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.

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.

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.

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.

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.

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.

Cavitation in a liquid-filled cavity surrounded by an elastic medium: Intercoupling of cavitation events in neighboring cavities.

The subject of the present theoretical study is the dynamics of a cavitation bubble in a spherical liquid-filled cavity surrounded by an infinite elastic solid. Two objectives are pursued. The first is to derive equations for the velocity and pressure fields throughout the liquid filling the cavity and equations for the stress and strain fields throughout the solid medium surrounding the cavity. This derivation is based on the results of our previous paper [A. A. Doinikov et al., Phys. Rev. E 97, 013108 (2018)10.1103/PhysRevE.97.013108], where equations for the evolution of a bubble inside a cavity were derived. The second objective is to apply the equations obtained at the first step of the study to ascertain if the cavitation process in one cavity can trigger the nucleation in a neighboring cavity. To this end, we consider a neighboring cavity in which a cavitation bubble is absent. We derive equations that describe the disturbance of the liquid pressure inside the second cavity, assuming this disturbance to be caused by the cavitation process in the first cavity. The developed theory is then used to perform numerical simulations. The results of the simulations show that the magnitude of the background negative pressure inside the second cavity increases at the second half period of the pressure disturbance, which in turn enhances the probability of nucleation in the second cavity.

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.

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.

Controlled rotation and translation of spherical particles or living cells by surface acoustic waves.

We show experimental evidence of the acoustically-assisted micromanipulation of small objects like solid particles or blood cells, combining rotation and translation, using high frequency surface acoustic waves. This was obtained from the leakage in a microfluidic channel of two standing waves arranged perpendicularly in a LiNbO3 piezoelectric substrate working at 36.3 MHz. By controlling the phase lag between the emitters, we could, in addition to translation, generate a swirling motion of the emitting surface which, in turn, led to the rapid rotation of spherical polystyrene Janus beads suspended in the channel and of human red and white blood cells up to several rounds per second. We show that these revolution velocities are compatible with a torque caused by the acoustic streaming that develops at the particles surface, like that first described by [F. Busse et al., J. Acoust. Soc. Am., 1981, 69(6), 1634-1638]. This device, based on standard interdigitated transducers (IDTs) adjusted to emit at equal frequencies, opens a way to a large range of applications since it allows the simultaneous control of the translation and rotation of hard objects, as well as the investigation of the response of cells to shear stress.

Radiation dynamics of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid.

A specific cavitation phenomenon occurs inside the stems of trees. The internal pressure in tree conduits can drop down to significant negative values, which causes the nucleation of bubbles. The bubbles exhibit high-frequency oscillations just after their nucleation. In the present study, this phenomenon is modeled by taking into account acoustic waves produced by bubble oscillations. A dispersion equation is derived, which is then used to calculate the resonance frequency and the attenuation coefficient of the bubble oscillations. Radiation damping is found to be predominant in comparison with viscous damping, except for very small bubbles. A typical number of oscillation cycles before the complete damping of the oscillation is found to be of the order of 10, as observed for cavitation bubbles in biomimetic synthetic trees.

Bubble-based acoustic micropropulsors: active surfaces and mixers.

Acoustic micropropulsors present great potential for microfluidic applications. The propulsion is based on encapsulated 20 µm bubbles excited by a contacless ultrasonic transducer. The vibrating bubbles then generate a powerful streaming flow, with speeds 1-100 mm s-1 in water, through the action of viscous stresses. In this paper we introduce a full toolbox of micropropulsors using a versatile three-dimensional (3D) microfabrication setup. Doublets and triplets of propulsors are introduced, and the flows they generate are predicted by a theoretical hydrodynamic model. We then introduce whole surfaces covered with propulsors, which we term active surfaces. These surfaces are excited by a single ultrasonic wave, can generate collective flows and may be harnessed for mixing purposes. Several patterns of propulsors are tested, and the flows produced by the two most efficient mixers are predicted by a simple theoretical model based on flow singularities. In particular, the vortices generated by the most efficient pattern, an L-shaped mixer, are analysed in detail.

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.

Acoustic streaming in a microfluidic channel with a reflector: Case of a standing wave generated by two counterpropagating leaky surface waves.

A theory is developed for the modeling of acoustic streaming in a microfluidic channel confined between an elastic solid wall and a rigid reflector. A situation is studied where the acoustic streaming is produced by two leaky surface waves that propagate towards each other in the solid wall and thus form a combined standing wave in the fluid. Full analytical solutions are found for both the linear acoustic field and the field of the acoustic streaming. A dispersion equation is derived that allows one to calculate the wave speed in the system under study. The obtained solutions are used to consider particular numerical examples and to reveal the structure of the acoustic streaming. It is shown that two systems of vortices are established along the boundaries of the microfluidic channel.

Acoustic streaming produced by a cylindrical bubble undergoing volume and translational oscillations in a microfluidic channel.

A theoretical model is developed for acoustic streaming generated by a cylindrical bubble confined in a fluid channel between two planar elastic walls. The bubble is assumed to undergo volume and translational oscillations. The volume oscillation is caused by an imposed acoustic pressure field and generates the bulk scattered wave in the fluid gap and Lamb-type surface waves propagating along the fluid-wall interfaces. The translational oscillation is induced by the velocity field of an external sound source such as another bubble or an oscillatory fluid flow. The acoustic streaming is assumed to result from the interaction of the volume and the translational modes of the bubble oscillations. The general solutions for the linear equations of fluid motion and the equations of acoustic streaming are calculated with no restrictions on the ratio between the viscous penetration depth and the bubble size. Approximate solutions for the limit of low viscosity are provided as well. Simulations of streamline patterns show that the geometry of the streaming resembles flows generated by a source dipole, while the vortex orientation is governed by the driving frequency, bubble size, and the distance of the bubble from the source of translational excitation. Experimental verification of the developed theory is performed using data for streaming generated by bubble pairs.

Effect of surface waves on the secondary Bjerknes force experienced by bubbles in a microfluidic channel.

An analytical expression is derived for the secondary Bjerknes force experienced by two cylindrical bubbles in a microfluidic channel with planar elastic walls. The derived expression takes into account that the bubbles generate two types of scattered acoustic waves: bulk waves that propagate in the fluid gap with the speed of sound and Lamb-type surface waves that propagate at the fluid-wall interfaces with a much lower speed than that of the bulk waves. It is shown that the surface waves cause the bubbles to form a bound pair in which the equilibrium interbubble distance is determined by the wavelength of the surface waves, which is much smaller than the acoustic wavelength. Comparison of theoretical and experimental results demonstrates good agreement.

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.

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.