Audrey Lasalle

Christian Guizard

Eric Maire

Jérôme Adrien

Sylvain Deville

Particles redistribution and structural defects development during ice templating

Keywords: Freeze-casting, ceramic material, cellular solids, mechanical properties, defects 10

The freezing of colloidal suspensions is encountered in many natural and engineering processes. It can be harnessed through a process known as ice templating, to produce porous materials and composites exhibiting unique functional properties. The phenomenon by itself appears simple: a solidification interface propagates through a colloidal suspension. We are nevertheless still far from a complete understanding and control of the phenomenon. Such lack of control is reflected in the very large scattering of mechanical properties reported for ice-templated ceramics, largely due to the formation of structural defects. Through systematic in situ investigations, we demonstrate here the role of the suspension composition and the role of particleparticle electrostatic interactions on defect formation during ice templating. Flocculation can occur in the intercrystal space, leading to a destabilisation of the solid/liquid interface triggering the growth of crystals perpendicular to the main ice growth direction. This mechanism largely contributes to the formation of structural defects and explains, to a large extent, the scattering of compressive strength values reported in the literature.

Introduction

The solidification or freezing of colloidal suspensions is commonly encountered in a variety of natural processes such as the freezing of soils and the growth of sea ice. It is also seen in everyday life and engineering situations such as food engineering, cryobiology, filtration, and water purification. In materials science, the solidification of colloidal suspension is finding applications in various processes such as the processing of particle-reinforced alloys and composites, and the processing of porous materials, usually referred to as ice-templating or freeze-casting. This simple process, where a colloidal suspension is simply frozen under controlled conditions and then sublimated before sintering, provides materials with a unique porous architecture, where the porosity is almost a direct replica of the frozen solvent crystals. When a colloidal suspension is frozen unidirectionally, an initial transient regime is observed, corresponding to the initial nucleation and growth of the ice crystals. After this transient regime, a steady state regime is established, where lamellar ice crystals grow steadily along the direction imposed by the temperature gradient.

Applications of ice-templating have been demonstrated for bone substitutes [1], drug delivery [2], acoustic insulation [3], solid oxide fuel cells [4,5] piezoelectric materials [6] and ultra-sensitive sensors [7]. The great interest in this versatile technique comes from the ease of implementation and the large range of porosity in terms of size (0.2 to 100µm), volume fraction (30 to 90%) and morphologies [8]. It was also shown that the composition of the ice-templated suspensions influences the final microstructures through the nature of additives [8] or the quantity of dispersant [9]. For any application, a proper control of the structure is of critical importance. Yet, little is understood about the dynamics of structure formation mechanisms during freezing. The characteristics of the colloidal suspension are often critical to the behaviour of the system during freezing, both in technological and natural occurrences of colloid freezing, and have rarely been analysed or understood.

A wide range of compressive strength values is reported for ice-templated materials (figure 1) when tested along their freezing direction. The compressive strength is of course dependent on composition and is greater for porous titanium or zirconia than for calcium phosphate, but the data show substantial variation even within identical systems. Because of the unusual spread in the literature data, we performed a careful review of the methods and microstructures in the literature. Microstructural observations revealed that many of the lowest strength samples in the literature had structural defects oriented perpendicular to the ice growth direction, as shown for example in figure 2b or figure 8 of reference [10]. This orientation is the worst case scenario for compressive strength measurements, and we believe that these defects are the root cause of many anomalously low strength ice templated materials found in the literature. High strength samples (figure 2a) are systematically free of such defects. The absence of such defects is clearly a necessary but not sufficient condition to obtain high compressive strength. Excessively large pore size can also lower the strength.

What we understand so far of the solidification of colloidal suspensions is derived primarily from analogies with dilute alloy systems or the investigated behaviour of single particles (or cells) in front of a moving interface. Many geological, biological, and industrial systems involve concentrated particle systems. In colloidal systems, unlike alloys, the particle-particle electrostatic interactions can strongly determine the behaviour of the system. Such aspects have not been taken into account so far. Owing to their neglect of particle-particle interactions, isolated particle models are not able to quantify the critical dependence of the final ice crystal morphologies on the initial colloid concentration -a crucially important operating parameter for industrial applications.

Through systematic in situ investigations, we demonstrate here the role of the suspension composition and the role of particle-particle electrostatic interactions on defect formation during ice templating. We performed in situ observations of crystal growth and particles redistribution by X-ray radiography and tomography. We show that particle-particle interaction can have a dramatic influence over the mechanisms controlling the formation of the structure.

Alumina content

Nature of additive Quantity of additive 32vol% D[NH4 + ] 0.2-0.4-0.

Experimental

We developed a panel of alumina suspensions (table 1), carefully characterized by measurements of the zeta potential (figure 3a), viscosity (figure 3b), carbon organic total (COT) and observations of the state of dispersion by Cryo-FEGSEM [12]. These characterizations show that 0.2-0.4wt% of dispersant is the optimal range to obtain the strong repulsive interactions between particles necessary for an optimal dispersion state and stability, a condition traditionally required for ceramic processing routes to minimize defect formation. Adding more dispersant compresses the thickness of the diffuse layer around particles and reduces the effective range of the repulsive 10.1016/j.actamat.2012.02.023 interactions. This causes the zeta potential values to decrease and the viscosity to increase (figure 3a).

Alumina powder (Ceralox SPA 0.5, Sasol, Tucson, AZ, USA), D50 = 0.3µm, specific surface area (SSA)= 8m².g -1 , was dispersed in distilled water with an organic dispersant. Alumina content was held constant at 32vol%. Three sorts of suspensions were prepared, each containing a different dispersant: (1) The dispersant concentration in each slurry was 0.2-2wt% with respect to the dried powder. Dispersant was stirred with distilled water for 30min and then the alumina powder was added. Alumina suspensions were ball-milled for 40h and de-aired before being ice-templated. In some cases, 0.5wt% (with respect to the dried powder) polyvinylic alcohol (PVA) was added as a binder.

The suspensions were first characterized by viscosity measurements performed in a concentric cylinder system (Bohlin viscosimeter, Malvern, Worcestershire, UK). The suspension was pre-sheared for 30 s followed by 30 s at rest. Viscosity was measured at a constant gradient of 50s -1 . Then a zetaprobe (Colloidal Dynamics, North Attleboro, MA, USA) was used to measure the zeta potential.

We adapted a freezing set-up on the beamline ID-19 at the European Synchrotron Radiation Facility in order to follow the freezing by X-ray radiography and subsequently observe the frozen microstructure by X-ray tomography. Suspensions were introduced into a polypropylene mold of 3mm of diameter with a syringe. Particular attention was paid to not introduce air-bubbles in suspension. The mold was placed onto a copper finger frozen from the bottom by a liquid nitrogen flux pumped from a dewar. The cooling rate was controlled by the liquid nitrogen flow rate and the temperature profile was monitored during the experiment, by a thermocouple located near the copper finger surface. The cooling rates were in the range 2-5°C.min -1 . When the cooling began, a monochromatic highly coherent X-ray beam with an energy of 20.5keV was sent through the sample. A CDD camera with 2048 x 2048 sensitive elements was placed 20mm behind the sample. The advancement of the freezing front was followed by fast acquisition radiography. For this we used a so called binning mode i.e. a reduction of the number of pixels in the projection by averaging the measurement of four neighbouring pixels from the CCD and combining them to create one pixel value. With this binning mode, we achieved a spatial resolution of 2.8µm in the radiographs. For the tomography, the frozen sample was maintained at a constant low temperature during the scan. An imaging configuration with high resolution and low acquisition speed was preferred here so the acquisition was performed without binning, with a spatial resolution of 1.4µm.

We used the sequence of radiographs to qualitatively investigate the local evolution of the concentration of colloidal particles. Alumina absorbing more than water, the X-rays absorption and thus the intensity of the signal on the radiograph is inversely related to the concentration of colloidal particles in suspension. To determine the change in colloid concentration in each image, we measured the change in intensity relative to the previous radiograph. Any increase of intensity is thus accompanied with a decrease of the local concentration of colloids (more beam coming through the suspension). Conversely, a decrease of the intensity reveals an increase of the local concentration. These variations can thus be measured qualitatively and dynamically, although not quantitatively. This image analysis was performed using the ImageJ software [13].

Results

In situ radiography of the advancing freezing front shows a behaviour drastically dependent on the quantity of dispersant, D[NH4 + ] in this case, introduced in suspension (figure 4a-c). For suspensions with an optimal dispersion (low dispersant quantity of 0.2-0.4wt%), the freezing front is composed of disoriented ice crystals above which a 430µm's thick layer of particles is accumulated. Above this accumulation, we observe a 20µm's thick particle-depleted region (figure 4a), where the particle concentration is lower than the average concentration (32vol%). Figure 4b shows that increasing the dispersant concentration to 1wt% causes the accumulated layer to decrease to 50µm. Ice crystals tend to align along the freezing direction, but the particle-depleted region remains (figure 4b).

The introduction of dispersant in large excess (2wt%) yields a cellular interface with no accumulated layer and no particle-depleted region (figure 4c). The corresponding three-dimensional tomography reconstructions of frozen microstructures show disoriented ice crystals at low quantity of dispersant (0.2wt%) (figure 4d). By increasing the dispersant quantity to 0.7wt%, ice crystals are more and more oriented (figure 4e) but defects are observed perpendicular to the freezing direction, as illustrated in figure 5 and indicated by black arrows. Since these defects are oriented perpendicular to the freezing direction, they resemble the defects found in the literature review, and shown for example in figure 2b. These defects form pores that traverse the dense ceramic walls, drastically affecting the integrity of the structure. A typical defect-free lamellar microstructure is obtained at 2wt% of D[NH4 + ] (figure 4f).

10.1016/j.actamat.2012.02.023

This behaviour is independent of the nature of the dispersants tested here. We obtain similar microstructures with similar dispersant contents for both D[Na + ] and d[NH4 + ]. The counter ion (NH4 + or Na + ) and the chain length of the dispersant (3 500 to 13 000g.mol -1 ) do not seem to affect the orientation of ice crystals. The same change of ice crystal morphology is observed with d[NH4 + ], the dispersant with a shorter chain length, with disoriented ice crystals at low quantity of dispersant (0.2wt%) (figure 6a) and a lamellar microstructure at 2wt% (figure 6b). We also obtain a similar morphological change from disoriented crystals to a lamellar microstructure with the addition of 0.5wt% of an organic binder (polyvinyl alcohol, PVA). A binder is usually required in ice-templated materials to ensure the cohesion between the particles during the freeze-drying stage, in a suspension containing a low quantity of dispersant. Thus, it is apparent that the formation of such defects is controlled largely by the quality of the dispersion, rather than other variables like dispersant counter-ion or dispersant chain length. The same morphological change is also observed when the cooling rate is increased from 2-5°C.min -1 to 13°C.min -1 . Growth kinetics therefore also play a critical role in the mechanisms controlling the formation of the microstructure.

Discussion

The development of defects perpendicular to the main ice growth direction during ice templating must absolutely be avoided. The microstructures obtained in conditions where such defects develop make such materials useless. We performed a review of the literature on ice growth, in particular in geophysics, and found that the perpendicular defects observed here in ice templated materials strongly resembles the ice lenses observed in geophysics. Ice lenses are ice crystals observed in frozen soils or during the directional solidification of colloidal suspension, growing perpendicular to the temperature gradient direction (for example figure 2c). A schematic view is represented in figure 2d. Ice lenses play a particularly important role in frost heave [11], by determining the soil's heave rate. The typical ice templated microstructures obtained in presence and in absence of perpendicular defects (shown in figures 2a and 2b) strongly suggest that such defects are indeed a replica of ice lenses. Since the porosity is a replica of the ice crystal network obtained after freezing during ice templating, ice lenses will result in the presence of crack-like pores perpendicular to the main ice growth direction (determined by the temperature gradient). The transverse ice crystals growing perpendicular to the main ice growth directions are therefore ice lenses.

A physically intuitive model of ice lens formation was just proposed [11], whereby the nucleation and growth of ice lens is controlled by the mechanical properties 10.1016/j.actamat.2012.02.023

(cohesion) of the concentrated colloidal suspension between the ice crystals. The presence of heterogeneities in the concentrated suspension could therefore be a major factor facilitating the nucleation and growth of ice lenses, locally reducing the cohesion of the concentrated suspension. These heterogeneities can result from flocculation and local formation of agglomerates, and conversely particle-depleted regions. Through a systematic investigation of the panel of suspensions developed, we identified three main parameters controlling the occurrence of particle depletion and ice lenses (figure 7): the ionic strength, the viscosity of the suspension and the velocity of the interface. These three factors are experimentally controlled by the introduction of the dispersant, the quantity of additives (dispersant, binder) and the imposed cooling rate, respectively. For each of these parameters, there is a threshold value below which the behaviour of the system is changing.

The formation of particle-rich and particle-depleted regions requires a driving force for particle redistribution during freezing. Based on our results, we will first discuss the possible driving force for the formation of the accumulated particles layer, and then propose a scenario for the formation of a particle-depleted region and the nucleation and growth of ice lens, leading to the formation of structural defects.

Origin of the particles in the layer of accumulated particles

Unidirectional ice templating usually results in the growth of lamellar ice crystals, oriented along the temperature gradient. A layer of accumulated particles above the freezing front is observed clearly in figures 4a and 4b. This seems to be related to the loss of an oriented lamellar microstructure. In addition, the presence of this layer impacts the freezing dynamics by decreasing the front velocity (figure 8). It thus plays a key role in the formation of the microstructure. The presence of regions with high and low particle concentrations implies a redistribution of the particles during freezing. The particles found in the accumulated particles layer can originate either from below, in the inter-crystals region, in which case a diffusion mechanism is probably involved, or from the non-frozen suspension above, whereby flocculation would be the driving force.

The freezing front velocities measured experimentally are in the range 5 to 30µm.s -1 . Calculations of the diffusion velocity (Appendix A1) show that the major part of particles diffuses slower than the freezing front advances. The diffusion model used considers an ideal case of spherical particles. The real diffusion coefficient is certainly lower than the one calculated here. The accumulation of particles above the tips of the ice crystals by a diffusion mechanism from below seems therefore unlikely. We propose that the accumulated particles flocculate from the depletion zone above.

10.1016/j.actamat.2012.02.023

Flocculation and depletion in the intercrystal regions

To explain the occurrence of a particle-depleted region, we propose a mechanism based on the flocculation of particles induced by their progressive concentration in the intercrystal regions, driven by the ice growth. The ice crystals grow in the direction of the thermal gradient, rejecting and concentrating alumina particles surrounded by the organic dispersant (figure 9a). The system can remain stable if the velocity is high enough. In optimal condition of particle dispersion, a monolayer of dispersant is adsorbed onto particles surface by the carboxylic groups -COO -and the counter ions NH4 + or Na + are attracted by electrostatic interactions but are not bonded to particles. When the dispersant is in large excess in suspension, a monolayer is adsorbed onto particles, and the excess not adsorbed remains in suspension. The solubility of any substance in ice being extremely low (10 -6 ), any compound or species in solution will be rejected by the growing crystals and thus concentrated in the intercrystal regions.

When particles are concentrated between growing crystals, the non-adsorbed ionic species yield a local increase of the ionic strength. The repulsive charge layer of the alumina particles is thus compressed under ionic strength effect. The repulsive interactions are diminished and particles can locally agglomerate. Once particle agglomerates are formed, they may sediment rapidly. Calculations of the sedimentation velocity of agglomerates (Appendix A2) show that this velocity (11µm.s -1 ) is compatible with the typical interface velocity (5 to 30µm.s -1 ). The formation of a particle-depleted region by flocculation and sedimentation is thus compatible with the growth kinetics encountered experimentally.

Depletion and freezing temperature

Flocculation (figures 9c) is responsible for a local increase of the freezing temperature in the particle-depleted region (figure 9d), due to particle volume fraction decrease [19], along with a decrease of the cohesive strength of the concentrated colloidal suspension. This depleted region is suddenly much more favourable to the growth of an ice lens. By the repetition of the flocculation/depletion/nucleation, more and more ice lenses are formed.

When the particle-depleted region moves above the tips of the growing ice crystals, the top of the crystals is in a zone with a higher freezing temperature. They can grow faster in this zone, resulting in an instability of the advancement of the freezing zone. Such instability has been previously attributed to the extension of a supercooling 10.1016/j.actamat.2012.02.023 zone above the freezing front, favoured by the diffusion of particles. The formation of the supercooled zone, that we reported previously [17], therefore originates not from particles diffusion from below but by a particles flocculation from above.

For the suspensions containing a low quantity of dispersant (0.2-0.4wt%), which corresponds to suspensions with a low viscosity (10 -2 Pa.s) and high zeta potential (-75mV) (figure 3), we observe that the particle-depleted region is present above the freezing front (figure 4 a,b). The displacement of the depleted region from the intercrystals space to above the freezing front is favoured by a low viscosity and a small excess of organic dispersant in suspension.

The accumulation of particles above the freezing front and the associated disorientation of the ice crystals do not occur directly after the transient regime of freezing. We can reasonably assume that the depletion occurs first between ice crystals and then moves above the freezing front because of the progressive accumulation of particles. The conditions for this accumulation mainly depend on the dispersant quantity (which controls the ionic strength), binder addition, cooling rate and viscosity of the suspension.

When the particle-depleted region is above the freezing front, in a region free of crystals (figure 7e), nucleation and growth of new ice lenses can take place, the depleted region being in a highly supercooled state (figure 7f). These crystals grow in the depleted region, thus in a direction perpendicular to the thermal gradient. This ice lens repels and packs particles in the direction of the thermal gradient and favours the accumulation of particles above the freezing front. This leads to a repetition of the same flocculation/depletion/nucleation mechanism and the cellular morphology of the crystals is lost. This explains the disoriented microstructure observed in figure 4d.

Parameters controlling the flocculation/depletion mechanism

This scenario provides explanations for the effect of the various parameters identified as controlling the structuring mechanisms. The excess of dispersant or the presence of an organic binder protects the alumina particles from the agglomeration/flocculation by creating steric repulsions and it increases the cohesion of the concentrated colloidal suspension between the crystals. Moreover the presence of ionic species in large excess in aqueous media favours the depression of the freezing temperature and the curvature of the freezing interface under Gibbs-Thomson effect. This increases the supercooling degree in the area of the top of oriented ice crystals and favors higher freezing front velocity. Then if the cooling rate is increased, the freezing front 10.1016/j.actamat.2012.02.023 velocity increases too and there is no time for flocculation to occur. In both cases, an oriented microstructure is obtained.

This also explains the previous observations of the apparent influence of particle size on the stability of the interface [17]. The previous set of experiments was performed with various powders of different granulometry, but the same mass concentration of dispersant. Decreasing the particle size with a constant dispersant mass concentration is equivalent to increasing the dispersant mass concentration with a constant particle size. For small particle sizes, all the dispersant is adsorbed onto the surface of the particles. The flocculation/depletion mechanism described here can then possibly take place, and it yields unstable interface propagation. When the particle size increases, the surface area available for adsorption decreases. The surface of the particles tends to saturate and the remaining dispersant is found in excess in the suspension, protecting the particles from the flocculation mechanism when the particle concentration increases.

Conclusions

The flocculation/depletion mechanism exposed here can facilitate the formation of ice lenses in ice-templated materials, which are responsible to some extent of the scattering of compressive strength values. The structures with low strength correspond to processing conditions yielding a lot of ice lenses, turning into transverse cracks in the final material. The presence of the defects is of course extremely deleterious to the integrity and strength of the samples. The structures with high strength correspond to defect-free structures, obtained with a stable freezing front yielding no ice lens. Our results show that flocculation can be a viable mechanism to facilitate ice lens nucleation and growth in such system, and are a first step towards incorporating particle-particle electrostatic interactions into our understanding and modelling of the freezing of colloids.

Ice-templating is a very unusual ceramic shaping route. Contrarily to the other ceramic shaping routes, we show here that it is deleterious to optimize the dispersion state of ceramic suspension, since these conditions lead to the destabilization mechanism exposed here. Working with an excess of dispersant or binder is indeed necessary to ensure the integrity of the obtained structures.

Figure 1 .

 1 Figure 1. Compressive strength vs. total porosity, data from references[1,. The colour code indicates the presence or absence of crack-like defects perpendicular to the main ice growth direction, as identified from the corresponding published figures. Such defects result from the ice lenses formation during freezing. The presence of ice-lenses induced defects is systematically correlated to a low compressive strength. A low strength can also results from excessively large pore size.

Figure 2 .

 2 Figure 2. Occurrence of ice lenses and corresponding microstructures. Typical microstructure (A) without and (B) with ice-lenses induced defects, (C) ice lens in 60wt% kaolinite clay suspension, frozen unidirectionally. The concentrated kaolinite is in white; the ice lenses are the dark horizontal stripes. Arrows indicate the main ice growth direction. Ice lenses grew approximately perpendicular to the main ice growth direction. (D) Schematic representation of the typical lamellar ice crystal growing along the temperature gradient and ice lenses growing perpendicularly. Scale bars (a, b) 500µm (c) 2 mm.

Figure 3 .

 3 Figure 3. Zeta potential values [A] and viscosity values measured at 50s -1 [B] for suspensions dispersed with D[NH4 + ], D[Na + ] or d[NH4 + ] with a concentration ranging from 0.2 to 2wt%.

Figure 4 .

 4 Figure 4. Crystal growth and particle redistribution during freezing and corresponding three-dimensional particle concentration. (A-C) In situ radiographs taken during freezing. The grey level is related to the concentration of particles. The superimposed profiles indicate the corresponding decrease or increase of particle concentration as the interface is moving from left to right, between two consecutive radiographs (see details in the experimental section). The ice-templating suspensions observed contain 0.2wt% [A], 1wt% [B] and 2wt% of D[NH4 + ] [C]. FZ: frozen zone, CT: crystals tips, APL: accumulated particle layer, PDR: particle-depleted region, LS: liquid suspension. Scale bar = 200µm. (D-F) 3D reconstructions from tomography of the particles rich phase regions for samples containing 0.2wt% [D], 0.7wt% [E] and 2wt% of D[NH4 + ] [F]. Principal ice growth direction: left to right. The black arrows show the cracks within the alumina walls, corresponding to the transverse ice crystals grown in the particle-depleted region. Scale: 140x140x140µm 3 .

Figure 5 :

 5 Figure 5: Close up view of the ice phase in presence of ice lenses. 3D reconstructions from tomography. The ice lenses are growing perpendicular to the main ice growth direction, bridging adjacent lamellar crystals. A few examples are pointed out by the arrows. Scale: 140x140x140µm 3 .

Figure 6 .

 6 Figure 6. 3D reconstructions from tomography of the particle rich phase regions for samples containing 0.2wt% [A], and 1wt% [B] of d[NH4 + ]. Principal ice growth direction: left to right. Scale: 140x140x140µm 3 .

Figure 7 .

 7 Figure 7. Occurrence of the accumulated particles layer as a function of ionic strength of the suspension, showing the effect of the binder addition (0.5wt% PVA) and increase of the cooling rate from 2-5°C.min -1 to 13°C.min -1 .

Figure 8 .Figure 9 .

 89 Figure 8. Influence of the thickness of the accumulated particles on the ice/particles interface velocity for suspensions dispersed with D[NH4 + ], D[Na + ] and d[NH4 + ]. All points are on the same trajectory, independently of the nature of the dispersant. The presence of an accumulated particles layer above the freezing front decreases the freezing front velocity. This decrease is more important as the thickness of the accumulated particles layer increases.

Table 1 .

 1 Composition of the ice-templated alumina suspensions.

	7-1-2wt%

Acknowledgements

Financial support was provided by the National Research Agency (ANR) of France, project NACRE in the non-thematic BLANC program, reference BLAN07-2_192446. Beamline access was provided by the ERSF, under proposal MA997. Acknowledgements are due, as usual, to local staff of the beamline: Elodie Boller, Paul Tafforeau and Jean-Paul Valade for the technical and scientific support on ID-19 at ERSF. We acknowledge Jérôme Leloup, Agnès Bogner, Catherine Gauthier, Loïc Courtois and Stephen Peppin for their participation to the X-Ray experiments. Thanks to Stephen Peppin and Robert Style for providing the ice lens picture in figure 2c. 10.1016/j.actamat.2012.02.023

Appendix

A1. Estimation of particles diffusion velocity

We can estimate the theoretical diffusion velocity of particles by using the generic diffusion equation 1 [START_REF] Glicksman | Diffusion in solids. Field Theory, Solid-State Principles, and Applications[END_REF]. 𝐿 = 2(𝐷𝑡) 0.5 (eq. 1)

This equation is used to determine the distance covered by a particle during a time t with a coefficient of diffusion D. The diffusion coefficient is calculated from the equation (2) proposed by Peppin & al [START_REF] Peppin | [END_REF]. D0 is the Stokes Einstein diffusivity and Z is the compressibility factor.

The particle size distribution (provided by the supplier) of the powder indicates that 80% of the particles are in the 50-350 nm range. By introducing the data corresponding to our system in terms of volume fraction, diameter of particles and maximal packing (obtained with the technique proposed by Liu [16] from viscosity measurements), we expect the smaller alumina particles (50nm) to diffuse at 7.5.x10 - 12 m².s -1 and the larger (350 nm) at 1.2x10 -12 m².s -1 . By using equation 1, the particle diffusion velocity is estimated between 2.2 and 5.5 µm.s -1 .

A2. Estimation of sedimentation velocity of agglomerates

We can estimate the sedimentation velocity, according to Wegst et al. [START_REF] Wegst | Hunger PM[END_REF]. The sedimentation velocity vp of an agglomerate of radius r is given by:

where g is the gravitational acceleration, h the dynamic velocity of the suspension, rA and rL the density of respectively the agglomerate and the liquid. We can estimate a typical sedimentation velocity of 11µm.s -1 for 2 µm agglomerates.


Abdelmajid Amine
email: amine@u-pec.fr

Countercultures of consumption: teenage heavy metal affiliates' coping responses to deviant labeling

Keywords: Abdelmajid Amine, Anis Jounaid. Countercultures of consumption: Teenage heavy Counterculture, Deviance, Labeling, Coping, Teenagers, Heavy Metal. Track: Consumer behaviour

come

Countercultures of consumption: Teenage heavy metal affiliates' coping responses to deviant labeling

Literature Review

Consumer behavior literature is replete with studies on consumer gatherings. They have been conceptualized either as subcultures of consumption, with a defined ethos, values and a hierarchical structure [START_REF] Schouten | Subcultures-of-Consumption-An-Ethnography-of-the-New-Bikers[END_REF] or as countercultures aiming to resist hegemony and, in fine, undermine the established social order [START_REF] Kozinets | Adversaries of Consumption: Consumer Movements, Activism, and Ideology[END_REF]. The latter and the former gatherings being differentiated by their relationship to the mainstream which is tied around consumption practices adopted by the community members. While subcultures may be marked by behaviors that deviate from the marketed consumption norms [START_REF] Amine | Rethinking resistance and anti-consumption behaviours in the light of the concept of deviance[END_REF], countercultures overtly demean the mainstream as resistance to established social norms and as a central identity-driven element inscribed in their ethos [START_REF] Hebdige | Subculture: The meaning of style[END_REF][START_REF] Kozinets | Adversaries of Consumption: Consumer Movements, Activism, and Ideology[END_REF].

Opposition to market hegemony can on take several forms. Some countercultural movements are inscribed in political activism and aim to denunciate capitalism's misdemeanors [START_REF] Kozinets | Adversaries of Consumption: Consumer Movements, Activism, and Ideology[END_REF]; others try to escape the market on a punctual basis, more or less [START_REF] Kozinets | Can Consumers Escape the Market? Emancipatory Illuminations from Burning Man[END_REF]. We focus on style based counter-cultures, that oppose and subvert dominant cultural forms and norms, thereby creating a cultural countervailing power [START_REF] Hebdige | Subculture: The meaning of style[END_REF]. Style represents the spectacular aspect of counter-cultures. It is composed of infrastructural (slang, codes and rituals) and plastic elements (music and sartorial aspect) [START_REF] Cléret | Gestion des relations et des tensions entre l'industrie musicale et les sous-cultures juvéniles: Le cas de l'Electrodance [Managing relations and tensions between the music industry and youth subcultures : The case of Electrodance[END_REF]) that serve as a means of expression, identification (between affiliates) and distinction (from the rest of the cultural spectrum). Style is central to the study of countercultures, being a symbol of overt resistance to cultural hegemony that can also be used for normalization and recuperation purposes by a number of mercantile actors [START_REF] Hall | Resistance through Rituals : Youth subcultures in post-war Britain[END_REF]. Style serves as a material manifestation of the aesthetics of the counterculture (Snell & Hodgetts, 2007), which, deviates from dominant social and cultural norms, and which, before being normalized, might stir up a negative labeling of affiliates [START_REF] Henry | Self-empowerment and consumption[END_REF] as explained in the next section.

Deviant labeling

Labeling theory developed by [START_REF] Becker | Outsiders. Studies in the sociology of deviance[END_REF] enables us to inscribe deviance in its socio-cultural context, providing a better understanding of the concept. [START_REF] Becker | Outsiders. Studies in the sociology of deviance[END_REF] posits that norms are constructs put in place by dominant social groups capable of establishing a social order favorable to their interests [START_REF] Link | Conceptualizing stigma[END_REF], and fostering "normal" behaviors while stemming "deviant" ones. The consequences and significations of a given behavior will vary, depending on the attitude of the social context towards the enacted behavior [START_REF] Amine | Rethinking resistance and anti-consumption behaviours in the light of the concept of deviance[END_REF]. In cases where the behavior is considered deviant, the individual will be labeled at the very least [START_REF] Becker | Outsiders. Studies in the sociology of deviance[END_REF], or sanctioned at the most. Becker's relativist conceptualization of deviance is based on a typology of deviant acts, in which he distinguishes covert and overt deviancy. We focus on the latter as the heavy metal (HM) counterculture uses a proper style to materialize it's ethos (Snell & Hodgetts, 2007).

Lyrical themes (suicide, Satanism, occultism, anti-social attitudes), musical characteristics (tonality, aggressiveness, minors keys) and moral panics associated to HM reflect a strong deviant image of this counterculture [START_REF] Arnett | Adolescents and heavy metal music: From the mouths of metalheads[END_REF][START_REF] Hjelm | Heavy Metal as Controversy and Counterculture[END_REF]. Thus defined, HM contrasts with conventional cultural products (POP, R&B) at both content and appearance levels [START_REF] Sinclair | Heavy metal figurations: Music consumption, subcultural[END_REF], making it a target for moral entrepreneurs [START_REF] Becker | Outsiders. Studies in the sociology of deviance[END_REF] like schools and religious movements.

Responses to labeling: Coping strategies

Lazarus (1966) and [START_REF] Lazarus | Stress, appraisal and coping[END_REF] provide for the analysis of stressful interpersonal interaction situations in the light of coping theory. Coping theory allows the identification and understanding of mechanisms mobilized by individuals when facing tension context that may alter their self-esteem, such as when they are subjected to social labeling or stigmatization. Building on that, we take interest in coping strategies exerted by Teenage Heavy Metal Affiliates (THMA) to manage the discrepancy and the tension between the identities they claim and the deviant ones imposed by society. Our main goal is to draw up a taxonomy of these strategies and develop an understanding of the social context on their enactment.

Therefore, our main research question can be formulated as follows: How do teenage heavy metal affiliates deal with their deviant labeling? Which can be declined into the following sub-questions: What are the types of labeling targeting those teenagers? To what coping strategies do they resort to manage this labeling depending on the interaction context? And how does this unfold through their stylistic and aesthetic consumption practices?

Methodology

Studies investigating HM's culture of consumption focus on adult affiliates [START_REF] Henry | Self-empowerment and consumption[END_REF]Snell & Hodgetts, 2007) who exhibit their style in carnival contexts such as festivals [START_REF] Chaney | Dress, transformation, and conformity in the heavy rock subculture[END_REF]. Our exploratory study investigates, within the French context, the countercultural affiliation's influence on teenagers' representations of social reality as well as their socialization to consumption, being in an identity construction phase [START_REF] John | Consumer Socialization of Children : A Retrospective Look at Twenty-Five Years of Research[END_REF]. While carnivals allow, nay impose, countercultural conformity displayed aesthetically, we deem more appropriate to consider day to day interactions between THMA and outsiders (people who have stopped or have never been HM affiliates) to study negative HM labeling management strategies.

Our main goal being to develop an understanding of HM labeling and affiliates' coping strategies, hence our choice of a qualitative perspective which allows us to grasp the sociocultural and symbolic dimensions of consumption, and inscribe consumption practices in their respective social contexts. Following an ethnographic research design [START_REF] Schouten | Subcultures-of-Consumption-An-Ethnography-of-the-New-Bikers[END_REF]Snell & Hodgetts, 2007), we resorted to face-to-face semi-structured interviews with informants1 that recruited in two sites : a HM-related accessories and clothes shop and a bar where a weekly HM gathering takes place. Observations we have conducted on both sites have enabled us to grasp the role of the aesthetic dimension (sartorial HM aspect and HM-related accessories displayed by affiliates) in generating sartorial and Satanist (antireligious) labeling, and in unfolding specific coping strategies (confrontation and concealment).

Findings

In the following, we present a typology of the social labeling faced by THMA, as well as the strategies they resort to in order to cope. We will then discuss how social contexts influence both enactment and management social labeling.

Labeling types

Satan's work: a well-established anti-religious labeling

HM bands' use of Satanist-related symbols and references, as well as aggression acts towards religious institutions [START_REF] Hjelm | Heavy Metal as Controversy and Counterculture[END_REF][START_REF] Sinclair | Heavy metal figurations: Music consumption, subcultural[END_REF], have strongly affected public opinions about HM, to the extent that it has become systematically linked to Satanism [START_REF] Arnett | Adolescents and heavy metal music: From the mouths of metalheads[END_REF]. Our data show how inseparable HM and anti-religious connotations have become, as teachers in both French public secular schools and private catholic educational institutions refer to it:

[Romain] (17 years old): "They've [Teachers] always been like: what are you doing, it's Satan and stuff."

Background noise: THMA's musical labeling

Music is one of the main reasons why HM is viewed as deviant genre. Stylistic specificities like rapidity, aggressiveness and guitar distortions, to mention only a few, give the impression that HM is nothing but "noise," as the following excerpt shows :

[Elodie] (16 years old): "Not everybody likes HM, and when we talk about it … people often think of clichés, guitar saturations, only screams…"

According to Elodie, these stereotypes contribute to HM's public unpopularity. Paradoxically, this musical transgression is at the core of HM's values, reaffirming its countercultural character for affiliates. Music labeling, then, would help delineate the boundaries of the HM counter-culture, as long as the THMA are aware of the stereotype linked to their musical genre and can thus distinguish the insiders from the outsiders (people who are not, or are no longer followers of HM).

THMA's sartorial labeling

The HM-related sartorial aspect is also one of the elements that inscribe this counterculture in deviance, generating social labeling targeting affiliates who display HM's deviant aesthetics. Outsiders' remarks range from harmless jokes to more violent statements:

[Sophie] (24 years old): "Oh nice outfit (…) Aren't you ashamed of dressing like that."

The hostility towards HM's aesthetics is due to the extravagance of clothes and accessories displayed by THMA who proceed to a stylization of culturally deviant forms (Snell & Hodgetts, 2007) through a combination of dark colors and anti-social symbols (skulls for example) that contrast with mainstream accepted aesthetics.

Conflict-based coping strategies

Confrontation as a form of resistance to stereotypes

The confrontation of the THMA with labelers involves both argumentation and an asserted display of the HM style (musical and clothing). This strategy is mostly mobilized in contexts of informal and non-institutional interactions (family home and interactions with peers). In the first case, followers try to deconstruct and reject stereotypes linked to HM [START_REF] Henry | Self-empowerment and consumption[END_REF], which signal ignorance and a lack of knowledge of the HM culture on the part of these outsiders. The THMA declared "defending" their style, and by extension "defending themselves," against these remarks and these prejudices, such as follows:

[Interviewer]: Okay, have you ever entered debates with people who denigrate heavy metal?

[Romain] (17 years old): "Yeah, not bad yeah, I try to defend as much as possible". Moreover, the consumption of cultural material resulting from HM is imbued with a very significant symbolic dimension (Arnould & Thompson, 2005). The HM clothing display is a means of rejecting and resisting mainstream aesthetic standards (Snell & Hodgetts, 2007). The THMA declare displaying their style on a daily basis despite being labeled and targeted in school as well as at home, as reported by Martin (17 years old):

[Interviewer]: "And suddenly, you're like that all the time, all the time, at school, out of school"

[Martin]: "Very regularly, yeah… every time I go to concerts I buy T-shirts…, then I love to always have a [musical] group T-shirt or a small patch, etc."

Denigration as a strategy to discredit outsiders

Since the term "denigration" has a broad spectrum of meanings, we mean any HM affiliates' discourse aiming to underline the ignorance of the labelers, ridicule their remarks or distance themselves from them, especially when interacting with peers of the same age. Indeed, one of the strong trends that emerge from the analysis of the interviews carried out is the fact that THMA do not fail to point out the "inculture" of those who designate them as deviant, such as Elodie (16 years old) who discredits the remarks and acquaintances of these friends concerning metal:

[Elodie]: "I think there are ... That there are not many people who will really try to understand the lyrics in metal, especially when they do not know".

Avoidance coping strategies

Dodging as a strategy for diffusing tensions

THMA state that in certain circumstances, they avoid confrontation so as not to have problems or worries. This contrasts with the confrontation strategy to the extent that the anticipation of negative consequences means that the related risks are judged more important as the normative power of school institutions and parental authority reduce the possibilities of resorting to conflict-based strategies. In some cases, Cécile (18 years old) avoids standing up to her parents because she feels it is not worth it. In other words, she does not consider it relevant to enter into a conflict with her parents because HM. Her evaluation of the interaction situation [START_REF] Lazarus | Stress, appraisal and coping[END_REF] then plays into Cecile's dodging decision. Indeed, she does not fully appropriate the HM style and considers resistance to labeling not that important to cause her to be reprimanded:

[Cécile]: "I was not trying, finally I did not enter into open conflict with them (her parents) for music…"

Concealing the HM style as a compromise strategy

The term "compromise" refers to an arbitration that THMA make between overt affiliation to HM and the specific constraints of certain social contexts [START_REF] Lazarus | Stress, appraisal and coping[END_REF]. If THMA cannot display their style either because they are forced or for personal reasons, they do not give up their affiliation so far. Similarly, our data show that affiliation to HM does not always imply a permanent display of the style in question.

Institutional pressure is one of the main reasons why THMA are led to adopt this strategy of concealment, the most common example being the internal rules in schools, especially private and/or religious high schools, where rules related to clothing are tighter than those in force in public secular schools, as reported by Marc (15 years old): "Torn jeans, I do not have the right, otherwise there are the stuff…uh ... No, after the rest is OK … well, they do not like it too much, but it's not forbidden…"

Discussion and Research Avenue

Because of the deviant image related to HM [START_REF] Arnett | Adolescents and heavy metal music: From the mouths of metalheads[END_REF][START_REF] Hjelm | Heavy Metal as Controversy and Counterculture[END_REF], its followers are the target of several types of labeling; in this case, anti-religious, musical and clothing-related. Labeling is not unique but multiple. This distinction between different types of labeling makes it possible from the outset to relativize the deviant perception of HM, which rules out the possibility of a frozen abnormal image since labels do not relate to the same "deviant" HM. It also allows us to contextualize THMA's social labeling as wearing symbols related to death and exhibiting a typical clothing aspect of HM do not have the same meaning depending on whether takes place in a public high school, where the outsider reactions will be limited to mere remarks, or within a private catholic institution in where THMA are subject to greater normative pressure and stricter sanctions. Indeed, institutional constraints and the pressure exerted by other social actors are all elements that can influence, even structure, the relationship of insiders with deviant HM aesthetics, causing them to use tricks and subterfuges to hide or circumvent the codes and standards imposed to manage the labeling that targets them.

In addition, we are broadening the spectrum of coping strategies deployed by HM affiliates in response to labeling and stigma. In light of the study by Henry & Cladwell (2006) who had previously explored strategies of confrontation and concealment, we uncover two additional coping strategies: one based on conflict, namely denigration, and another based on avoidance, namely dodging. We postulate that the four coping strategies called upon and implemented by our respondents (confrontation, concealment, denigration and dodging) are not fixed or exclusive, but rather tend to evolve depending on the particularities of the interaction between THMA and their social environment [START_REF] Lazarus | Stress, appraisal and coping[END_REF]. Our results constitute a good example of this as our respondents did not generally resort to only one coping strategy in order to deal with labeling. Moreover, these strategies can influence each other (denigrating an outsider may rule out the possibility of confrontation for example) and strongly depend on the anticipation of the consequences of the institutional pressure (unequal distribution of power between secular and religious schools), the degree of involvement in the HM counterculture and THMA's perceived risks related to the situation of interaction.

By comparing types of labeling and coping strategies studied earlier, it is possible to build a social designation management model that targets AAHM:

-THMA resort more often to avoidance strategies (i.e. dodging) in response to the Satanist labeling as they consider that the latter as a sign of labelers' ignorance, which they can also denigrate without having to confront them.

-Music labeling often leads to a confrontation strategy as a means to deal with outsiders, involving argumentation. This is probably due to the fact that this type of labeling targets, if not threatens, the core of the HM counterculture (i.e. musical production), and denotes, at best, an interest about HM which affiliates deem worthy of a response.

-Clothing labeling, which concerns the most visible dimension of HM followers, is common to all THMA interactions (in school, at home or with peers). It allows describing the different coping strategies identified above, ranging from avoidance in a context of unequal and highly constrained interactions (school) to those based on conflict, applied in a more egalitarian social context (peers).

Finally, THMA labeling and the coping strategies identified highlight dimensions of distinction, opposition, and resistance with respect to the consumption of HM [START_REF] Hall | Resistance through Rituals : Youth subcultures in post-war Britain[END_REF][START_REF] Hebdige | Subculture: The meaning of style[END_REF][START_REF] Hjelm | Heavy Metal as Controversy and Counterculture[END_REF]. The interactions of THMA with outsiders illustrate the separation made between mainstream and the counterculture, and emphasize the central role played by consumption, including through strategies involving revealing and concealing one's affiliation. This separation is present in commercial variations clothes brand H&M product offerings, which are seen by THMA as an attempt to recover and democratize counter-cultural consumption [START_REF] Hall | Resistance through Rituals : Youth subcultures in post-war Britain[END_REF] especially as they are the work of market actors offering more conventional HM-related products. Our study provides information on the need to appreciate the symbolic dimension of counter-cultural consumption in the construction of commercial offers for THMA and, in particular, elements that create a separation and distinction with respect to the rest of the cultural spectrum. This could be achieved by playing with the atmosphere present at the sales point, which should be reflective of the HM aesthetic, and resorting to commercial variations that would not limited to best-known HM references.

Beyond the aesthetic affiliation, HM counter-cultural consumption may indicate identity issues on the part of THMA, as is the case with other countercultural consumption practices such as anti-consumerist movements [START_REF] Kozinets | Adversaries of Consumption: Consumer Movements, Activism, and Ideology[END_REF]. Our research thus gives rise to a reflection on the relationship between the role of affiliation to aesthetic countercultures and the identity paths of young consumers (Arnould & Thompson, 2005). Typically, how does belonging to countercultural deviant aesthetic tendencies influence the identity trajectories of consumers during the adolescent period? Does this affiliation structure the registration of followers in a (quasi) permanent way to the counterculture, or is it restricted to the transitional period of adolescence? Finally, in addition to the social context, do individual characteristics have a greater influence on the application of strategies by adult affiliates whose personalities are more structured, compared to an audience of teenagers in the midst of identity construction and undergoing a stronger influence from the social context? control and civilizing processes. Marketing Theory, 15(3), 423-441. Snell, D., & Hodgetts, D. (2007). Heavy Metal, identity and the social negotiation of a community of practice. Journal of Community & Applied Social Psychology,17(6),[430][431][432][433][434][435][436][437][438][439][440][441][442][443][444][445]

8 Teenagers as principal informants (15 to

years old) and 5 young adults as complementary informants (21 to 25 years old).


Marc Medale
email: marc.medale@univ-amu.fr

Sergey Semenov

David Brutin

Characterization of the main instability mechanisms in sessile droplet evaporation

While the involved physical phenomena are nowadays properly understood, sessile droplet evaporation remains an active research area since several experiments are not comprehensively explained. Indeed, recent experimental works have provided very interesting dynamics [START_REF] Sefiane | On hydrothermal waves observed during evaporation of sessile droplets[END_REF][START_REF] Brutin | Infrared visualization of thermal motion inside a sessile drop deposited onto a heated surface[END_REF][START_REF] Sobac | Thermocapillary instabilities in an evaporating drop deposited onto a heated substrate[END_REF][START_REF] Carle | Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels[END_REF][START_REF] Karapetsas | Convective Rolls and Hydrothermal Waves in Evaporating Sessile Drops[END_REF], whose characteristics strongly depend on control parameters, such as substrate temperature, ambient pressure and the various thermo-physical properties of substrate, droplet liquid and surrounding gas. There is no general agreement in the scientific community about the root-causes of the observed behavior. Are they hydro-thermal waves, Rayleigh-Bénard-Marangoni instabilities, or even something else? One of the means to unmistakably answer this question would consist in conducting a stability analysis of the fully coupled and transient fluid flow, heat and mass transfer problem [START_REF] Dijkstra | Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation[END_REF]. However, to do so, one must first overcome two major difficulties. The first one concerns the computation of the transient base state, whose complexity arises from the strong non-linearities associated with the three competing driving mechanisms: i) Stefan flow draining liquid towards the interface and more specifically to the triple line when the latter is pinned; ii) buoyancy in the liquid and vapor inducing thermo-solutal convection; iii) surface tension gradient along the liquid-gas interface inducing thermo-soluto-capilary convection. The second level of complexity to perform a relevant stability analysis consists in the intrinsic unsteadiness of the sessile drop evaporation process, in which several time scales co-exist.

For particular evaporation configurations, the dynamics of perturbations lies in a much shorter time scale than the total evaporation time, so in this case one can separate perturbations from the base state in a frozen time approach. This enabled us to find that the prevalent perturbations of the base state mainly come from the liquid droplet in which they trigger tridimensional flow structures. Therefore, we have then conducted 3D computations restricted to the droplet and its substrate with a one-sided model, in which heat and mass transfer across the liquid-gas interface is modeled in a semi-analytical way. These unsteady computations are performed during the first stage of the evaporation process in which the triple line is pinned to the substrate, so that the droplet diameter is kept constant, meanwhile the contact angle continuously decreases over time. The obtained results are in good agreement against several experiments performed either under terrestrial conditions or reduced gravity (parabolic flights), cf. figure 1.

Figure 1 -3D unsteady computations: thermal and velocity fields over the droplet surface and in a cut plane.

These one-sided model computations helped us to understand one of the potential instability scenarios. At the beginning, a torus roll appears in the wedge close to the pinned triple line and drives eventually an inner roll by viscous stress depending on the droplet aspect ratio (height/radius). As their intensity increases over time they split into thermo-capillary cells owing to Rayleigh-Bénard-Marangoni instability. Then, the number of cells evolves in time owing to the fact that the plane wavelength of these cells is closely related to their depth. As in the first stage of droplet evaporation the triple line is pinned the wetting angle consequently decreases, so does the liquid height, changing correspondingly the thermal Bond number (ratio of Rayleigh to Marangoni numbers). As the number of thermo-convective cells changes over time, hydro-thermal waves take place to redistribute the internal energy in the droplet. In the second stage of evaporation the droplet diameter continuously decreases, so does its perimeter, while the wetting angle stays roughly constant. Therefore the height of peripheral cells remains also constant; consequently their number has to decrease in order to match the droplet perimeter. Here again, hydro-thermal waves enter the game to redistribute the internal energy in the droplet.

The dark side of this approach is that computing times are still prohibitive to perform any parametric study this way. Therefore we have conducted a dimensional analysis to account for the main physical components of the problem. As usual, one assumes perturbations 3rd International Conference on Droplets University of California Los Angeles, USA, July 24 th to 26 th , 2017 been able to destabilize the base state provided their energy reaches a certain amount of the total energy of the system, made-up of the liquid droplet and its surrounding gas (air + liquid vapor). To approximate these energy levels, prevalent terms have to be evaluated. In terrestrial conditions the two prevalent driving terms are buoyancy (thermal and solutal) together with surface tension gradients (thermo and soluto-capillary forces). The first one can be quantified thanks to thermal and solutal Rayleigh numbers, meanwhile the second one can be quantified by thermal and solutal Marangoni numbers. On the other hand, the energy involved in the evaporation process is related to the vapor flux throughout the droplet interface times the latent heat of vaporization. Therefore, a linear combination of all these terms enables to quantify the total energy involved in the evaporation process.

Computing the latter in various experiments where instabilities have been either observed or not (cf. figure 2), enabled us to empirically determine a threshold of instability occurrence. This semi-empirical analysis enables us to discern instances of instability depending on experimental sets of parameters. However, some further work has to be performed to improve the described model in order to become predictable.

Figure 2 -

 2 Figure 2 -Top view images from infra-red camera of sessile drop evaporation revealing somehow their internal flow patterns (same thermal conditions but different fluids and gravity levels).

Acknowledgements. The authors acknowledge the French spatial agency (CNES) for funding support: parabolic flight experiments and second author's post-doc.


Jean-Claude Moissinac
email: moissinac@telecom-paristech.fr

Cyril Concolato
email: concolato@telecom-paristech.fr

Jean Le Feuvre
email: lefeuvre@telecom-paristech.fr

SuperPath : A Necessary Primitive for Vector Graphic Formats

Keywords: Picture description languages, multimedia languages, vector graphic, map, adaptation, anti-aliasing I

Most 2D graphic languages deployed on the Internet today lack the ability to represent the topology of contiguous regions efficiently. This is becoming problematic with the growing number of map-based applications. In this paper, we introduce a new graphical primitive, called SuperPath, to extend existing languages for 2D vector graphics, such as SVG. This primitive provides a way to represent the contours in a 2D graphic with a set of reusable chunks of contour. We present the motivations for this work with examples of 2D maps and some associated problems related to their editing, rendering, or adaptation. We give some results, which were obtained using the new primitive.

INTRODUCTION

With the increasing diversity of terminals and networks, modern multimedia technologies need to address multipublication and adaptation of multimedia services and documents to environmental contexts such as terminals and user preferences. Some previous works, like [START_REF] Bulterman | Specification and Support of Adaptable Networked Multimedia[END_REF], have shown that the more structured a document is, with rich metainformation, the greater the capability to process it, to modify or adapt it is.

In our work on multimedia documents, we usually work with common 2D graphic formats such as SVG -Scalable vector Graphics-or MPEG-4 BIFS -Binary Format for Scene-and MPEG LASeR -Lightweight Application Scene Representation-as well as other, more specialized languages (MIF -MapInfo Interchange Format-, InkML, etc.). SVG is becoming a common representation for 2D graphic documents (web browsers, Linux distributions) and, with the adoption of the Tiny profile by groups such as MPEG, OMA -Open Mobile Alliance-or 3GPP -3 rd Generation Partnership Project-, it is expected to become a central format on mobile devices among which phones and, portable media players. MPEG-4 BIFS is used to display text, media and graphics for interactive services in the T-DMB broadcasting system, used in Korea for mobile TV and in France for digital radio.

Both formats rely on a similar representation of 2D vector graphics based on the use of contours with filling and stroking properties. However, these languages have limitations when editing, adapting or interacting with complex graphic content. More precisely, both languages lack the ability to define an area as a list of references to pieces of contour. This feature is present, for example, in the MapInfo Interchange Format (MIF/MID) [START_REF]MIF File Format[END_REF] dedicated to map representation. In this paper, we present an extension to the SVG language called SuperPath, which makes it possible to define a region as a set of contours.

The remainder of this paper is organized as follows. Section 2 describes related works. Section 3 presents the motivations of this work and explains the benefits of the SuperPath approach. Then, Section 4 proposes a syntax to use the SuperPath extension with SVG. Section 5 evaluates the proposal; finally, Section 6 concludes this paper and indicates future work.

II. RELATED WORK

The following works and technologies described in this section are related to our proposal.

In [START_REF] Gangnet | Incremental Computation of Planar Maps[END_REF], Gangnet & al. present the benefits of representing a 2D graphic by a structure where all the different regions don't share anything except the borders. They call this structure a planar map. The advantage of such representations is a complete knowledge of the topology of a drawing, enabling powerful processing and rendering. However, the main drawback of this approach is its complex data structure, not suited for usage on mobile devices. Moreover, such a structure is not well suited to our scenario, because the concepts used are too far from those available in SVG or MPEG-4 BIFS.

In a compromise between the planar map representation and the contour representation, the Flash format [START_REF][END_REF] defines Shape objects. Shape objects are the smallest graphical entity that can be manipulated: either for transformations or for user interaction. The content of a Shape object is a sequence of lines and curves, for which a color to the left, a stroke color and a color to the right are defined. This representation enables a very efficient conversion to bitmap and solves some of the problems mentioned in this paper (e.g. antialiasing and format compactness). On the other hand, there is no notion of region within a Shape, and points within a Shape cannot be reused in another Shape. It is therefore quite difficult to maintain the semantics of original regions in Flash content.

In [START_REF] Dailey | Suggestions for additions to the W3C Specification for SVG[END_REF], Dailey proposes useful new elements in the SVG language independently of our work. One of them has some aspects in common with our approach. A major advantage of our proposal compared to this work is to preserve structural information in a simple way, closer to the SVG design. We have furthermore followed a language-agnostic approach, applicable to other languages.

III. RATIONALE OF SUPERPATH

In this section, we will first present the interest of such a primitive through an example. We then highlight a series of benefits of its adoption.

A. The map example

Fig. 1 represents some of the departments and regions of France. The regions are composed of several departments, thus the borders of each department belong to two polygons, those in neighboring departments, and also to the polygons that define the regions. Finally, it is common that a department border is defined by the course of a river. Some contour chunks will be redefined up to five times in the same way: two for contours of the departments, two for the contours of a region, one for the course of a river. Figure 1. A map with reuse of some geometric elements Such a representation is common for a map; two neighboring contours commonly share a piece of contour. Existing languages for 2D vector graphics such as SVG cannot currently express this relationship. This leads to problems in several applications when editing, adapting or rendering graphics. The following section details the benefits of using a more adequate representation.

B. Benefits of SuperPath

Benefit 1 -To enable coherent adaptation

If the SVG file contains the information that two chunks of contours are the same, both contours can be adapted in a coherent manner, processing it only once (Fig. 2) and avoiding artifacts produced by divergent adaptations (Fig. 3). Here, a point in the middle of the red diagonal is moved to the left on the grid while the corresponding points on the blue and green path don't move, leaving a hole between them.

Xiaofeng [START_REF] Xiaofeng | Abstraction of 2D Shapes in Terms of Parts[END_REF] presents a detailed paper about how to adapt some vector graphics to reduce their complexity. Kazi-Aoul [START_REF] Kazi-Aoul | PAAM : a Web Services Oriented Architecture for the Adaptation of Composed Multimedia Documents[END_REF] presents the most common reasons to adapt a multimedia document to a particular context. If the SVG file contains the information that two chunks of contours are the same, an editor can suggest to the user either to modify both in the same manner, or to make different modifications.

Benefit 3 -To manage the anti-aliasing problem

The rendering model of SVG, commonly shared by other technologies, presents a problem with regards to anti-aliasing as illustrated in Fig. 4. The SVG rendering model assumes that drawing on the canvas follows the painter's algorithm, i.e. objects encountered first in the document are drawn first, and objects following in the document are rendered on top. Imagine that a black triangle is rendered first against a white background. Its border will be anti-aliased using a mix of white and black giving some grey pixels. Then, when another black triangle is rendered, sharing a side of the previous triangle, its borders will be anti-aliased as a mix of black and previously rendered grey pixels. Hence, instead of having a mix between black and black, which is black, the result is a mix between black and grey which is dark grey. So, some pixels on the border between both triangles are brighter than they should be. In such a case, knowing that the border is common between both black triangles would make it possible to produce a better anti-aliased result. For a lot of vector graphics, among which maps and cartoon drawings, the main part of the data resides in the representation of the points that define the contours. When a group of points is duplicated, the file size is unnecessarily increased. Using a single representation of duplicated group of points will therefore reduce the file size.

Holes are contours inside a contour which define a region excluded from the main contour (and presumably transparent). Using a better representation of duplicated chunks also allows for better representation of holes.

Figure 5 Representing holes always implies reusing parts of paths

Fig. 5 shows two ways to get a blue shape containing a green shape containing a hole which lets you see what is behind the green and blue shapes. In the first way (first line of the figure), the green shape shares its external contour with the blue shape. In the second way (second line in the figure), the green and blue shapes share the description of the hole.

Benefit 5 -To optimize the display

A player that knows that two chunks of contours are the same can optimize the rendering operations, for example performing the linearization of Bezier curves into straight segments only once.

More generally, it is useful and simple to preserve the semantics of chunk identity for various processing applications covering a wide range of scenarios.

IV. SUPERPATH IN SVG

This section presents the solution offered by SuperPath to the aforementioned problems and then details the proposed syntax for the SVG language.

A. Principles

As mentioned above our approach is language-agnostic and can be applied to any vector graphic format using a contour-based representation of objects. To add SuperPath, there are generic principles to follow for these formats.

Defining the chunks

We need to introduce the concept of chunks using the target language model. As a chunk can be used by different contours with different display styles, a chunk must not be dependent on a style. The chunk therefore only contains geometrical data (points and control points).

Using chunks references

We need to be able to reuse these chunks in different shapes. This is usually achieved through an explicit or implicit identifier for the chunk and further referencing in each shape which uses this chunk. Obviously, if the targeted language has syntax to express references, we need to be coherent with that syntax for chunk referencing (e.g., SVG xlink or BIFS DEF/USE mechanisms).

Reversing the chunk order

As illustrated in Fig. 6, duplicated chunks could be used as they are first defined or in the reverse order. The syntax must enable such usage.

Figure 6 Three shapes and the sequence of points along each contour

Defining chunk joins

We need to define how two successive chunks of a path are joined. The simplest way is to draw a line between the end of a chunk and the beginning of the next.

B. Proposed syntax for SVG

In this section, we present a syntax of SuperPath for the SVG language which is compact and easy to author. We propose the following new SVG elements:

-<superpath>: this element has no specific attribute. It supports traditional SVG attributes such as id, transform, class… It is used as a container element for the elements below and defines its own styling. -<subpath>: this element declares a chunk used in a SuperPath . Its syntax is the same as the standard SVG <path> element, but the semantics are different. This element is only displayed when it is a child of a <superpath> element.

A subpath can have two forms:

-It can contain a d attribute, analog to the one in the path element; if it has an id attribute, then the d part can be reused by referencing another SuperPath; -It can contain an xlink:href attribute which references the id of another subpath. In this case, its geometry is defined by the d attribute of the referenced subpath.

In addition, the geometry of a subpath can be used in the reverse order, as explained in 4.A. An "order" attribute is therefore defined with possible values 'direct' or 'reverse'; the 'direct' value is the default.

In both forms, the "cmd" attribute expresses how the subpath is joined with the previous one. There is currently only one possible value "line", indicating that a straight line is used to join the chunks.

Please note that the definition of a chunk can be similar to the definition of the corresponding part of the original content. An overhead will come from the size of the references to the chunk.

As an example, Fig. 4 can be represented as follows:

<superpath id="redpath" fill="red"> <subpath id="sp1" d="M.. The subpath with id sp1 is the one shared by the green and red shapes; the subpath with id sp2 is shared by the red and blue shapes; the subpath with id sp4 is shared by the green and blue shapes.

C. Evaluation

As explained previously, the SuperPath approach provides great advantages in many cases (adaptation, interactivity). We must however check the compactness of the proposed representation.

We have implemented a program which takes an SVG file, finds all the <path> elements, computes all reused chunks and then produces an SVG file extended with the superpath /subpath elements (the process could be done in a SVG renderer, but the CPU cost will be repeated for each rendering and the semantic not apparent in the file) .

We can note that when the original content has no path or when no path chunk is reused, our algorithm does not modify the content. For other cases, our algorithm produces files in which semantic information about regions is restored, thanks to <superpath>. We present below some results for relevant sample files.

Table I presents significant characteristics of our samples. As we can see in Table 1, these samples (representative of our tests) are mainly composed of path data. Therefore, a better representation of path data is likely to result in a reduction of size. File 'mapfrance' is a map. File 'toon1' is a step in a cartoon animation. We can see some results in Table II. The first column is the name of the original file. The second column is the size in kilobytes of that file. The third column is the size of the generated file using the <superpath> element.

The files used are SVG files taken from the web (maps from Wikipedia) or from previous projects (extracts from cartoons) [START_REF] Concolato | Representing 2D cartoons using SVG[END_REF][3]). As we can see, a reduction in size is observed in much of the test content, and in other cases the increase in size is quite small. GAEcho is a special case to illustrate the case where the whole points are duplicated; in that case, as predictable, the size is halved. The benefit (about size) mainly depend of the number of reused subpath/points. The main result here is: we benefit of a better structuration without cost in size.

The reduction could be really greater if the file were properly built, particularly in maps. As an example, it is common with hand-made maps that the frontier between two regions is present in two <path> elements with slight differences due to the authoring tool. In such cases, our algorithm cannot currently determine that the points are semantically identical, and the resulting file size is therefore not as compact as it could be if the content were properly authored.

D. Conclusion

We have shown that a SuperPath feature is quite useful for modern vector graphic formats. We have also described how such a feature could be introduced into these languages, and provided the proposed syntax for the SVG language. This syntax has been tested on several sequences and generally provides a reduction in size.

In future work, we will further improve the structure for better compactness of the representation and investigate other chunk join types. We plan to propose this feature to the W3C SVG Working Group, and to propose a similar feature in MPEG-4 BIFS.

Figure 2 Figure 3

 23 Figure 2 Coherent adaptation: two neighboring polygons share a border part; when adapting that part, the adaptation must be coherent

Figure 4

 4 Two black triangles (a) with common antialiasing problem (b) and without (thanks to SuperPath) Benefit 4 -To reduce the file size

  .." /> <subpath id="sp2" d="...." /> <subpath id="sp3" d="...." /> </superpath> <superpath id="greenpath" fill="green"> <subpath id="sp4" d="M...." /> <subpath id="sp5" d="...." /> <subpath xlink:href="#sp1" /> </superpath> <superpath id="bluepath" fill="blue"> <subpath xlink:href="#sp2" /> <subpath id="sp6" d="...." /> <subpath xlink:href="#sp4" order="reverse" /> </superpath>

Table I . Test set

 I

	Filename		mapfrance	Toon1
	File size (KB)		119	103
	Number of SVG	336	50
	paths
	Number of points	9452	21179
	Number	of	5434	12961
	duplicated points
	Cumulated	path	81	101
	size (KB)
	Path data/total size	68%	98%

Table II Size with and without SuperPath

	SVG File	Original (KB)	With SuperPath
			(KB)
	AfricaMap	642	571
	FranceMap	873	851
	Toon1	103	105
	GAEcho	102	55
	G0005	36	34

ACKNOWLEDGMENT

This work was supported by the JEMTU project in the Institut Telecom.