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Journal of Molecular Structure

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Revealing the solid-like nature of glycerol at ambient temperature

L. Noirez *, P. BaroniLaboratoire Léon Brillouin (CEA-CNRS), CE-Saclay, 91191 Gif-sur-Yvette Cédex, France

a r t i c l e i n f o

Article history:Received 26 November 2009Received in revised form 3 February 2010Accepted 5 February 2010Available online xxxx

Keywords:Shear elasticityLiquid stateSolid-like correlationsPrimary linear regime

0022-2860/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.molstruc.2010.02.013

* Corresponding author. Tel.: +33 1 69 08 63 00; faE-mail address: laurence.noirez@cea.fr (L. Noirez).

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a b s t r a c t

We report on new dynamic measurements indicating a low frequency solid-like behaviour far above theglass transition and above the melting point in glycerol. Several tens micron thicknesses of pure (anhy-drous) glycerol are deposited on highly wetting substrates. The response of the material to a mechanicalstress is probed at room temperature as a function of the time and the frequency. The first type of exper-iment consists in measuring the linear dynamic response in a frequency range from 0.1 up to 10 rad/s.The second type of experiment consists in measuring the stress relaxation under a weak constant shearstress. In both cases, these independent experiments reveal that the glycerol exhibits a non-vanishingshear elasticity indicating a macroscopic solid-like character above its melting point. These results arecompared with recent important observations reported, in particular, in the liquid state of glycerol bydielectric relaxation and in its supercooled states using low stress rheology.

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1. Introduction mentary light on the mechanisms involved in the supercooled states,

Liquids are defined by the absence of shear elasticity in contrastto solids or plastic fluids that require a finite stress for flowing [1]. Re-cent studies seem to indicate that this definition is too restrictive. In-deed, new rheological measurements carried out by improving theboundary conditions between the fluid and the substrate show thatviscous liquids (mainly low molecular weight polymers) that are ex-pected to be pure viscous liquids, exhibit actually a finite macro-scopic shear elasticity away from any phase transition [2,3]. Theidentification of hitherto neglected long-range elastic correlationsin these Van der Waals liquids is of fundamental importance. This so-lid-like property is possibly not specific to Van der Waals liquids butmay be generic involving the strength of the intermolecular interac-tions (Van der Waals, polar, H-bond interactions). The paper exam-ines the case of the liquid state of H-bond glass formers. Thechosen H-bond liquid is the glycerol (C3H8O3). Glycerol is widelypresent in life science (cell energy storage), industry (plasticizers,cosmetics, foods, medication). It is also widely academically studiedbecause of its rich dynamic behaviour in the glass and the super-cooled states [4]. In this paper, we restrict the study of glycerol to atemperature domain far away from the glass transition and abovethe melting point. We therefore aim at understanding the a priorisimplest state of glycerol: the liquid state. Thus a purely viscousbehaviour is expected using conventional rheology. By applying fullwetting boundary conditions, the rheological response exhibits itselastic behaviour confirming the generic character of this propertyin the liquid state of glass formers. This result should shed a comple-

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Baroni, J. Mol. Struct. (2010), do

in thermal history and more generally on the knowledge of the pre-glassy behaviour of glass formers.

We examine the dynamic response of a thin but macroscopic(several tens’ microns) thickness of pure glycerol submitted to asmall (linear) shear solicitation. Two different procedures are ap-plied. The first one consists in scanning at a constant shear strainthe material response versus frequency (x); this method providesa dynamic profile displaying the instantaneous response and the de-layed response in terms of elastic shear modulus (G0(x)) and viscousmodulus (G0 0(x)), respectively. The second procedure consists inapplying a constant strain stress to the material and examining itsresponse versus time. The liquid-like character is defined by a van-ishing response whereas a solid-like behaviour exhibits a non-van-ishing response at the time scale of the experiment. A transitionfrom a solid-like behaviour to a flowing state obtained by increasingthe shear stress (yield stress) indicates a plastic behaviour.

This technique requires a high care to optimise the boundaryconditions between the substrate and the material. These bound-ary conditions play indeed a key role since the stress has to be asintegrally as possible transmitted by contact from the surface tothe material. The material response has to be also as integrally aspossible transmitted by the sample to the surface linked to thetransducer. This is the necessary condition to guaranty a physicallymeaningful signal. Surface roughness, presence of gas, wettabilityare known as possible parameters favouring the violation of theno-slip boundary condition [5]. Very few studies aim at optimisingthese experimental conditions. By choosing adequately the surfacein order to ensure total wetting conditions with the fluid, we haverecently shown that it is possible to improve the dynamic responseand reveal a non-vanishing low frequency shear modulus far above

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the glass transition in various viscous liquids [2,3]. This measure-ment protocol is here applied to glycerol. It confirms the non-van-ishing behaviour of the shear elasticity (G0 ? G0 when thefrequency vanishes) at room temperature, thus at about 100 �Cabove Tg (Tg = 190 K). This observation implies that these long-range solid-like correlations have a generic character and have tobe taken into account for a better understanding of the glyceroldynamics from ambient down to low temperatures.

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Fig. 1. Importance of the nature of the substrate on the wettability properties. (a)Glycerol drop (coloured with a carmine) deposited on an aluminium substrate. (b)Glycerol drop (coloured with a carmine) deposited on a zero-porosity ceramic(alumina) substrate. (c) Variation of the contact angle h of glycerol measured as afunction of the time on aluminium ( ) and zero-porosity ceramic (alumina) ( ).(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this paper.)

2. Experimental

Anhydrous glycerol (C3H8O3) was purchased from Acros Organ-ics (99.8% purity). It presents a glass transition at �83 �C and amelting point at 19 �C. All the experiments are carried at roomtemperature (22 ± 1 �C). Before the experiment, the liquid was ob-served by optical microscopy (to ensure the absence of air bubbles)and maintained under vacuum before the experiment. The sampleis rapidly deposited on disk-like alumina surfaces freshly cleanedby thermal treatment (400 �C). The two surfaces are approacheduntil the full contact with the liquid is achieved. Different gapthicknesses are chosen for the experiment ranging typically from20 up to 50 lm. The set is closed in a chamber (gas pulsed cham-ber). To avoid water contamination (the glycerol is very hygro-scopic), a nitrogen gas circulation is kept throughout all theexperiment. It is important to point out that the sample is directlytaken from the bottle, observed at room temperature without hav-ing been submitted to any thermal treatment.

The experiments are carried out using a ARESII rheometer (TA-Instruments). The shear strain is applied by imposing a small rota-tion of a disk with respect to the other. The second disk is immobileand coupled with a transducer on its central axis. It measures thetorque transmitted by the material under solicitation. The moduliare classically extracted from the difference between the inputand the output signals; the component in phase with the straindetermines elastic (or storage) modulus (G0), whereas the out ofphase component defines the viscous (or loss) modulus (G0 0).

3. Importance of the boundary conditions

The surface is at the central place in this experiment since it isat the origin of the motion transfer that probes mechanically thesample. The transmission of the shear stress to the material is opti-mised by using appropriate boundary conditions between the sub-strate and the liquid. This is here achieved by using zero-porosityalumina substrates freshly regenerated by thermal treatment.The optical observation of the contact angle between the liquidand the surface allows the determination of the quality of the wet-ting [6,7]. The profile of a drop deposited on the surface is mea-sured versus time. The contact angle h is defined by the droptangent to the surface. In the case of a total wetting, the drop ex-tends entirely on the surface. The liquid progresses via a thin liquidlayer (precursor film [8]) in the front of the drop. The completevanishing of the contact angle indicates that total wetting condi-tions are achieved.

The total wetting improves the dynamic transfer and avoids theslippage on the substrate during the liquid progression. Fig. 1ashows that the metallic substrate (aluminium), conventionallyused for the rheological measurements, does not provide a totalwetting interaction; the precursor film is absent and a non-vanish-ing stationary contact angle (h = 20�) is observed. In contrast, a ra-pid propagation of the liquid via a precursor film and a totalwetting final state (h � 0) is observed on non-porous alumina(Fig. 1b). The total wetting ‘‘sticks” the molecules on the surface.It also limits the risks of formation of an interlayer due for exampleto the migration of nanobubbles [9]. This phenomenon is particu-

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larly present on partial wetting or no-wetting surfaces since thenanobubbles are expulsed from the liquid to create an interface be-tween the liquid and the substrate [10]. Fig. 1c illustrates quantita-tively different qualities of wetting via the measurement of thecontact angle.

The rheological experiment consists in applying a small shearstress/strain to the fluid. The boundary conditions are thereforeessential. An incomplete dynamic transfer (partial slippage) under-estimates the material response. The reinforcement of the bound-ary conditions carried out by total wetting, improves the contacts,reduces the slippage ability and guaranties a better dynamic trans-fer towards true no-slip boundary condition. Different followingrelationship (as the Tolstoï formula [11]) relates the wetting prop-erty (determined via the contact angle h method) to the slippageability (via the slippage length b defined as the distance from thesurface corresponding to the origin of the velocity gradient asshown): b � exp(r2�c(1 � cos h)/kT) � 1, b = 0 when h = 0 in thecase of total wetting (r is related to the molecule size and c tothe surface tension). b is of the order of several nanometers atthe interface for partial wetting conditions (which is typically thecase of a glycerol deposited on an aluminium substrate, h reaches70�).

We see on the next paragraph that the differences of wettingproduce under the same stress conditions, different viscoelasticbehaviours. The boundary conditions have thus important andmultiple consequences.

4. Results: the soft solid-like properties of glycerol

To illustrate the influence and the importance of the boundaryconditions on the result, we display in Fig. 2a the response ob-tained on zero-porosity alumina fixtures (total wetting conditions)and the conventional viscous response expected for the glycerol

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Fig. 2. Glycerol at room temperature. The viscoelastic moduli (G0 and G0 0) are determined as a function of the frequency (x), using: (a) the improved boundary conditionprotocol. Gap thickness: 0.040 mm, ceramic plate–plate (20 mm diameter), 2% strain amplitude (linear regime). The dotted line (---) correspond to the pure viscous behaviourconventionally expected for glycerol. (b) Non-cleaned ceramic surfaces (20 mm diameter). (c) Aluminium surfaces (plate–plate geometry (40 mm diameter)).

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(the dynamic viscosity measured in the flow regime follows therelationship: G0 0 = g�x with g = 1.1 Pa.s). The reinforcement of theboundary conditions produces a spectacular increase of the lowfrequency dynamic moduli (Fig. 2a–c are displayed with the samescale units). Fig. 2b is the dynamic response obtained under thesame experimental conditions as Fig. 2a but without ‘‘regenerat-ing” the alumina surfaces (the ceramic surfaces are rapidly pol-luted at atmospheric air, they have to be sterilised at hightemperature prior the experiment – see Section 2). Fig. 2c is ob-tained using aluminium surfaces, therefore under partial wettingconditions and displays only a viscous response (within the fre-quency window) scaling as x as conventionally expected.

On alumina substrate (total wetting conditions), Glycerol exhib-its in this frequency domain, a non-negligible shear elastic re-sponse in addition to the viscous response. How to interpret theemergence of the predominant shear elasticity? The experimentalprocedure depends directly on the efficiency of the transmission ofthe stress via surface contacts. The contacts are reinforced undertotal wetting conditions. Similarly to what was already reportedon low molecular weight polymers [2,3], the reinforcement ofthe boundary interactions allows a better transmission of thestress. Reciprocally the degradation of the solid-like boundary con-tacts can be obtained using large strain amplitude oscillatory shearor by applying a continuous shear flow.

Fig. 3a displays the evolution of the elastic signal of the glycerolversus strain amplitude (from 0.75% up to 10%). Both elastic andviscous moduli decrease non-linearly by increasing the strainamplitude, showing the fragility of this solid-like response with re-

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Elastic and viscous moduli of Glycerol versus strain (%)(e = 50µm)

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Fig. 3. (a) Dynamic response of glycerol with increasing strain amplitude (at a given low fthe gap thickness e: c = dl/e (gap thickness: 0.050 mm, ceramic plate–plate (20 mm diammodulus G0 0: : 0.75%, : 1%, : 2%, : 3%, : 5%, : 10%. The figure at right gatherssmaller modulus values compared to Fig. 2 are due to the larger gap, in agreement with eastrain amplitude: at low strain amplitudes, the linear elastic regime (L–E) dominates (Glinear regime: N–L) with a faster decrease of the elastic contribution with the strain. Atwith a dominating viscous component (G0 0 > G0). The circle indicates the area correspond

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spect to the strain parameter and also the experimental difficultyto access to this primary elastic regime. This behaviour fits withthe scheme already observed for ordinary polymer melts [2,3]. Atlarge strain amplitude, the viscous modulus keeps high values athigh frequency, and decreases progressively from high to low fre-quency to depict the conventional x-scaling-like. At high strainamplitude and high frequency, the elastic modulus becomes negli-gible with respect to the viscous modulus as in the case of a flowregime. The scheme (Fig. 3b) gathers the elastic and the conven-tional viscoelastic regime. The linear elastic response is measuredin ‘‘L-E Regime”. ‘‘L-E Regime” corresponds typically to low strainrates of 0.05% up to 1%. At higher strain amplitudes, the low fre-quency moduli lower (entrance in the non-linear regime (NL)) witha decrease of the elastic modulus more pronounced than the vis-cous one. The strain induced lowering affects all frequencies exceptgradually a high frequency zone (typically above 10 rad/s). Thishigh frequency zone corresponds precisely to the zone where theconventional flow behaviour of the viscoelastic curve emerges(‘‘V-E Regime”). This solid-like regime (‘‘L-E Regime”) is prior tothe viscoelastic regime (V-E); the conventional linear viscoelasticbehaviour is thus a second linear domain, obtained once the so-lid-like response is lowered by entering into a strong non-linear re-gime. The action of the strain amplitude is similar as a transitionfrom total to partial wetting conditions. This transition is dynamic:fast relaxation time contacts are easily restored and give rise to theconventional flow behaviour whereas long time relaxation (solid-like) contacts bear only small strains and exhibit the elasticresponse. Since the lowest strain amplitudes ensure the weakest

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requency). The strain amplitude is defined as the rate of the linear displacement dl toeter)). Elastic modulus G0: : 0.75%, : 1%, : 2%, : 3%, : 5%, : 10%. Viscous

the evolution of the plateau values of G0(c) and G0 0(c) versus strain amplitude. (Therlier observations [2,3].) (b) Scheme of the evolution of G0 and G0 0 as a function of the0 > G0 0). At moderate amplitudes, both elastic and viscous responses diminish (non-high strain amplitudes, both viscous and elastic responses are linear (L–VE regime)ing to the experimental data presented in (a).

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Fig. 4. Strain stress relaxation test on glycerol at room temperature. Applied strainstress: c = 2%, plate–plate geometry (20 mm diameter), 0.04 mm gap thickness.

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perturbations of the sample, i.e. to fulfil the causality–linearityconditions, the elastic response of the fluid corresponds actuallyto the first linear response of the material.

Another procedure to evidence the solid-like character con-tained in the liquid state of glycerol is a relaxation measurement.A small but constant shear strain is applied on the liquid. Thetransmitted shear stress is measured. Fig. 4 shows the relaxationbehaviour (G(t)) of glycerol submitted to a constant shear strainof c = 2%. This measurement is carried out at room temperature,at 0.04 mm gap thickness and using total wetting boundary condi-tions. As it can be seen, the liquid displays a significant elasticity(G � 80 Pa) and does not flow under strain; the shear stress doesnot collapse after more than 103 s. This is typical of a solid-like re-sponse, coherent with the previous dynamic relaxationobservations.

5. Discussion

No-vanishing viscoelastic moduli at low frequency in the liquidviscous state above any phase transition might appear as a surpris-ing observation. It is indeed commonly admitted that viscous liq-uids do not exhibit shear modulus in opposition to solids andyield stress materials. However, looking back at old and recent lit-erature, a series of papers indicates that the situation is not soclear.

To our knowledge, the first observation of a non-vanishing elas-ticity on ordinary liquids is due to Derjaguin and collaborators [12]since at least 1983, using the vibration of a piezoelectric system(resonator). The measurement is carried out at the micron scaleand at a relatively low frequency (73 KHz). At higher frequencies(10 MHz) and using a similar technique, other authors (Bund andSchwitzgebel [13]) report also on the existence of elasticity inlow and medium viscosity fluids. They notice that medium viscousliquids as glycerol exhibits considerable elasticity. In a differentdomain but using also the piezoelectric system, Gallani et al. reporton ‘‘abnormal” gel-like behaviour identified in the isotropic phaseof liquid-crystal polymers [14] that they attribute to specific li-quid-crystal properties. In 2003, a low frequency gel behaviour isidentified by Collin on 15 lm thickness of a low molecular weightpolystyrene in the molten state [15]. In 2004, McKinley and co-workers reported on a 3–4 lm thickness elasticity on a polystyrenesolution using a microrheometer but attributed it to trapped dustparticles [16]. In 2005, Noirez and co-authors reported on elasticbehaviours in the isotropic phase of liquid-crystal polymers usinga conventional rheometer at the millimeter scale [17]. Since2006, solid-like behaviours (G0 and G0 0 constant with G0 > G0 0 atlow frequency) are identified by the same authors at the sub-mil-limeter scale, using total wetting surfaces, in glass formers and or-dinary polymers [2,3]. In 2007, Wang [18] reproduced the results

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of [2] using the total wetting protocol. In 2008, Zondervan et al. re-ported on a delicate millimeter thickness solid-like network that itis possible to reveal in the supercooled state of glycerol and o-ter-phenyl, by applying very weak stresses [19]. The same authors ex-plain that this solid-like network is usually neglected inconventional rheology since the large stresses employed shear-melts the solid-like structure.

These converging results indicate that an elastic state has beenso far missed in the conventional viscoelastic description of the li-quid state of glass formers. What are the specificities of theseexperiments? In piezorheometer measurements, the appliedstrains originate from the molecular vibration and thus are extre-mely low. In the case of the mechanical measurements (conven-tional equipment), small gap thicknesses (reduced volumes) areused reducing the displacement on the surface at low strain andspecific surfaces are used to reinforce the molecular anchoring. Inthe case of the elasticity revealed in the isotropic phase of liquid-crystal polymers, the high anchoring ability of the liquid-crystalmoieties avoids wall slippage. The common point is the absence/minimisation of dissipation of the stress at the surface/liquidboundary and in the volume. As observed by different authors,the elastic response disappears above a critical strain amplitude,it indicates the yield stress nature of the liquid state.

Apart from mechanical measurements, low frequency elasticityhas been also evidenced using very different techniques as X-rayphoton correlation [20]. These developments carried out on super-cooled polypropyleneglycol suggest that the supercooled state ofglass formers is made of solid clusters present as infinite or extre-mely long-range density fluctuations characterized by slow relax-ation times which make them appear as elastic clusters on theexperimental time scales, confirming the very early observationsof dynamic clusters by Fischer using dynamic light scattering[21]. However, in the Zondervan’ works, thermal treatment effects,aging effects are clearly identified as a parameter controlling orfavouring the emergence of the elasticity. In the present paper,the elasticity identified in the liquid state of glycerol, thus awayfrom the temperatures of the supercooled state and far away fromthe glass transition can hardly be interpreted as aging since the re-sponse does not evolve with time on the experimental time scales(which have been tested over a week in case of low molecularweight polymers). The solid-like correlations observed in thesupercooled state are huge with respect to those described hereabove the melting point. In the supercooled state, the solid formedis extended over the millimeter scale (1 mm gap thickness), and ischaracterized by non-negligible shear moduli (about 106 Pa after2 weeks aging). The much modest characteristics observed abovethe melting point (thickness probed less than 0.045 mm, and weakshear moduli of about 80 Pa) indicate nevertheless that the originof the (supercooled) lowest temperature solid-like contributionmight have to be found above the melting point.

Finally, a remarkable work carried by Swensson and co-workers[22] shows that it is possible by broadening the frequency spec-trum of dielectric relaxation, to identify a so far unknown slowrelaxation process in pure glycerol, diluted glycerol and evenwater. Relating these slow relaxation mechanisms is beyond thescope of this paper, these results show nevertheless that it is ur-gent to reconsider the key role of intermolecular interactions fromthe liquid state down to low temperatures. This should influencethe way we study dynamic phenomena.

6. Conclusions

Nowadays, the boundary conditions are at the centre of re-search areas related to filmic, surfacic, tribology, slippage processes[22]. The control or at least the improvement of the boundary con-

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Fig. 5. Frequency dependence of the elastic G0(x): and viscous moduli G0 0(x): ,measured for polypropyleneglycol – PPG4000, Mw = 4000, Tg = �75 �C) at T = +5 �C(0.075 mm gap thickness – 20 mm alumina plate–plate).

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ditions in the frame of techniques probing mechanically the liquidsample response is indispensable. This paper illustrates the impor-tance of these improvements for glycerol revealing an elasticity inthe viscous state away from any phase transition. This result iscoherent with previous data obtained mostly on Van der Waals liq-uids [2,3,7,9,13,15].

The Refs. [3,20] report on a low frequency elasticity observed onanother glass former: the polypropyleneglycol PPG4000. The dy-namic measurements indicate a shear modulus of 200 Pa at0.075 mm and 80 �C away from the glass transition (Tg = �75 �C)(Fig. 5). The present study on glycerol shows that the low fre-quency elasticity is not specific to polymeric structures but canbe extended to molecular glass formers. It points out the veryimportant role of the H-bond interactions.

Interestingly, it seems that the low frequency elasticity is obser-vable above the melting point at small gap only, typically below50 lm using full wetting boundary conditions, whereas a solid-likenetwork is measurable at the millimeter scale in the supercooledstate [19]. Above 50 lm thickness in the liquid state, the low fre-quency elasticity weakens and reaches the sensibility limit of thedevice (revealing only a viscous modulus). The dependence withthe thickness reveals a dimensional character and reminds whatwas already observed on polymer melts [2,3,15]. It might addition-ally reveal the limits of mechanical techniques to probe delicatesolid-like properties.

This solid-like property is restricted to small dimensions. Whyis it important to take it into account at a macroscopic scale? First,this elasticity is an intrinsic liquid property, it might elucidate theorigin of various flow instabilities, non-linear behaviours [23] sofar unexplainable in the frame of the conventional moleculartheories [24]. The measurement of elastic correlations restoresthe central role of the intermolecular interactions in the flowmechanisms. It imposes a reinterpretation of the conventionalviscoelastic description which is based on a phenomenological ap-proach. In the frame of the conventional viscoelastic approach, themacroscopic dynamics is interpreted as directly resulting from theelementary dynamic at a molecular scale (concept of ‘‘terminaltime”). This single molecular picture neglects intermolecular inter-actions and thus ignores the cohesive nature of the fluidic state.Some theoretical approaches have pointed out the limits of theconventional single chain statistics (Rouse, reptation models).The EKNET model (energetic kinetic network) considers theelementary dynamic unit as a set of multiple chains called ‘‘ball”interacting through a dynamic network [25]. These interesting‘‘interacting” approaches are usually not widely spread in therheology field.

The shear elasticity which is measurable at low but macroscopicgaps becomes too weak to be measurable using this technique

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when the sample thickness increases. This interesting dimensionalproperty might shed a new light on the apparent discontinuity ofthe dynamic properties from microscopic to macroscopic scale inviscous fluids. Nano and microfluidics properties report on surfaceeffects and/or elastic effects that vanish at macroscopic scale. Aremarkable microfluidic study carried out by Bocquet and co-authors, has recently evidenced tens micron finite-size effects inthe flow behaviour in emulsions [26]. The authors insist on thegeneric character of these effects. Other dimensional propertiesare experimentally evidenced in various heterogeneous materialsas cimentary, pastes, foams, large structures [27]. The introductionof the concept of non-extensivity of the physical parameters seemsto be required for the description of long range correlations in flu-ids. Such a concept is introduced in the NEVET (non-extensive vis-coelastic theory) [28]. Clearly these new experimental results haveto be extended and certainly still improved, but they are alreadyrich of perspectives for a better understanding of the nature ofthe liquid state and of its flow properties.

Acknowledgments

The authors thank F. Volino for enlightening discussions con-cerning the physics of liquids and for critically reading the manu-script and C. Thibierge for the fruitful discussions on the glycerolproperties.

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