Polyhedral Bubble Vibrations.

Underwater bubbles are extremely good acoustic resonators, but are freely evolving and dissolving. Recently it was found that bubbles can be stabilized in frames, but the influence of the frame shape is still undocumented. Here we first explore the vibration of polyhedral bubbles with a low number of faces, shaped as the five Platonic solids. Their resonance frequency is well approximated by the formula for spherical bubbles with the same volume. Then we extend these results to shapes with a larger number of faces using fullerenes, paving the way to obtain arbitrary large resonant bubbles.

Acoustic interaction between 3D-fabricated cubic bubbles.

Spherical bubbles are notoriously difficult to hold in specific arrangements in water and tend to dissolve over time. Here, using stereolithographic printing, we built an assembly of millimetric cubic frames overcoming these limitations. Indeed, each of these open frames holds an air bubble when immersed into water, resulting in bubbles that are stable for a long time and are still able to oscillate acoustically. Several bubbles can be placed in any wanted spatial arrangement, thanks to the fabrication process. We show that bubbles are coupled acoustically when disposed along lines, planes or in 3D arrangements, and that their collective resonance frequency is shifted to much lower values, especially for 3D arrangements where bubbles have a higher number of close neighbours. Considering that these cubic bubbles behave acoustically as spherical bubbles of the same volume, we develop a theory allowing one to predict the acoustical emission of any arbitrary group of bubbles, in agreement with experimental results.

Acoustics of Cubic Bubbles: Six Coupled Oscillators.

We introduce cubic bubbles that are pinned to 3D printed millimetric frames immersed in water. Cubic bubbles are more stable over time and space than standard spherical bubbles, while still allowing large oscillations of their faces. We find that each face can be described as a harmonic oscillator coupled to the other ones. These resonators are coupled by the gas inside the cube but also by acoustic interactions in the liquid. We provide an analytical model and 3D numerical simulations predicting the resonance with very good agreement. Acoustically, cubic bubbles prove to be good monopole subwavelength emitters, with nonemissive secondary surface modes.

Revealing catastrophic failure of leaf networks under stress.

The intricate patterns of veins that adorn the leaves of land plants are among the most important networks in biology. Water flows in these leaf irrigation networks under tension and is vulnerable to embolism-forming cavitations, which cut off water supply, ultimately causing leaf death. Understanding the ways in which plants structure their vein supply network to protect against embolism-induced failure has enormous ecological and evolutionary implications, but until now there has been no way of observing dynamic failure in natural leaf networks. Here we use a new optical method that allows the initiation and spread of embolism bubbles in the leaf network to be visualized. Examining embolism-induced failure of architecturally diverse leaf networks, we found that conservative rules described the progression of hydraulic failure within veins. The most fundamental rule was that within an individual venation network, susceptibility to embolism always increased proportionally with the size of veins, and initial nucleation always occurred in the largest vein. Beyond this general framework, considerable diversity in the pattern of network failure was found between species, related to differences in vein network topology. The highest-risk network was found in a fern species, where single events caused massive disruption to leaf water supply, whereas safer networks in angiosperm leaves contained veins with composite properties, allowing a staged failure of water supply. These results reveal how the size structure of leaf venation is a critical determinant of the spread of embolism damage to leaves during drought.

Buckling Instability Causes Inertial Thrust for Spherical Swimmers at All Scales.

Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number (Re). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all Re regimes. An optimal displacement caused by nontrivial history effects is reached at intermediate Re. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high-frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.

Acoustic streaming generated by two orthogonal standing waves propagating between two rigid walls.

An analytical solution is derived for the acoustic streaming generated by two orthogonal standing waves in a fluid confined between two plane rigid walls. It is assumed that the standing waves have the same frequency but, in general, are out of phase. The main restriction is that the boundary layer thickness is much smaller than the acoustic wavelength. It is shown that the acoustic streaming gives rise to vortices in which fluid particles, when moving between the walls, are rotating about axes perpendicular to the walls. The location, the form, the sense of rotation of the vortices and the vortex strength are governed by the phase shift between the driving waves.

Visual quantification of embolism reveals leaf vulnerability to hydraulic failure.

Vascular plant mortality during drought has been strongly linked to a failure of the internal water transport system caused by the rapid invasion of air and subsequent blockage of xylem conduits. Quantification of this critical process is greatly complicated by the existence of high water tension in xylem cells making them prone to embolism during experimental manipulation. Here we describe a simple new optical method that can be used to record spatial and temporal patterns of embolism formation in the veins of water-stressed leaves for the first time. Applying this technique in four diverse angiosperm species we found very strong agreement between the dynamics of embolism formation during desiccation and decline of leaf hydraulic conductance. These data connect the failure of the leaf water transport network under drought stress to embolism formation in the leaf xylem, and suggest embolism occurs after stomatal closure under extreme water stress.

The fast dynamics of cavitation bubbles within water confined in elastic solids.

Many applications such as ultrasonic cleaning or sonochemistry use the ability of bubbles to oscillate and drive liquid flow. But bubbles have also received attention in porous media, where drying may cause cavitation, a phenomenon occurring in plant tissues. Here we explore the dynamics of cavitation bubbles when the liquid is fully entrapped in an elastic solid, using light scattering, laser strobe photography and high speed camera recordings. Our experiments show unexpectedly fast bubble oscillations in volume. They depend on the confinement size and elasticity, which we explain with a simple model where liquid compressibility is a key parameter. We also observe rich non-spherical dynamics, with ejection away from the walls and bubble fragmentation, which reveal extreme fluid motion at short timescales.

The walk and jump of Equisetum spores.

Equisetum plants (horsetails) reproduce by producing tiny spherical spores that are typically 50 µm in diameter. The spores have four elaters, which are flexible ribbon-like appendages that are initially wrapped around the main spore body and that deploy upon drying or fold back in humid air. If elaters are believed to help dispersal, the exact mechanism for spore motion remains unclear in the literature. In this manuscript, we present observations of the 'walks' and 'jumps' of Equisetum spores, which are novel types of spore locomotion mechanisms compared to the ones of other spores. Walks are driven by humidity cycles, each cycle inducing a small step in a random direction. The dispersal range from the walk is limited, but the walk provides key steps to either exit the sporangium or to reorient and refold. Jumps occur when the spores suddenly thrust themselves after being tightly folded. They result in a very efficient dispersal: even spores jumping from the ground can catch the wind again, whereas non-jumping spores stay on the ground. The understanding of these movements, which are solely driven by humidity variations, conveys biomimetic inspiration for a new class of self-propelled objects.

Birth and growth of cavitation bubbles within water under tension confined in a simple synthetic tree.

Water under tension, as can be found in several systems including tree vessels, is metastable. Cavitation can spontaneously occur, nucleating a bubble. We investigate the dynamics of spontaneous or triggered cavitation inside water filled microcavities of a hydrogel. Results show that a stable bubble is created in only a microsecond time scale, after transient oscillations. Then, a diffusion driven expansion leads to filling of the cavity. Analysis reveals that the nucleation of a bubble releases a tension of several tens of MPa, and a simple model captures the different time scales of the expansion process.

The role of fluctuations and stress on the effective viscosity of cell aggregates.

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses ("fluctuation-induced flow"). If not, changing the aggregate's shape requires a sufficiently large applied stress ("stress-induced flow"). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress tau*, the aggregate as a whole flows with an apparent viscosity eta*, and at higher stress it is a shear-thinning fluid. An increasing cell-cell tension results in a higher eta* (and thus a slower stress relaxation time t(c)). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find t(c) of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.

Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation.

Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation.

Ultra-fast underwater suction traps.

Carnivorous aquatic Utricularia species catch small prey animals using millimetre-sized underwater suction traps, which have fascinated scientists since Darwin's early work on carnivorous plants. Suction takes place after mechanical triggering and is owing to a release of stored elastic energy in the trap body accompanied by a very fast opening and closing of a trapdoor, which otherwise closes the trap entrance watertight. The exceptional trapping speed--far above human visual perception--impeded profound investigations until now. Using high-speed video imaging and special microscopy techniques, we obtained fully time-resolved recordings of the door movement. We found that this unique trapping mechanism conducts suction in less than a millisecond and therefore ranks among the fastest plant movements known. Fluid acceleration reaches very high values, leaving little chance for prey animals to escape. We discovered that the door deformation is morphologically predetermined, and actually performs a buckling/unbuckling process, including a complete trapdoor curvature inversion. This process, which we predict using dynamical simulations and simple theoretical models, is highly reproducible: the traps are autonomously repetitive as they fire spontaneously after 5-20 h and reset actively to their ready-to-catch condition.

Acoustically bound microfluidic bubble crystals.

Bubbles confined in microchannels self-organize without directly contacting one another when excited by an external acoustic field. The bubbles tend to form periodic "crystal"-like lattices with a finite interbubble distance. This equilibrium distance can be adjusted by simply tuning the acoustic frequency. This new type of crystal is purely mediated by acoustic surface waves emitted by the pulsating bubbles. Because these waves are reflected at the channel boundaries, the bubbles interact with their own images across the boundary.

Buckling resistance of solid shell bubbles under ultrasound.

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed: the solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.

Multi-directional bubble generated streaming flows.

In previous work, we have demonstrated the use of single-holed Armoured Microbubbles (AMBs) for microfluidic mixing and self-propulsion. AMBs are hollow partial spheres, inside which we capture a bubble. Under ultrasound, the bubble oscillates, generating a streaming flow with velocities of 1-100 mm/s in water. In this paper, inspired by our successful fabrication of a C60 geometry (buckyball), we study AMBs with multiple surface holes. We show more holes generate additional pairs of fast circulations around the AMB. However, as the number of holes increases further, the circulations become small and the in-plane flow is dominated by a source or sink flow. For an AMB with two different sized holes, we demonstrate each hole can be independently activated, potentially useful for multi-directional swimming.

Drying of channels by evaporation through a permeable medium.

We study the drying of isolated channels initially filled with water moulded in a water-permeable polymer (polydimethylsiloxane, PDMS) by pervaporation, when placed in a dry atmosphere. Channel drying is monitored by tracking a meniscus, separating water from air, advancing within the channels. The role of two geometrical parameters, the channel width and the PDMS thickness, is investigated experimentally. All data show that drying displays a truncated exponential dynamics. A fully predictive analytical model, in excellent agreement with the data, is proposed to explain such a dynamics, by solving water diffusion both in the PDMS layer and in the gas inside the channel. This drying process is crucial in geological or biological systems, such as rock disintegration or the drying of plant leaves after cavitation and embolism formation.

Nonlinear dynamics of two coupled bubbles oscillating inside a liquid-filled cavity surrounded by an elastic medium.

A theory is developed to model the nonlinear dynamics of two coupled bubbles inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim is to study how the conditions of full confinement affect the coupled oscillations of the bubbles. To make the problem amenable to analytical consideration, the bubbles are assumed to be located on a diameter of the cavity, which makes the problem axisymmetric. Equations for the pulsation and translation motion of the bubbles are derived by the Lagrangian formalism. The derived equations are used in numerical simulations. The behavior of two bubbles in a cavity is compared with the behavior of the same bubbles in an unbounded liquid. It is found that both forced and free oscillations of two bubbles in a cavity occur differently than those in an unbounded liquid. In particular, it is shown that the eigenfrequencies of a two-bubble system in a cavity are different from those in an unbounded liquid.

Model for the growth and the oscillation of a cavitation bubble in a spherical liquid-filled cavity enclosed in an elastic medium.

Equations are derived that describe the growth and subsequent damped oscillation of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid. It is assumed that the nucleation and the growth of the bubble are caused by an initial negative pressure in the cavity. The liquid is treated as viscous and compressible. The obtained equations allow one to model, by numerical computation, the growth and the oscillation of the bubble in the cavity and the oscillation of the cavity surface. It is shown that the equilibrium radius reached by the growing bubble decreases when the absolute magnitude of the initial negative pressure decreases. It is also found that the natural frequency of the bubble oscillation increases with increasing bubble radius. This result is of special interest because in an unbounded liquid, the natural frequency of a bubble is known to behave oppositely, namely it decreases with increasing bubble radius.

Acoustic streaming induced by two orthogonal ultrasound standing waves in a microfluidic channel.

A mathematical model is derived for acoustic streaming in a microfluidic channel confined between a solid wall and a rigid reflector. Acoustic streaming is produced by two orthogonal ultrasound standing waves of the same frequency that are created by two pairs of counter-propagating leaky surface waves induced in the solid wall. The magnitudes and phases of the standing waves are assumed to be different. Full analytical solutions are found for the equations of acoustic streaming. The obtained solutions are used in numerical simulations to reveal the structure of the acoustic streaming. It is shown that the interaction of two standing waves leads to the appearance of a cross term in the equations of acoustic streaming. If the phase lag between the standing waves is nonzero, the cross term brings about circular vortices with rotation axes perpendicular to the solid wall of the channel. The vortices make fluid particles rotate and move alternately up and down between the solid wall and the reflector. The obtained results are of immediate interest for acoustomicrofluidic applications such as the ultrasonic micromixing of fluids and the manipulation of microparticles.