetic fields, dipole-dipole interactions compete with capillary attraction. This combination of forces has recently given promising results towards controllable self-assemblies, as well as low Reynolds swimming systems. The elementary unit of these assemblies is a pair of particles. Although equilibrium properties of this interaction are well described, dynamics remain unclear. In this letter, the properties of magnetocapillary bonds are determined by probing them with magnetic perturbations. Two deformation modes are evidenced and discussed. These modes exhibit resonances whose frequencies can be detuned to generate non-reciprocal motion. A model is proposed which can become the basis for elaborate collective behaviours

Remote control of self-assembled microswimmers

Physics governing the locomotion of microorganisms and other microsystems is dominated by viscous damping. An effective swimming strategy involves the non-reciprocal and periodic deformations of the considered body. Here, we show that a magnetocapillary-driven self-assembly, composed of three soft ferromagnetic beads, is able to swim along a liquid-air interface when powered by an external magnetic field. More importantly, we demonstrate that trajectories can be fully controlled, opening ways to explore low Reynolds number swimming. This magnetocapillary system spontaneously forms by self-assembly, allowing miniaturization and other possible applications such as cargo transport or solvent flows.Comment: 5 pages, 5 figures articl