Sujet de these 2015- fiche francais.doc

ED SMAER

Sujet de thèses 2015 Laboratoire : Institut d’Alembert Etablissement de rattachement : Université Pierre et Marie Curie Directeur de thèse et section CNU ou CNRS : R. Wunenburger (CNU 60) Codirection et section CNU ou CNRS : J.P. Delville (CNRS 05) Titre de la thèse : Mesure sans contact de tension de surface et de viscoélasticité de gouttelettes Collaborations dans le cadre de la thèse : A. Antkowiak (CNU 60), S. Neukirch (CNRS 09), F. Vollrath (Oxford Univ., UK) Rattachement à un programme : ANR Windlass (2014-2018) Le sujet peut être publié sur le site web de l’ED SMAER : OUI NON rayer la mention inutile.

Résumé du sujet :

NOTA : l’ED SMAER collecte environ 100 fiches par an. Merci de limiter cette fiche à 1 page maxi. L’ANR Windlass dans laquelle s’inscrit cette thèse a pour objectif premier d’élucider le mécanisme d’origine élasto-capillaire selon lequel les fils de soie de capture des toiles d’araignée sont naturellement tendus par enroulement à l’intérieur des gouttes de glue de taille sub-millimétrique réparties sur ces fils. Ce mécanisme assure à la fois une auto-tension des fils et une grande extensibilité qui évite leur rupture lors de la capture des proies. Pour atteindre cet objectif, une mesure in-situ et in-vivo de la tension de surface et des propriétés visco-élastiques de la glue naturelle et nécessaire. Le but de cette thèse est de mettre en œuvre deux techniques complémentaires de mesure sans contact de ces propriétés basées sur les effets mécaniques de la lumière et des ondes acoustiques. Ces techniques déjà éprouvées sur des interfaces liquides macroscopiques seront d’abord mises au point sur des gouttes-modèle, puis appliquées aux gouttes de glue naturelle. La mise au point de ces techniques bénéficiera du co-encadrement de J.P. Delville (LOMA, UMR 5798 CNRS-Univ. Bordeaux), collaborateur régulier depuis une dizaine d’années sur les aspects de dynamométrie optique.

Sujet de these 2015- fiche francais.doc

Sujet de these 2015- fiche francais.doc

Sujet développé (à présenter en 2 ou 3 pages maximum, en précisant notamment le contexte, les objectifs, les résultats attendus)

Non-contact measurement of surface tension andviscoelastic properties of glue droplets suspended alongspider capture threads

Abstract

The global project within which the PhD thesis takes place is to study a natural mechanismtaking place in spider webs and to reproduce this mechanism with synthetic materials in orderto develop industrial applications at the microscale. A spider web comprises three kind ofthreads: radial, frame, and capture threads. Our object of interest is the capture thread withwhich the web spiral is constructed. The biological function of these capture threads is tohold the web together and to catch flying insects, that is to act as tension cables and shockabsorbers. A key feature of the capture thread is that it is decorated by regularly spaced liquiddroplets, thought to have the role of a glue that would stick to the incoming prey. It appearsthat these glue droplets have yet another function. In 1989 it was proposed by one of theproject participant that the glue droplets would draw the capture thread inside them, therebyholding the thread in tension. During a shock event the spare amount of fiber in the dropletwould be used to provide extensibility to the system. Moreover the dissipation generated byrelative motion of the fluid and the fiber would absorb energy. We want to mechanicallyinvestigate this windlass mechanism, prove it to be the main cause of the great extensibility ofcapture threads, and draw biological implications. Furthermore, using a biomimetic approach,we want to reproduce the mechanism on synthetic fibers and droplets, and to explore possibleapplications of this mechanism in micro-systems. Finally, as the liquid droplets are the keycomponent in the system, we will develop new contactless tools to measure their physicalproperties. More precisely we will have to be able to measure surface tension, elasticity, andviscosity of the droplet in-situ, that is when they lie on the fiber. To this end we will designcontactless measurement techniques, using laser or acoustic radiation pressures to poke thedroplet and monitor its subsequent relaxation.

I. Presentation of the project

State of the art on spider silk threads

Orb-webs, such as produced by the common garden cross spider Araneus diadematus or thegolden silk spider Nephila clavipes are assembled by the spider using five different silks woveninto a complex thread network. Its structure consists of frame with a wheel of radial ‘spokes’consisting of two kinds of silks and a geometric spiral made of core fibres covered by a highlyviscous aggregate (AG) capture silk coating, see Fig. 1-left. Capture silk composite couples verylow initial stiffness with large stretchability. More precisely, the capture thread has stretcha-bility that is orders of magnitude larger than any other known material and the fully stretchedfibre lacks any hysteresis (sagging) when relaxed to its original length and below. This remark-able mechanical behaviour relies on a surprising phenomenon in the context: a self-assemblingmicron-scale windlass mechanism. The silk coating appears as a collection of droplets which siton the spiral thread like pearls on a string, as a result of Plateau-Rayleigh instability? ? . Im-portantly, ? have demonstrated that these aqueous droplets act like tiny windlasses: capillaryforces exerted by the droplets on the thread compress its wet parts (see Fig. ??a). Thanks tothe micron-sized diameter of the silk thread, these capillary forces overcome the force thresholdfor buckling and result in coiling (capillary windlass), collecting the loose core fibres inside thedroplets? , as seen in Fig. 1-right-a. This is why the threads do not sag even after rapid andstrong strain cycles? ? .

Recently, a pilot collaboration has allowed our Paris group working with Prof Vollrath fromOxford in residence, to observe for the first time in-situ dynamic coiling and uncoiling ofcore filament ‘windlass-balls’ on capture silk threads, see Fig. 1-right-b. This breakthrough

I PRESENTATION OF THE PROJECT

FIG. 1. Left: An orb-weaving spider web comprises frame thread, radial threads, and capture (spiral)

threads. In red a capture thread decorated by glue droplets (from ?). Right: (a) capture thread laid

onto a glass slide (from ?), (b) First in-situ observation of ball yarns within glue droplets decorating a

Nephila edulis spider capture thread: experimental evidence of capillary windlass on a spider capture

thread.

emboldens the team to consider an in-depth, quantitative investigation of natural and syntheticmodels of the in-droplet micron-scale windlass phenomenon.Further investigation enabled us to assemble a functional semi-artificial windlass system basedon the combination of a natural silk fibre and synthetic droplets, and to obtain preliminarytension-extension curves. The concept of artificial windlass has just been patented.

Goals of the project

The major goal of the project is to prove that the exceptional extensivity of thecapture fiber is not due to chemical architecture but to the windlass mechanism.We will as well show that this mechanism is responsible for the self-tension in the web spiral andfor its dissipative properties. These mechanisms, which confer important mechanical propertiesto the spider web, will be shown to have an elasto-capillary origin, largely independent of theprecise chemical structure of the fibers and glue their coating.We claim the windlass effect of droplets to be due to the action of capillarity. To demonstratethis mechanism, we need to measure the surface tension of natural droplets as function ofthe spider specie, temperature and air humidity. Besides, the reasons for the immobility of thedroplets along the capture silk fibers are still unknown. Possible reasons for this crucial propertycould be a weak elasticity of the droplets, possibly combined with geometrical and/or chemicalroughness of the silk fibers responsible for the triple contact line pinning. To elucidate this, weneed to measure the elastic modulus of natural droplet and to probe the surface properties ofthe capture silk fiber as function of the spider specie, temperature and air humidity.Finally, prey capture in orb webs involves the absorption of the entire kinetic energy of thecaptured insect by the orb web during its impact without breaking. To evaluate the contributionof the capillary windlasses to the energy absorption, we need to measure the viscosity of naturaldroplets, also as function of the spider specie, temperature and air humidity.We thus need to measure the surface tension, the elasticity and the viscosity of natural dropletsin situ, that is of droplets suspended on capture silk fibers. Note that measuring these proper-ties on liquid samples with sub-millimetric size constitutes in itself a far reaching technologicalprogress with highly attractive potential applications to high-throughput chemical and biolog-ical screening which go beyond the characterization of natural spider orb web droplets. Toachieve this goal, we propose to develop two kinds of contactless measurement techniques, thento apply them in situ on natural droplets. These techniques share the same physical principle:

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I PRESENTATION OF THE PROJECT

(a) (b) (c) (d)

FIG. 2. (a) Liquid drop levitating in an ultrasonic standing wave levitator and undergoing steady

deformation. (b) (top) Unsteady deformation of a water free surface resulting from a pulsed, focused

ultrasonic beam , with (bottom) time-dependent curvature at the hump tip, experiment and model

(from ?). (c) (top) Unsteady deformation of a soft liquid interface resulting from a step-like focused

laser beam, with (bottom) time-dependent curvature at the hump tip, experiment and model (from ?

?). (d) Numerical simulation of the steady deformation of a sessile droplet by a focused laser beam? .

the deformation of the droplet by the radiation pressure of an electromagnetic or acoustic radi-ation. The static amplitude and transient evolution of the deformation depend not only on theirradiating beam power and diameter, but also on the surface tension, elasticity and viscosityof the droplet liquid and on the droplet size and shape.

State-of-the-art of contactless measurement techniques of surface and bulk liquid properties

Among all the various techniques developed for the measurement of surface (surface tension,surface visco-elasticity) and bulk (visco-elasticity) liquid properties, those based on the analysisof the deformation of the liquid surface are extremely attractive for several reasons:

• All the targeted properties of the liquid can be deduced from the analysis of the staticdeformation of the liquid surface and of its temporal evolution, by investigating several dynamicregimes (static, inertial, overdamped. . . ).

• The liquid surface deformations can be obtained without contact in several ways: (i) bynatural thermal fluctuations? , (ii) by applying an electrostatic field? ? , (iii) by irradiating thesurface using an electromagnetic beam? ? ? , (iv) or an acoustic beam? ? ? ? .Technique (i), which is based on the scattering of light by thermal fluctuations of the liquidsurface, requires large signal acquisition durations for reaching acceptable levels of signal-to-noise ratio. Techniques (ii-iv), which involve larger surface excitations, are more attractive,but technique (ii) is extremely sensitive to sample vibrations, which can result in the damagingcontact between the sample and the tip-like electrodes. This is why we selected techniques (iii)and (iv), hereafter called optical technique and acoustic technique, respectively, whichappear as the most adapted technique for measurements on natural droplets. The principleof the optical and acoustic techniques is the following. An electromagnetic/acoustic beamimpinging on the liquid surface exerts on it normal stresses called radiation pressure, as theresult of the change in momentum density of the wave at the liquid surface. The radiationpressure imparts a deformation to the liquid surface. The liquid properties of interest arethen deduced from the measurement of the surface deformation shape, amplitude or temporalevolution using free surface flow models valid for mall amplitude surface deformations.The technique used to measure the liquid surface deformation depends on the ratio of thebeam diameter to the liquid sample size and on the obtained deformation amplitude. Thedeformations of initially spherical liquid droplets deformed by acoustic radiation pressure can

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be measured either by direct optical observation when they are sufficiently large, as shown inFigure 2a? , or by light transmission analysis when they are weak? . For initially flat surfacesthat are deformed by locally exerted radiation pressure, the time and space-dependent height,slope or curvature of the surface can be measured either by direct optical observation whenthey are sufficiently large, as shown in Figure 2bc, or by optical interferometry? , confocalmicroscopy? , acoustic microscopy? , or by simply measuring the deviation or defocus of a laserprobe beam reflected by the liquid surface? ? ? when they are weak.When the irradiation is continuous, the resulting surface deformation attains a steady state.The deformation amplitude depends on the ratio between the radiation force and the restoringforces that are surface tension, gravity and possibly elasticity. Thus, surface tension can bededuced from the measurement of the steady surface deformation of the liquid surface, e.g. ofdrops? ? , see Figure 2a.When the irradiation is time-dependent, i.e. either pulsed or amplitude-modulated, equilibriumand transport properties can be simultaneously determined from the response of the liquid sur-face to the time-dependent excitation using models of flow and surface deformation. Suchfree-surface flow models addressing several dynamic regimes (purely inertial, weakly damped,overdamped regimes) and several geometries have already been developed, among which ? forflat surfaces in any dynamic regime, and ? for spherical drops in weakly damped regime. Usingtime-dependent irradiation, regular surface tension? ? ? ? ? ? , ultra-low interfacial tension? ? ? ,regular and large bulk viscosities? , surface visco-elasticity of complex fluids? ? and bulk elas-ticity of gels? could be measured using the optical and/or acoustic techniques. In particular,it has been shown using the optical technique on flat gel surfaces that both the complex elasticmodulus G and the surface tension g of the gel could be simultaneously measured by vary-ing the beam diameter w from the capillarity-dominated dynamic regime w � g/G to theelasticity-dominated regime w � g/G? .During the last decade, the Bordeaux team and R. Wunenburger (working within the Bordeauxteam from 2002 to 2012) have significantly contributed to both the optical and the acoustictechniques:

• measurement of ultralow interfacial tension using the optical technique? ? , see Figure 2c,• full hydrodynamic model of the dynamics of free liquid surface deformations by optical and

acoustic radiation pressure, which allows for the measurement of liquid properties on initiallyflat surfaces in any dynamic regime, with experimental and numerical validation? ,

• numerical investigation of the deformation of sessile droplets by radiation pressure usingthe Boundary Element Method? , see Figure 2d,

• identification and modeling of the perturbing effect of bulk flows induced by light scatteringon the optical technique? ? ,

• metrology with the acoustic technique? , see Figure 2b.

II. PhD thesis work

The state-of-the-art has shown that it is possible to measure the surface tension, elasticityand bulk viscosity of liquids (or soft solids) in a contactless manner using optical or acoustictechniques. The main challenge of the project is to apply these emerging techniquesto natural glue droplets suspended on capture silk fibers in situ, in particularto adapt the optical technique to suspended droplets. To our knowledge, theimplementation of these techniques on natural samples in situ has never beenperformed.Besides, adapting the optical technique to liquid samples with sub-millimetric sizeconstitutes in itself a far reaching technological progress with attractive potentialapplications to chemical / biological high-throughput screening which go beyondthe characterization of natural spider orb web droplets. Liquid samples with nanoliter-scale volumes deposited as sessile droplets on multiwell-plates are indeed commonly involvedfor automated, high throughput biological/chemical screening. In this context, a contactlesstechnique of measurement of surface tension, elasticity, and bulk viscosity would enable to

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monitor in real time several kinds of chemical reactions / phase transitions occurring withinsessile droplets.

Comparative assets of the optical and acoustic techniques

• optical technique: liquid surface excitation with small spatial extent (∼ 10-200 µm)allows for the simultaneous measurement of elastic modulus and surface tension, sinceg/G ∼ 50µm with g ∼ 5 · 10−2 N/m and G < 103 Pa.

• acoustic technique:◦ since both optical and acoustic radiation pressures scale as I/c, where I is the wave

intensity and c the propagation speed, for a given intensity the acoustic radiationpressure, for which c ∼ 103 m/s, is intrinsically much larger than optical radiationpressure, for which c ∼ 108 m/s. Therefore, larger signal to noise ratios are inprinciple achievable using the acoustic technique.

◦ airborne acoustics is usually performed in the 10 kHz - 1 MHz frequency range. Inthis range, the spatial extent of acoustic excitation (35 mm - 350 µm) is larger thanthe natural droplets (diameter 100-200 µm). As a consequence, the perturbing effectof droplet vibrations on the measurements is expected to be weaker than with theoptical technique.

Foreseen Issues

Foreseen issues are:• concerning the optical technique:

◦ possible insufficient signal to noise ratio due to the vibrations of the suspendeddroplets,

◦ perturbing effect of the possible heating of droplets by absorption of the laser beam(induced phase change of the droplets, evaporation). To our knowledge, opticalabsorption of spider glue has never been performed. However, optical absorptionmeasurements of spider silk constituting the fibers did not evidence any absorptionpeak in the visible window? .

• concerning the acoustic technique: since the wavelength of the acoustic beam (equal to3.5-0.35 mm at targeted frequency 105-106 Hz in air) will be larger than g/G ∼ 50µ m,it will be probably impossible to separate the effects of elasticity and of surface tensionon the dynamics of surface deformation using the acoustic technique.We propose to implement simultaneously both techniques, which have comple-mentary assets and possible drawbacks, in order to maximize the chances of success.

Implementation of the optical technique

The optical technique will be implemented according to the sketch shown in Figure 3a? . Inthis setup, the probe laser beam is focused on the top of the surface hump induced by thepump laser beam. The hump acting on the probe beam as a spherical mirror with focal lengthequal to the inverse of its curvature, the defocus of the reflected probe beam allows to monitorthe time-dependent curvature of the hump. Configurations with increasing complexity will beimplemented:

• flat sample surface, simple liquids: measurement of surface tension and viscosity usingamplitude modulated excitation and lock-in detection by analysis of experimental datausing already developed theoretical model? .

• flat sample surface, gels: measurement of surface tension, viscosity and elasticity usingvariable pump beam focusing? and already developed model.

• sessile droplet of simple liquids:◦ adaptation of the setup to account for the defocus of the probe beam by the droplet

curvature at rest, see Figure 3b.◦ investigation of the influence of pump beam diameter and of droplet radius on the

surface deformation dynamics using pulsed and amplitude modulated excitation

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FIG. 3. (a) Sketch of the setup to be implemented for the optical technique (AOM : acousto-optic

modulator). (b) Variant adapted to sessile droplets. (c) sketch of suspended droplets.

FIG. 4. (Left) Elongated droplet in a standing wave ultrasonic levitator (from ?). (Right) Successive

pictures of a droplet undergoing quadrupolar deformations forced using an amplitude modulated

acoustic standing wave in a levitator (from ?).

◦ determination of surface tension and viscosity by fitting the measured curvaturesignal with numerical predictions performed by H. Chraıbi? .

• sessile droplet of gels:◦ investigation of the influence of pump beam diameter and of droplet radius on the

surface deformation dynamics in presence of bulk elasticity◦ implementation of elasticity in free-surface flow simulation program based on Bound-

ary Element Method by H. Chraıbi◦ measurement of surface tension, viscosity and elasticity using variable pump beam

focusing by fitting the measured curvature signal with numerical predictions.• suspended, artificial droplets of simple liquids, then of gels: same program as for sessile

droplets with particular attention to the effect of droplet vibrations, see Figure 3c.• Implementation of the optical technique on suspended natural droplets in vitro with

particular attention to the possible effects of droplet vibrations on the measurements andof irradiation on droplet ageing.

• Thorough study of the the influence of spider specie, temperature and air humidity ondroplet surface and bulk properties.

Implementation of acoustic techniques

The implementation of the acoustic techniques on natural droplets is planned to be twofold:

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Implementation of a standing wave ultrasonic levitatorA commercial standing wave ultrasonic levitator working at 100 kHz frequency will be usedto measure the surface and bulk properties of the natural droplets, as illustrated in Figure 2a.What will be exploited is not directly the ability to levitate liquid droplets in air but rather thehigh intensity of the standing acoustic field established in the levitator, which allows to deformirradiated liquid droplets in air. Two kinds of experiments will be conducted :

• Determination of surface tension of natural droplets from their steady ellipsoıdal deforma-tion under steady irradiation, as shown in Figure 4a? . The chosen working frequency ofthe levitator allows the product kR to reach values around 0.2 (k is the acoustic wavenum-ber and R the droplet radius), a value for which steady droplet deformations obtainedusing acoustic levitators have already been measured and quantitatively exploited? .

• Resonant forcing of the quadrupolar deformation mode of natural droplets by theamplitude-modulated acoustic standing wave? ? , as shown in Figure 4b. Surface tensionand bulk viscosity are deduced from the frequency and damping of the droplet shapeoscillations? ? . The response of droplets to the time-dependent acoustic forcing will bedetected using a Lock-in amplifier.

Both steady deformation and shape oscillations of the droplets will be detected by laser trans-mission analysis? . Both kids of experiments will be conducted according to the following steps:

• Benchmark experiments on model liquid and visco-elastic artificial droplets with varioussizes, levitating or suspended on artificial threads.

• Experiments on in vitro natural glue droplets suspended on silk fibers: thorough study ofthe the influence of spider specie, temperature and air humidity on droplet surface andbulk properties.

The risks associated with this standing wave technique are possible perturbing effects of soundabsorption by the droplet and/or the surrounding medium: (i) acoustic streaming (permanentair flows associated to sound absorption) leading to droplet vibrations and evaporation, (ii)droplet heating. This is why (i) the implementation of a humidity-controlled chamber has beenplanned has been included and (ii) we plan to implement a high-frequency, pulsed variant ofthis technique.

Implementation of a focused, high frequency, pulsed acoustic beamWe plan to implement a high-frequency, pulsed variant of this technique, whose principle isthe following: a focused, high-frequency (500 kHz), pulsed, progressive acoustic beam deformsimpulsively the droplet surface. Surface tension and bulk viscosity are deduced from its relax-ation using modal analysis inspired from ?. This technique shares several features with theoptical technique except the pump laser which is replaced by a focused acoustic beam. Thepulsed excitation should reduce the effects of sound absorption on the measurement and onthe natural samples. Energy concentration larger than in the levitator resulting from higherfrequency and beam focusing should compensate for the short duration of the excitation.

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