Marc Fermigier

Microscopic artificial swimmers

Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

AGGREGATION KINETICS OF PARAMAGNETIC COLLOIDAL PARTICLES

Magnetic‐field‐induced chain formation of superparamagnetic latex particles is investigated via optical microscopy and digital image analysis. Our experiment is unique in that the aggregation process takes place in the bulk, where particles are free to diffuse in three dimensions, rather than on a surface. We find that the mean chain size 〈s(t)〉 has a power‐law dependence on time, 〈s(t)〉∼tz, as predicted by the Smoluchowski equation and three‐dimensional simulations of diffusion‐limited aggregation of oriented particles. The value of the exponent z is found to have a weak inverse dependence on particle volume fraction φ and dimensionless dipole strength λ. We propose a new model for a characteristic time scale proportional to 1/λ and 1/φ. Comparison with experimental observations shows this scaling to be very effective but to break down suddenly above a critical volume fraction.

An experimental investigation of the dynamic contact angle in liquid-liquid systems

Abstract We report measurements of dynamic contact angles performed during the displacement of silicone oil/air and silicone oil/glycerin interfaces in capillary glass tubes. The data obtained for the liquid/air interfaces are in good agreement with other experiments performed by other authors. They also agree with the so-called Hoffman-Tanner law, and with theoretical estimates done by Cox. On the other hand, results obtained with liquid/liquid interfaces show a systematic increase of the dynamic angle compared to theoretical predictions. There are two possible explanations of this fact, which is also reported by other authors. One of them is related to the additional energy dissipation occurring when the contact line moves on a heterogeneous surface. The other one is based on molecular dynamics simulations by Robbins and Thompson, and relies on the influence of slip boundary conditions on the dynamic angle.

Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer

We study experimentally and theoretically the evolution of two-dimensional patterns in the Rayleigh—Taylor instability of a thin layer of viscous fluid spread on a solid surface. Various kinds of patterns of different symmetries are observed, with possible transition between patterns, the preferred symmetries being the axial and hexagonal ones. Starting from the lubrication hypothesis, we derive the nonlinear evolution equation of the interface, and the amplitude equation of its Fourier components. The evolution laws of the different patterns are calculated at order two or three, the preferred symmetries being related to the non-invariance of the system by amplitude reflection. We also discuss qualitatively the dripping at final stage of the instability.

On the dynamics of magnetically driven elastic filaments

Following a novel realization of low-Reynolds-number swimming (Dreyfus et al. , Nature , vol. 436, 2005, p. 862), in which self-assembled filaments of paramagnetic micron-sized beads are tethered to red blood cells and then induced to swim under crossed uniform and oscillating magnetic fields, the dynamics of magnetoelastic filaments is studied. The filament is modelled as a slender elastica driven by a magnetic body torque. The model is applied to experiments of Goubault et al. ( Phys. Rev. Lett. , vol. 91, 2003, art. 260802) to predict the lifetimes of metastable static filament conformations that are known to form under uniform fields. A second experimental swimming scenario, complementary to that of Dreyfus et al. (2005), is described: filaments are capable of swimming even if not tethered to red blood cells. Yet, if both ends of the filament are left free and the material and magnetic parameters are uniform along its length then application of an oscillating transverse field can only generate homogeneous torques, and net translation is prohibited by symmetry. It is shown that fore–aft symmetry is broken when variation of the bending stiffness along the filament is accounted for by including elastic defects, which produces results consistent with the swimming phenomenology.

Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation

The relaxation of a dewetting contact line is investigated theoretically in the so-called ‘Landau–Levich’ geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified ‘quasi-static’ theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Ca c , the contact line is linearly stable at all wavenumbers. Away from the critical point, the dispersion relation has an asymptotic behaviour σ∝| q | and compares well to a quasi-static approach. Approaching Ca c , however, a different mechanism takes over and the dispersion evolves from ∼| q | to the more common ∼ q 2 . These findings imply that contact lines cannot be described using a universal relation between speed and apparent contact angle, but viscous effects have to be treated explicitly.

Gravitational instabilities of thin liquid layers: dynamics of pattern selection

Abstract We present recent results obtained in the study of the instabilities induced by gravity on liquid layers hanging below solid surfaces, in situation of perfect wetting (without contact lines). Two cases are discussed: two-dimensional films of constant volume, and films continuously supplied with “fresh” liquid by an external source. In the first case, we show experimental evidences suggesting that the formation of a two-dimensional structure within the film arises by means of front propagation mechanisms. In the simplest situation, propagation of a one-dimensional structure (“roll” formation), the measured front speed is close to that deduced from the linear marginal stability theory. In the second case, the liquid film is hanging below an horizontal overflowing half-cylinder. Depending on the rate of supply, different regimes are observed (dripping, arrays of parallel jets, triangular sheets). The arrays of drops and jets exhibit interesting spatio-temporal phase dynamics: oscillations, pairing or nucleation of cells, forced tilt waves.

Relaxation of a dewetting contact line. Part 2. Experiments

The dynamics of receding contact lines is investigated experimentally through controlled perturbations of a meniscus in a dip-coating experiment. We first describe stationary menisci and their breakdown at the coating transition. Above this transition where liquid is deposited, it is found that the dynamics of the interface can be interpreted as a quasi-steady succession of stationary states. This provides the first experimental access to the entire bifurcation diagram of dynamical wetting, confirming the hydrodynamic theory developed in Part 1. In contrast to quasi-static theories based on a dynamic contact angle, we demonstrate that the transition strongly depends on the large-scale flow geometry. We then establish the dispersion relation for large wavenumbers, for which we find a decay rate σ proportional to wavenumber | q |. The speed dependence of σ is described well by hydrodynamic theory, in particular the absence of diverging time scales at the critical point. Finally, we highlight some open problems related to contact angle hysteresis that lead beyond the current description.

Force-velocity measurements of a few growing actin filaments.

The authors propose a new mechanism for actin-based force generation based on results using chains of actin-grafted magnetic colloids.

Do magnetic micro-swimmers move like eukaryotic cells?

Recent advances in micro-machining allow very small cargos, such as single red blood cells, to be moved by outfitting them with tails made of micrometre-sized paramagnetic particles yoked together by polymer bridges. When a time-varying magnetic field is applied to such a filament, it bends from side to side and propels itself through the fluid, dragging the load behind it. Here, experimental data and a mathematical model are presented showing the dependence of the swimming speed and direction of the magnetic micro-swimmer upon tunable parameters, such as the field strength and frequency and the filament length. The propulsion of the filament arises from the propagation of bending waves between free and tethered ends: here we show that this gives the micro-swimmer a gait that is intermediate between a eukaryotic cell and a waggled elastic rod. Finally, we extract from the model design principles for constructing the fastest swimming micro-swimmer by tuning experimental parameters.