Research

Instabilities of a liquid film coating a vertical fiber

with F. Giorgiutti-Dauphiné, S. Kalliadasis and C. Ruyer-Quil

Wave interactions in a active dispersive-dissipative media: formation of bound states

with D. Tseluiko, S. Saprykin, S. Kalliadasis and F. Giorgiutti-Dauphiné

Elastocapillary imbibition

with J. Aristoff and H. Stone

Fiber coating is of practical importance and occurs in many technical procedures, for example in the manufacturing process of optical fibers. We study experimentally the evolution of a viscous liquid film flowing axisymetrically down a vertical fiber. This system is a simple example of a nonlinear medium with instability, energy dissipation and dispersion, and can thus be used as a prototype for the study of the pattern-formation dynamics of nonlinear systems. The film is always unstable and spontaneously breaks up into a drop-like wavetrain. The competition between this instability (Rayleigh-Plateau) and the gravity-driven flow leads to two different scenarios. At low flow rates, the system exhibits a self-sustained dynamics with the selection of a regular pattern with a well defined intrinsic frequency, characteristic of an abolsute linear instability. At larger flow rates, irregular wavetrains triggered by inlet noise are observed, corresponding to the characteristic response of a convectively unstable flow. In the convective regime, the flow can be synchronized by imposing periodic perturbations at the inlet. We then observe saturated non-linear traveling waves.

The surface-tension-driven coalescence of flexible structures (elastocapillarity) is relevant to a number of engineering and biological systems, such as the clumping of hair, the failure of micro devices during wet lithography, or more generally whenever a liquid-air interface is moving through a deformable media. We study the dynamics of wetting of flexible boundaries with a combination of experiments, scaling arguments and theory. We consider two model systems, by studying the rise and the spontaneous imbibition of a liquid between flexible sheets clamped at one end, and free to deflect at the other end. The pressure-induced inward deflection of the sheets leads to an unusual propagation of the meniscus, that deviates from the classical diffusive-like behavior.

Bound states, i.e. composites of two or more building blocks (particles/bodies) behaving as single objects, appear often in a wide variety of physical settings, from atomic physics and quantum mechanics to biological systems and complex fluids. Here we demonstrate experimentally for the first time novel bound-state-formation phenomena in low-Reynolds-number interfacial hydrodynamics. We consider a viscous film flowing down a vertical fiber. The film is always unstable and spontaneously breaks up into a drop-like wavetrain. In certain regimes the interface is dominated by solitary pulses which continuously interact with each other (i.e. attract or repel) to form bound states. We show that there is a finite number of possible distances between successive pulses. Those distances can be captured by imposing a weak external forcing, thus forming regular patterns of 2-pulses or 3-pulses bound states.

Wetting of flexible fiber arrays

with S. Protière and H. Stone

Fibrous media are ubiquitous functional materials, which often consist of flexible high aspect ratio fibers that can easily deform under capillary forces with many industrial and ecological consequences. We study the influence of a mist of droplets on an elastic array of fibers by considering a finite volume drop on a pair of two flexible fibers, clamped at one end and free to deflect at the other. The elastocapillary deformation of the fibers leads to the spontaneous motion of the drop toward the free ends. The drop either remains compact with minimal spreading or spreads into a long liquid column that coalesces the fibers. We find that there is a critical volume of liquid, hence a critical drop size, above which this coalescence does not occur, and we identify another drop size which maximizes spreading, thus liquid capture. These ideas are applicable to a wide range of fibrous materials.

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Below are a few examples of my research.

Microfluidic in situ fabrication and characterization of gels

with H. Berthet, J. Wexler, O. du Roure and A. Lindner

Photopolymerized hydrogels have found numerous applications in biology, chemistry, physics or mechanics. In particular, they provide a functional template for micro-particles which can then be used for model suspensions, biology tools, flow sensors or micro-reactors. The control and knowledge of the mechanical properties of the gels are paramount to many of these applications. We propose a novel microfluidic based method that directly measures the mechanical properties of a photopolymerized gel upon its fabrication. We designed a microfluidic channel containing slots filled with a solution of oligomers and photoinitiator; a free standing beam of precisely controlled rectangular shape is fabricated in situ within these slots, using the stop-flow microscope-based projection photolithography method. The solution then flows over the beam, applying an hydrodynamic force on the gel that deforms accordingly. This method, where both the load applied to the beam and its geometry are precisely controlled and known, gives a direct access to the Young's modulus of the material.

We use this method to determine the modulus of poly(ethylene glycol) diacrylate (PEGDA) under various experimental conditions. We identify the relevant control parameters in order to obtain a gel of desired modulus. The mechanical properties of the gel can be highly tuned, yielding two order of magnitude in the Young's modulus.

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Transport of confined fibers in microchannels

with J. Capello, M. Daieff, O. du Roure, A. Lindner, M. Nagel, G. Balestra, F. Gallaire

The motion of rigid or flexible particles in viscous flows has been extensively studied; a particular example are elongated objects, like fibers, whose transport is important in a variety of small-scale applications, from swimming micro-organisms and biofilm streamers in blood capillaries to fabrication of non-woven fibrous media. We consider the transport of elongated objects in pressure-driven flows in microfluidic Hele-Shaw cells, and study the effect of confinement, shape and flexibility on the trajectories.

In shallow Hele-Shaw cells or narrow pores, where the height of the fiber is comparable to the transverse channel height (i.e. the fiber nearly blocks the channel), the confinement causes viscous friction between the fiber and the surrounding walls. This friction reduces the velocity of the fiber, that is thus slower than the surrounding fluid, with a velocity that depends on its orientation: the fiber moves faster when oriented perpendicular to the flow direction than when parallel to the flow. When oriented at an arbitrary angle with the flow direction, the fiber thus drifts.

The fiber also interacts with the lateral walls; its trajectory is a combination of drift and rotation due to the presence of the bounding walls. Depending on its initial orientation angle, the fiber exhibits oscillations around 0◦ (glancing) or 90◦(reversing) . As the initial fiber angle increases, the drift velocity increases, while the rotation velocity remains nearly constant: as a consequence, the amplitude of the oscillations increases with increasing angle, i.e. the fiber glances closer to the wall and explores a larger part of the channel.

The fiber thus behaves like an oscillator. We build a bifurcation diagram as a function of the fiber orientation and spanwise position in the channel. The fiber either exhibits closed orbits (glancing and reversing oscillations) or open orbits near the walls (pole-vaulting and wiggling). We analyze the oscillatory regimes and show that the trajectories can be tuned by adjusting the confinement, i.e. changing the magnitude of the viscous drag.