Denis Terwagne

Curvature-induced symmetry breaking determines elastic surface patterns

Symmetry-breaking transitions associated with the buckling and folding of curved multilayered surfaces-which are common to a wide range of systems and processes such as embryogenesis, tissue differentiation and structure formation in heterogeneous thin films or on planetary surfaces-have been characterized experimentally. Yet owing to the nonlinearity of the underlying stretching and bending forces, the transitions cannot be reliably predicted by current theoretical models. Here, we report a generalized Swift-Hohenberg theory that describes wrinkling morphology and pattern selection in curved elastic bilayer materials. By testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions for the critical curves separating labyrinth, hybrid and hexagonal phases. Furthermore, a comparison to earlier experiments suggests that the theory is universally applicable to macroscopic and microscopic systems. Our approach builds on general differential-geometry principles and can thus be extended to arbitrarily shaped surfaces.

Smart Morphable Surfaces for Aerodynamic Drag Control

Smart Morphable Surfaces enable switchable and tunable aerodynamic drag reduction of bluff bodies. Their topography, resembling the morphology of golf balls, can be custom-generated through a wrinkling instability on a curved surface. Pneumatic actuation of these patterns results in the control of the drag coefficient of spherical samples by up to a factor of two, over a range of flow conditions.

Droplets sliding on fibres

We present the results of a combined experimental and theoretical investigation of oil droplets sliding on fibres. First, both the axisymmetric shape and the motion of a droplet on a vertical fibre are described. The motion is shown to result from a balance between the droplet weight and the viscous stresses. On a long-term range, the droplet loses some mass through coating the fibre, which decreases its velocity. In a second time, we rationalize the behaviour of a droplet that encounters a junction between vertical and horizontal fibres. Depending on its size, the droplet may cross the junction or remain blocked. The transition is well described by an ordinary differential equation equivalent to a damped harmonic oscillator truncated to the neighbourhood of the horizontal fibre. This simple system is the basic element for more complex fiber networks that would be useful in microfluidic applications involving droplets.

Digital microfluidics on a wire

In this letter, we discuss the behavior of droplets on fiber networks. An on/off transition is observed when a droplet comes around an intersection between several fibers: large droplets cross the junction while small droplets remain pinned. We show that fibers perform advantageously most operations of digital microfluidics, such as multiplexed biochemical microreactions: intersections are the basic component of fiber-based microfluidic devices.

Wave propelled ratchets and drifting rafts

Several droplets, bouncing on a vertically vibrated liquid bath, can form various types of bound states, their interaction being due to the waves emitted by their bouncing. Though they associate droplets which are individually motionless, we show that these bound states are self-propelled when the droplets are of uneven size. The driving force is linked to the assymetry of the emitted surface waves. The direction of this ratchet-like displacement can be reversed, by varying the amplitude of forcing. This direction reversal occurs when the bouncing of one of the drops becomes sub-harmonic. As a generalization, a larger number of bouncing droplets form crystalline rafts which are also shown to drift or rotate when assymetrical.

Resonant and rolling droplet

When an oil droplet is placed on a quiescent oil bath, it eventually collapses into the bath due to gravity. The resulting coalescence may be eliminated when the bath is vertically vibrated. The droplet bounces periodically on the bath, and the air layer between the droplet and the bath is replenished at each bounce. This sustained bouncing motion is achieved when the forcing acceleration is higher than a threshold value. When the droplet has a sufficiently low viscosity, it significantly deforms: spherical harmonic Ylm modes are excited, resulting in resonant effects on the threshold acceleration curve. Indeed, a lower acceleration is needed when l modes with m=0 are excited. Modes m≠0 are found to decrease the bouncing ability of the droplet. A break of degeneracy is observed for the m parameter. In particular, when the mode l=2 and m=1 is excited, the droplet rolls on the vibrated surface without touching it, leading to a new self-propulsion mode.

Dancing droplets onto liquid surfaces

Reference EPFL-ARTICLE-218225doi:10.1063/1.2335905 URL: http://trioslab.ulb.ac.be/wp-content/uploads/2014/09/2006-Phys.-Fluids-Vandewalle.pdf Record created on 2016-04-28, modified on 2017-05-10

Wrinkling crystallography on spherical surfaces

Significance Curved crystals cannot comprise hexagons alone; additional defects are required by both topology and energetics that depend on the system size. These constraints are present in systems as diverse as virus capsules, soccer balls, and geodesic domes. In this paper, we study the structure of defects of the crystalline dimpled patterns that self-organize through curved wrinkling on a thin elastic shell bound to a compliant substrate. The dimples are treated as point-like packing units, even if the shell is a continuum. Our results provide quantitative evidence that our macroscopic wrinkling system can be mapped into and described within the framework of curved crystallography, albeit with some important differences attributed to the far-from-equilibrium nature of our patterns. We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples self-organizes on the surface of the shell. Stresses are relaxed by both out-of-surface buckling and the emergence of defects in the quasi-hexagonal pattern. Three-dimensional scanning is used to digitize the topography. Regarding the dimples as point-like packing units produces spherical Voronoi tessellations with cells that are polydisperse and distorted, away from their regular shapes. We analyze the structure of crystalline defects, as a function of system size. Disclinations are observed and, above a threshold value, dislocations proliferate rapidly with system size. Our samples exhibit striking similarities with other curved crystals of charged particles and colloids. Differences are also found and attributed to the far-from-equilibrium nature of our patterns due to the random and initially frozen material imperfections which act as nucleation points, the presence of a physical boundary which represents an additional source of stress, and the inability of dimples to rearrange during crystallization. Even if we do not have access to the exact form of the interdimple interaction, our experiments suggest a broader generality of previous results of curved crystallography and their robustness on the details of the interaction potential. Furthermore, our findings open the door to future studies on curved crystals far from equilibrium.

Tibetan singing bowls

We present the results of an experimental investigation of the acoustics and fluid dynamics of Tibetan singing bowls. Their acoustic behaviour is rationalized in terms of the related dynamics of standing bells and wine glasses. Striking or rubbing a fluid-filled bowl excites wall vibrations, and concomitant waves at the fluid surface. Acoustic excitation of the bowl’s natural vibrational modes allows for a controlled study in which the evolution of the surface waves with increasing forcing amplitude is detailed. Particular attention is given to rationalizing the observed criteria for the onset of edge-induced Faraday waves and droplet generation via surface fracture. Our study indicates that drops may be levitated on the fluid surface, induced to bounce on or skip across the vibrating fluid surface.

The role of the droplet deformations in the bouncing droplet dynamics

Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion, and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical bouncing dynamics by neglecting the deformation of the surface of the bath. To be under this favorable condition, low viscous oil droplets are dropped over a highly viscous oil bath that is vibrated. These droplets bounce vertically on the surface of the bath and exhibit many periodic trajectories and resonant modes when tuning the forcing parameters, i.e., the oscillation of the bath. This complex dynamics emphasizes the interplay between elastic energy storage and energy dissipation in droplets at each bounce. We propose to model droplets using a bouncing mass-spring-damper system that mimics a deformable droplet bouncing on a non-deformable liquid bath. From the experimental measurements, we constructed bifurcation diagrams of the bouncing trajectories and challenge...