arXiv subjects

Philippe Brunet

Publications and source records attributed to Philippe Brunet.

18 recordsLinked to original sources

arXiv2022

Elucidating the oscillation instability of sessile drops triggered by surface acoustic waves

The oscillation instability of sessile drops is ubiquitous in surface acoustic wave (SAW)-powered digital microfluidics. Yet, the physics underlying these phenomena has not been elucidated owing to the interplay between hydrodynamics, acoustics and capillarity. We decipher the instability by combining high-speed imaging with pressure measurements. We rationalize the observed behaviour with a model inspired from optomechanics, which couples an intracavity acoustic mode excited by the SAW to a surface deformation eigenmode through amplitude modulation and delayed radiation pressure feedback.

physics.flu-dyn↗

arXiv2020

Acoustic streaming generated by sharp edges: the coupled influences of liquid viscosity and acoustic frequency

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, \textcolor{blue}{owing to the strongly focused inertial effect experienced by the acoustic flow near the tip.} We conducted experiments with Particle Image Velocimetry to quantify this streaming flow through the influence of liquid viscosity $ν$, from 1 mm$^2$/s to 30 mm$^2$/s, and acoustic frequency $f$ from 500 Hz to 3500 Hz. Both quantities supposedly influence the thickness of the viscous boundary layer $δ= \left(\fracν{πf}\right)^{1/2}$. For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. As a characteristic streaming velocity, the maximal velocity is located at a distance of $δ$ from the tip, and it increases as the square of the acoustic velocity. We then provide empirical scaling laws to quantify the influence of $ν$ and $f$ on the streaming velocity. Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.

physics.flu-dyn↗

arXiv2020

Unveiling of the mechanisms of acoustic streaming induced by sharp edges

Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls, of typical thickness $δ$. In microchannels, the acoustic wavelength $λ$ is adjusted to twice the channel width $w$ to ensure a resonance condition, which implies the use of MHz transducers. Recently though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with $λ\gg w$), owing to the presence of sharp-tipped structures of curvature radius at the tip $r_c$ smaller than $δ$. The present study quantitatively investigates this sharp-edge acoustic streaming via the direct resolution of the full Navier-Stokes equation, using Finite Element Method. The influence of $δ$, $r_c$ and viscosity $ν$ on the acoustic streaming performance are quantified. Our results suggest choices of operating conditions and geometrical parameters, via dimensionless quantities $r_c/δ$ and $δ/w$ and provide guidelines on how to obtain strong, optimal sharp-edge acoustic streaming.

physics.flu-dyn↗

arXiv2020

Vortex elongation in outer streaming flows

We study the secondary time-averaged flow (streaming) generated by an oscillating cylinder immersed within a fluid, under high amplitude forcing so that inertial effects are significant. This streaming is decomposed into a viscous boundary layer flow where vorticity is created, and an outer flow of larger size. We operate under conditions of relatively low viscosity, so that the boundary layer is smaller than the object diameter. While for low Keulegan-Carpenter (KC) number (small enough amplitude), the size of the outer flow is typically that of the object, here we show that at large enough forcing, the outer flow stretches along the direction of the vibration by up to 8 times, while the flow still keeps its axial symmetry. We quantify the elongation through PIV measurements under an unprecedented range of frequency and amplitude, so that the streaming Reynolds number reaches values much larger than unity. The absence of significant unsteady component of vorticity outside the viscous boundary layer - and the fact that the length of elongation scales well with the streaming Reynolds number - suggest that the stretching should be due to the convection of stationary vorticity by the streaming flow itself.

physics.flu-dyn↗

arXiv2020

Directional motion of vibrated sessile drops : a quantitative study

The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate. As previously evidenced \cite{Brunet07,Brunet09,Noblin09}, the mechanical vibrations induce drop deformations which combine axisymmetric and antisymmetric modes. In this paper, we establish quantitative trends from experiments conducted within a large range of parameters, namely the amplitude $A$ and frequency $f$ of the forcing, the liquid viscosity $η$ and the angle between the substrate and the forcing axis $α$. These experiments are carried out on weak-pinning substrates. For most parameters sets, the averaged velocity $ $ grows linearly with $A$. We extract the mobility, defined as $s=\frac{Δ }{ΔA}$. It is found that $s$ can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode $f_p$. The value of $s$ tends to be almost independent on $η$ below 50 cSt, while $s$ decreases significantly for higher $η$. Also, it is found that for peculiar sets of parameters, particularly with $f$ far enough from $f_p$, the drop moves in the reverse direction. Finally, we draw a relationship between $ $ and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.

physics.flu-dyn↗

arXiv2020

A criterion for the pinning and depinning of an advancing contact line on a cold substrate

The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at $T_p < T_f$, of infinite thermal conductivity, where $T_f$ is the melting temperature. We propose a model derived from lubrication theory of contact-line dynamics, where an equilibrium between capillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple line where the vapour, liquid, solidified liquid and basal substrate meet. The Stefan thermal problem is solved in an intermediate region between molecular and mesoscopic scales, allowing to predict the shape of the solidified liquid surface. The apparent contact angle versus advancing velocity $U$ exhibits a minimal value, which is set as the transition from continuous advancing to pinning. We postulate that this transition corresponds to the experimentally observed critical velocity, dependent on undercooling temperature $T_f-T_p$, below which the liquid is pinned and advances with stick-slip dynamics. The analytical solution of the model shows a qualitatively fair agreement with experimental data. We discuss on the way to get better quantitative agreement, which in particular can be obtained when the mesoscopic cut-off length is made temperature-dependent.

physics.flu-dyn↗

arXiv2018

Drop spreading and gelation of thermoresponsive polymers

Spreading and solidification of liquid droplets are elementary processes of relevance for additive manufacturing. Here we investigate the effect of heat transfer on spreading of a thermoresponsive solution (Pluronic F127) that undergoes a sol-gel transition above a critical temperature $T_m$. By controlling the concentration of Pluronic F127 we systematically vary $T_m$, while also imposing a broad range of temperatures of the solid and the liquid. We subsequently monitor the spreading dynamics over several orders of magnitude in time and determine when solidification stops the spreading. It is found that the main parameter is the difference between the substrate temperature and $T_m$, pointing to a local mechanism for arrest near the contact line. Unexpectedly, the spreading is also found to stop below the gelation temparature, which we attribute to a local enhancement in polymer concentration due to evaporation near the contact line.

physics.flu-dyn↗

arXiv2016

Influence of viscosity on acoustic streaming in sessile droplets: an experimental and a numerical study with a Streaming Source Spatial Filtering (SSSF) method

When an acoustic wave travels in a lossy medium such as a liquid, it progressively transfers its pseudo-momentum to the fluid, which results in a steady acoustic streaming. Remarkably, the phenomenon involves a balance between sound attenuation and shear, such that viscosity vanishes in the final expression of the velocity field. For this reason, the effect of viscosity has long been ignored in acoustic streaming experiments. Here, we show experimentally that the viscosity plays a major role in cavities such as the streaming induced by surface acoustic waves in sessile droplets. We develop a numerical model based on the spatial filtering of the streaming source term to compute the induced flow motion with dramatically reduced computational requirements. We evidence that acoustic fields in droplets are a superposition of a chaotic field and a few powerful caustics. It appears that the caustics drive the flow, which allows a qualitative prediction of the flow structure. Finally, we reduce the problem to two dimensionless numbers related to the surface and bulk waves attenuation and simulate hemispherical sessile droplets resting on a lithium niobate substrate for a range of parameters. Even in such a baseline configuration, we observe at least four distinct flow regimes. For each of them, we establish a correlation of the average streaming speed in the droplet, which is increasingly dependent on the bulk wave attenuation as the viscosity increases. These correlations extend our results to a wide range of fluids and actuation frequencies.

physics.flu-dyn↗

arXiv2016

Dynamics of sessile and pendant drop excited by surface acoustic waves: gravity effects and correlation between oscillatory and translational motions

When sessile droplets are excited by ultrasonic traveling surface acoustic waves (SAWs), they undergo complex dynamics with both oscillations and translational motion. While the nature of the Rayleigh-Lamb quadrupolar drop oscillations has been identified, their origin and their influence on the drop mobility remains unexplained. Indeed the physics behind this peculiar dynamics is complex with nonlinearities involved both at the excitation level (acoustic streaming and radiation pressure) and in the droplet response (nonlinear oscillations and contact line dynamics). In this paper, we investigate the dynamics of sessile and pendant drops excited by SAWs. For pendant drops, so-far unreported dynamics are observed close to the drop detachment threshold with the suppression of the translational motion. Away from this threshold, the comparison between pendant and sessile drop dynamics allows us to identify the role played by gravity or more generally by an initial or dynamically induced stretching of the drop. In turn, we elucidate the origin of the resonance frequency shift, as well as the origin of the strong correlation between oscillatory and translational motion. We show that for sessile drops, the velocity is mainly determined by the amplitude of oscillation and that the saturation observed is due to the nonlinear dependence of the drop response frequency on the dynamically induced stretching.

physics.flu-dyn↗

arXiv2015

A liquid contact line receding on a soft gel surface : dip-coating geometry investigation

We studied the dynamics of a liquid contact line receding on a hydrophobic soft gel (SBS-paraffin). In order to realize a well-defined geometry with an accurate control of velocity, a dip-coating setup was implemented. Provided that the elastic modulus is small enough, a significant deformation takes place near the contact line, which in turn drastically influences the wetting behaviour. Depending on the translation velocity of the substrate, the contact line exhibits different regimes of motions. Continuous motions are observed at high and low velocities, meanwhile two types of stick-slip motion, periodic and erratic, appear at intermediate velocities. We suggest that the observed transitions could be explained in terms of the competition between different frequencies, i.e., the frequency of the strain field variation induced by the contact line motion and the crossover frequency of the gel related to the material relaxation. Our results provide systematic views on how the wetting of liquid is modified by the rheological properties of a complex soft substrate.

physics.flu-dyn↗

arXiv2015

Irreversible Collective Migration of Cyanobacteria in Eutrophic Conditions

In response to natural or anthropocentric pollutions coupled to global climate changes, microorganisms from aquatic environments can suddenly accumulate on water surface. These dense suspensions, known as blooms, are harmful to ecosystems and significantly degrade the quality of water resources. In order to determine the physico-chemical parameters involved in their formation and quantitatively predict their appearance, we successfully reproduced irreversible cyanobacterial blooms in vitro. By combining chemical, biochemical and hydrodynamic evidences, we identify a mechanism, unrelated to the presence of internal gas vesicles, allowing the sudden collective upward migration in test tubes of several cyanobacterial strains (Microcystis aeruginosa PCC 7005, Microcystis aeruginosa PCC 7806 and Synechocystis sp. PCC 6803). The final state consists in a foamy layer of biomass at the air-liquid interface, in which micro-organisms remain alive for weeks, the medium lying below being almost completely depleted of cyanobacteria. These "laboratory blooms" start with the aggregation of cells at high ionic force in cyanobacterial strains that produce anionic extracellular polymeric substances (EPS). Under appropriate conditions of nutrients and light intensity, the high photosynthetic activity within cell clusters leads the dissolved oxygen (DO) to supersaturate and to nucleate into bubbles. Trapped within the EPS, these bubbles grow until their buoyancy pulls the biomass towards the free surface. By investigating a wide range of spatially homogeneous environmental conditions (illumination, salinity, cell and nutrient concentration) we identify species-dependent thresholds and timescales for bloom formation. We conclude on the relevance of such results for cyanobacterial bloom formation in the environment and we propose an efficient method for biomass harvesting in bioreactors.

physics.bio-ph↗

arXiv2013

Oscillating and star-shaped drops levitated by an airflow

We investigate the spontaneous oscillations of drops levitated above an air cushion, eventually inducing a breaking of axisymmetry and the appearance of `star drops'. This is strongly reminiscent of the Leidenfrost stars that are observed for drops floating above a hot substrate. The key advantage of this work is that we inject the airflow at a constant rate below the drop, thus eliminating thermal effects and allowing for a better control of the flow rate. We perform experiments with drops of different viscosities and observe stable states, oscillations and chimney instabilities. We find that for a given drop size the instability appears above a critical flow rate, where the latter is largest for small drops. All these observations are reproduced by numerical simulations, where we treat the drop using potential flow and the gas as a viscous lubrication layer. Qualitatively, the onset of instability agrees with the experimental results, although the typical flow rates are too large by a factor 10. Our results demonstrate that thermal effects are not important for the formation of star drops, and strongly suggest a purely hydrodynamic mechanism for the formation of Leidenfrost stars.

physics.flu-dyn↗

arXiv2012

Particle deposition after droplet evaporation on super-hydrophobic micro-textured surfaces

We study the size and shape of the final deposit obtained when a drop with colloidal particles has dried on a super-hydrophobic surface made of micro-posts. As expected, most of the particles lie inside a circular area, which radius roughly corresponds to the Laplace pressure threshold for liquid impalement inside the structure (Cassie-Wenzel transition), inducing a coffee-stain deposit due to contact-line pinning. Less expected is the observation of tiny deposits on top of posts in the area external to the main ring, despite the low macroscopic liquid/solid friction. Experiments are carried out varying the concentration in particles and initial volume of drops, in order to determine the influence of these parameters on the size distribution of deposits. A microscopic insight of the tiny deposits is proposed, based on recent experiments of non-volatile liquid sliding drops.

cond-mat.soft↗

arXiv2012

Low power sessile droplet actuation via modulated surface acoustic waves

Low power actuation of sessile droplets is of primary interest for portable or hybrid lab-on-a-chip and harmless manipulation of biofluids. In this paper, we show that the acoustic power required to move or deform droplets via surface acoustic waves can be substantially reduced through the forcing of the drops inertio-capillary modes of vibrations. Indeed, harmonic, superharmonic and subharmonic (parametric) excitation of these modes are observed when the high frequency acoustic signal (19.5 MHz) is modulated around Rayleigh-Lamb inertio-capillary frequencies. This resonant behavior results in larger oscillations and quicker motion of the drops than in the non-modulated case.

physics.flu-dyn↗

arXiv2010

Quantitative testing of robustness on super-omniphobic surfaces by drop impact

The quality of a liquid-repellent surface is quantified by both the apparent contact angle $θ_0$ that a sessile drop adopts on it, and the value of the liquid pressure threshold the surface can withstand without being impaled by the liquid, hence keeping a low-friction condition. We designed surfaces covered with nano-wires obtained by the vapor-liquid-solid (VLS) growth technique, that are able to repel most of the existing non-polar liquids including those of very low surface tension, as well as many polar liquids of moderate to high surface tension. These super-omniphobic surfaces exhibit apparent contact angles ranging from 125 to 160$^{\circ}$ depending on the liquid. We tested the robustness of the surfaces against impalement by carrying out drop impact experiments. Our results show how this robustness depends on the Young's contact angle $θ_0$ related to the surface tension of the liquid, and that the orientational growth of NWs is a favorable factor for robustness.

physics.flu-dyn↗

arXiv2008

Rayleigh-Plateau instability causes the crown splash

The impact of a drop onto a liquid layer and the subsequent splash has important implications for diverse physical processes such as air-sea gas transfer, cooling, and combustion. In the {\it crown splash} parameter regime, the splash pattern is highly regular. We focus on this case as a model for the mechanism that leads to secondary droplets, and thus explain the drop size distribution resulting from the splash. We show that the mean number of secondary droplets is determined by the most unstable wavelength of the Rayleigh-Plateau instability. Variations from this mean are governed by the width of the spectrum. Our results for the crown splash will provide the basis for understanding more complicated splashes.

physics.flu-dyn↗

arXiv2008

Maximum size of drops levitated by an air cushion

Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as it is observed for water drops on a heated plate, kept aloft by a stream of water vapor. We investigate the limit of small flow rates, for which the size of the gap between the drop and the substrate becomes very small. Above a critical drop radius no stationary drops can exist, below the critical radius two solutions coexist. However, only the solution with the smaller gap width is stable, the other is unstable. We compare to experimental data and use boundary integral simulations to show that unstable drops develop a gas "chimney" which breaks the drop in its middle.

physics.flu-dyn↗

arXiv2003

Elastic properties of cellular dissipative structure

Transition towards spatio-temporal chaos in one-dimensional interfacial patterns often involves two degrees of freedom: drift and out-of-phase oscillations of cells, respectively associated to parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigated in the case of a single domain propagating along a circular array of liquid jets. As observed by Michalland and Rabaud for the printer's instability \cite{Rabaud92}, the velocity $V_g$ of a constant width domain is linked to the angular frequency $ω$ of oscillations and to the spacing between columns $λ_0$ by the relationship $ V_g = αλ_0 ω$. We show by a simple geometrical argument that $α$ should be close to $1/ π$ instead of the initial value $α= 1/2$ deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate.

cond-mat↗