Markéta Jakešová

Rethinking the Body as a Network Drawing Inspiration from Japanese Animated Cyborg Bodies 1

Keywords: Actor-network theory, anime, Japan, organ transplantations, phenomenology

. This may indicate an understanding of the body as a compact and bounded entity, however a lot of Japanese anime movies and series offer a rather different picture. First, the differences between animal, human, vegetal or mechanical bodies are fluid and unsteady, so they change both their form and substance, and second, the bodies seem to flow between material, virtual, and dream realities without any apprehensible anchoring.

This paper aims to propose an integrated understanding of these two techno-socio-cultural phenomena by using some of the philosophical approaches that draw on both Japanese and Western traditions. The philosopher Ichikawa Hiroshi describes various types of the body: some of

them are not limited by the skin but rather represent a structure or a network intimately connected to their environment, other bodies included. The philosopher Yuasa Yasuo treats the well-known problems of subjectivity and body-mind unity but instead of taking this unity as the point of departure and then explaining it, he sees it as a possible goal of bodily techniques inspired by Buddhist meditation practice.

Thus it seems that not only is the subject fundamentally embodied (as for example in the phenomenology of Maurice Merleau-Ponty) but most importantly, it appears to be able to absorb and integrate into itself anything (both biological and mechanical) from its environment, and change with it. I will argue that this way of thinking can offer some alternatives to the highly individualistic Western milieu and could even be a better departure for responding to environmental issues while more justly treating all possible relations and connections between different people, biological species, and other entities.

Transplantations in Japan

In Japan, there has until recently been a very strict law dating from 1997 concerning the donation of organs. Not only was it an opt-out instead of an opt-in system i but there was also a restriction with regard to age (15 years old), and family consent was necessary. This changed with the law of 2010: there is now an opt-out system but there continues to be a considerable shortage of organ donors. [START_REF] Egawa | Current Status of Organ Transplantation in Japan[END_REF] Scholars usually agree on four main causes for the fact that organ transplantations are not particularly popular among the Japanese: The first possible reason is the first Japanese heart transplantation, which was performed on Hokkaido in 1968 (only one year after the first semisuccessful human heart transplantation in the world). It is known as the 'Wada case' and it provoked a scandal because the patient died not long after the operation and the surgeon was later accused of murdering both the donor (it was later revealed that the declaration of the donor's death before removing the heart might have not been entirely justifiable) and the patient (whose own heart may not have been in such a bad state). Thus the public has often perceived organ transplantations as a mere means of career advancement for doctors instead of the regular treatment for the patient's sake. [START_REF] Lock | The Problem of Brain Death: Japanese Disputes about Bodies and Modernity[END_REF] The second problem is that of gift exchange. The infinite gratitude saved people feel towards the dead donors is always psychologically problematic [START_REF] Varela | Intimate Distances: Fragments for a Phenomenology of Organ Transplantation[END_REF]) but the sophisticated system of gift exchange in Japan and the impossibility of the enormous gift of a vital organ to fit into it makes this problem almost unsolvable. [START_REF] Ohnuki-Tierney | Brain death and organ transplantation: cultural bases of medical technology[END_REF] The two last usually discussed factors are differing approaches to bodily integrity and brain death.

These are interconnected and I will focus on them more. In Japan, the identity of a person is usually understood as a complete body (五体 -gotai -five body parts) compared to the Western concept where identity is situated in the head, that is in rationality. So for some people, the organ transplant is an unnatural rationalization which comes from the West. The emphasis on bodily integrity can be also supported by anthropological evidence like the lack of interest in ear-piercing, never adopting foot binding from China, etc. Even though the fact of having someone else's organ in one's own body is surely an unusual experience for most people regardless of the culture he or she feels to be part of [START_REF] Nancy | The Intruder[END_REF], the Japanese seem to see it as especially problematic. [START_REF] Lock | The Problem of Brain Death: Japanese Disputes about Bodies and Modernity[END_REF][START_REF] Ohnuki-Tierney | Brain death and organ transplantation: cultural bases of medical technology[END_REF] The notion of brain death is related to this. If personhood is distributed in the whole body, why should a person be dead if it is 'only' his or her brain that does not work? Brain-dead people still have a lot of traits which are associated with life: a brain-dead person usually has a normal skin color, is warm, their heart is beating, their digestion works, they can even deliver a child (e.g. [START_REF] Kinoshita | Healthy baby delivered vaginally from a brain-dead mother[END_REF]. Personhood is not necessarily located in the brain exclusively, so the fact that the brain itself is dead does not have to indicate the death of the person. All this is again set to be connected to Western rationalization: when it comes to stating brain death, relatives have to rely on proclamations of experts educated in Western science. To continue with life support thus does not have to mean only the unnecessary expenses spent on already dead people. Instead, it is the prolongation of life or the natural way of dying slowly rather than one moment of declaration of (brain) death and then turning off the machine. To pay for the life support is also seen as the family members' manifestation of gratitude towards their (older) relatives and future ancestors.

Anime

We have seen that although the situation has been changing lately, a general distrust towards the notion of brain death and transplantations in general is still prevalent. However, probably everybody who has ever seen some anime, i.e. Japanese animated movies or series that are extremely popular both inside and outside of the country, knows that deformations and reformations of space and human or humanoid bodies in particular are very common themes.

These can be connected to some Western scholars as well. Donna Haraway in her famous 'Cyborg Manifesto' from 1985 describes three dichotomies typical for our Western type of thinking which, according to her, it is now high time to abandon: human/animal, organism/machine, physical/nonphysical. [START_REF] Haraway | Manifestly Haraway[END_REF] Many anime cross all of these three boundaries. The human/animal can be seen in the internationally renowned work of the director Miyazaki Hayao, but for me, the other two boundaries are more interesting. The famous anime Ghost in the Shell [START_REF] Oshii | Ghost in the Shell[END_REF] is about a state employee, the cyborg Major Kusanagi whose only organic part is a small piece of a brain and she therefore longs for exploring a mysterious identity with which she feels to have a lot in common. The entity is not only entirely artificial (i.e. without any organic part), but most importantly, it originated in virtual space (so it does not have a fixed material identity) and came into existence solely on its own. In one of the scenes, the major, inspired by the questions the cyberspace entity provoked, talks about her own personality and the problem of identity in general:

"We can quit but we'd have to give back our cyborg parts and augmented brains to the government. All components that make me up as an individual. There are countless ingredients that make up the human body and mind. A face and voice to distinguish oneself from others, the hand you see when you wake up, your childhood memories and feelings about your future. And that's not all. There's also the ability to access vast amounts of information from an infinite network … All of that blends to create a mixture that forms me, and gives rise to my conscience."

In the screenshot (Figure 1), there is Kusanagi trying to get access to the cyber entity. Her body is falling apart, which she does not care about and probably also does not feel. After that, she managed to merge with the cyber entity and with cyberspace. Major Kusanagi is an elevated organic form -part human, part machine, as all of us are to some, even if to a lesser extent. ii Another type of machine-person mergings are mechas -big robots in human shapes controlled from inside by a person, usually used for fighting or sometimes for work.

In Neon Genesis Evangelion (Anno et al., 1995(Anno et al., -1996)), there is an extraterrestrial invasion of battling angels coming successively and the only way to fight against them are mechas with teenagers controlling them from the inside. In order to be able to do this, the chosen children have to synchronize with them: they enter the machine and after a while, their movements are directly reflected in the movements of the mechas. Many problems arise precisely from these connections: connections are either too strong -so the mechas are impossible to disconnect -or too weak -so they start to act on their own, etc.

In Figure 2, there are two mechas: one of them is going berserk because it is infected by the angels, the other one was deliberately disconnected from a boy's body, after the boy refused to fight the first one because of a child being inside of it. Then this mecha in a 'dummy mode', that is controlled by auto-pilot, tore the infected mecha into pieces. You can see that the 'dying' mecha actually resembles a living body with all the blood and flesh flying around.

My last example of anime with uncanny connections is Paprika (Kon, 2006)

Conclusions

We see that when it comes to transplantations, the Japanese are against breaking bodily boundaries, whereas in anime, it happens very often -and not always in an utterly negative way. It needn't be such a contradiction after all: it is almost a cliché by now that if an anthropologist finds out about a strict rule, it often means that there is something dangerous to be taken care of. [START_REF] Ohnuki-Tierney | Brain death and organ transplantation: cultural bases of medical technology[END_REF] for example writes that the boundary between monkeys and humans in Japan is not so strict which may be one of the reasons why the Japanese are careful about animal transplants. By contrast, in the West there is an insurmountable difference between humans and animals, wherefore an animal implant cannot endanger our (mostly psychological) identity. The anime thus show the possibilities and risks related to permeable bodies, that is: with bodily changes come also substantial changes in personal identity. Whereas in the West, consciousness is mostly seen as independent of the body and more or less constant.

One of the approaches that can help, is the philosophy of the French phenomenologist Maurice Merleau-Ponty. He sees the subject and the Self as fundamentally emerging from the body: the Self is the embodied subject. However, the felt body does not have to always be identical to the actual biological body -for example the white cane used by the visually impaired can work as a full replacement of a bodily part; on the other hand, people often experience the phenomenon of a phantom limb. iii (Merleau-Ponty 1945) But Merleau-Ponty still considered the body and the subject to be a compact entity.

Yuasa Yasuo, a Japanese philosopher of the second half of the 20 th century, took a very different approach. While making use of Western phenomenology and connecting it to the Japanese philosophical but also practical tradition, he inverted the argument: Westerners are quite used to taking the unity of body and soul and the compactness of the self in general for granted but rather than the point of departure, it can be the goal to achieve -by meditation, or other holistic exercises. [START_REF] Yuasa | The Body: Toward an Eastern Mind-Body Theory[END_REF] Another approach is that proposed by Ichikawa Hiroshi: in his book The Body as Spirit (1975), he ultimately seeks to elevate the body to become spirit but rather than two entities that are or are not closely connected, he sees them as the two extremes of the same phenomenon. We should strive for harmony, but this does not mean that our bodily personhood has been one and indivisible since ever and will be so forever. He introduces many types of the body divided into two classes: The body as phenomenon -the body as itself, as object, subject, or as seen by me through the eyes of the other -and the body as structure -oriented towards the environment. Some types of the body (especially from the second class) reach beyond the skin. Through the integration of all (the) bodily versions, one can achieve unity -but not of the body and mind as separate entities but of the body as spirit. [START_REF] Nagatomo | Ichikawa's View of the Body[END_REF][START_REF] Silva | Beyond Body/Mind? Japanese Contemporary Thinkers on Alternative Sociologies of the Body[END_REF] Among Western scholars, among the closest one to these ways of thinking may be Annemarie Mol, who writes about the body multiple, that is -a body that is more than one but less than many [START_REF] Mol | The Body Multiple: Ontology in Medical Practice[END_REF]. Our usual problem is that we commonly think in the framework of either and or but some contemporary Western scholars -for example in the tradition of ANT -and Japanese scholars who try to integrate Japanese and Western philosophy show us that everything can change and that there could be lots of layers or versions of reality and also our bodies.

The Japanese public may be more aware of it than the Western one and may need more time to come to terms with the newest medical technology coming from the West. But we also experience a lot of dissonance, both in relation to medical practice and outside of it. A more holistic approach towards ourselves and our milieu without sharp differentiations could also help us to behave more responsibly in relation to environmental issues. I propose to let this 'Japanese-inspired' multiple style of thinking into our lives -for academical, personal, and social reasons.

Notes:

i This means that people are not considered to be potential organ donors automatically and they have to explicitly state their consent. A similar situation can for example be found in the United States or Germany. In the Czech Republic and in Austria (among others), there is by contrast the opt-out system.

ii This is Donna Haraway's claim in The Cyborg Manifesto and we can easily perceive it around us or feel it in ourselves: all human (and other) bodies are shaped by technology, starting with techniques of food preparation, wearing clothes most of the time, or repairs of body parts, such as teeth, joints etc. iii A phantom limb is the sensation that a missing limb is still attached.

Figure 1

 1 Figure 1

  fighting each other.

Figure 2 Figure 3

 23 Figure 2

This publication was supported by the The Ministry of Education, Youth and Sports -Institutional Support for Longterm Development of Research Organizations -Charles University, Faculty of Humanities (2018).


P Meunier

& F Nadal

From a steady plume to periodic puffs during confined carbon dioxide dissolution

In this paper, the stability of a laminar plume due to solutal convection is addressed from experimental, numerical and theoretical points of view. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide (CO 2 ). The diffusion of CO 2 at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilizes via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the chemical Rayleigh number Ra. This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution.

The wavelength, frequency, onset time and phase velocity of the instability are explored using Particle Image Velocimetry (PIV) measurements over two decades of Rayleigh numbers. The characteristics of the instability appear to be almost independent of the Bond number but strongly dependent on the chemical Rayleigh number and the aspect ratio. The phase velocity is very close to the fluid velocity of the plume before the instability, which has been predicted in various works to scale as Ra 2/3 (ln Ra) 1/3 . The wavelength is close to 4.5 times the radius of the cylinder (independent of aspect ratio, Bond number and Rayleigh number) such that the frequency scales as the phase velocity. The onset time, which is proportional to the height of the cylinder, scales as Ra -0.55 and depends on the Bond number. A simplified model inspired from Lorenz' waterwheel is proposed to explain the destabilization process after partial fill-up of the cylinder. Although very qualitative, the model captures the key features of the experimental observations.

Introduction

Buoyancy driven convection plays a central role in a great number of geophysical processes occurring at large and medium scale (convective flows in the mantle, volcanoes, fires, hydrothermal vents). Because mixing and dispersion issues motivated the very first studies on the topic, plume dynamics have been extensively addressed in the case of sustained turbulent regimes. The now classical entrainment assumption introduced in classical works by [START_REF] Batchelor | Heat convection and buoyancy effects in fluids[END_REF] and [START_REF] Morton | Turbulent gravitational convection from maintained and instantaneous sources[END_REF] still generates new developments [START_REF] Kaminski | Turbulent entrainment in jets with arbitrary buoyancy[END_REF][START_REF] Carazzo | The route to self-similarity in turbulent jets and plumes[END_REF][START_REF] Carazzo | The rise and fall of turbulent fountains: a new model for improved quantitative predictions[END_REF]. Here, because the typical size of the system and fluid velocities are small (few centimeters and few millimeters per second), the Reynolds number is of the order of a few hundreds. Consequently, the confined plumes under consideration in the present study are not turbulent.

Analytical solutions for laminar plumes emitted by a point source have been first obtained by [START_REF] Yih | Free convection due to a point source of heat[END_REF], [START_REF] Fujii | Theory of the steady laminar natural convection above a horizontal line heat source and a point heat source[END_REF] and [START_REF] Pera | On the stability of laminar plumes : some numerical solutions and experiments[END_REF] for fixed values of Prandtl numbers equal to 1 and 2. The case of an infinite Prandtl number has been solved later by [START_REF] Worster | The axisymmetric laminar plume: asymptotic solution for large Prandtl number[END_REF] in the case of an infinite medium and by Whittaker & Lister (2006a) in the case of a semi-infinite medium (i.e. over a horizontal plane). Finally, extended sources of buoyancy have been considered by [START_REF] Umemura | Axisymmetric convection at large Rayleigh and infinite Prandtl number[END_REF], Whittaker & Lister (2006b) and [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF]. The radial confinement of the plume has been studied within the scope of geological applications where the variation of viscosity with temperature leads to narrow conduit structures with high-velocity cores (see e.g. [START_REF] Olson | Structure of axisymmetric mantle plumes[END_REF]). This viscosity driven confinement generally leads to the same scalings in Rayleigh number for the core velocity as that resulting from direct mechanical confinements [START_REF] Umemura | Axisymmetric convection at large Rayleigh and infinite Prandtl number[END_REF][START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF].

In general, whereas numerous studies have been devoted to either laminar or turbulent buoyant plumes in confined environments, not many have addressed the mechanisms of transition from steady to unsteady regimes [START_REF] Cetegen | Experiments on stability and oscillatory behaviour of planar buoyant plumes[END_REF][START_REF] Maxworthy | The flickering candle: transition to a global oscillation in a thermal plume[END_REF][START_REF] Soteriou | Lagrangian simulation of the unsteady near field dynamics of planar buoyant plumes[END_REF][START_REF] Williams | The response of buoyant laminar diffusion flames to low-frequency forcing[END_REF]. As pointed out by [START_REF] Lopez | Instability of plumes driven by localized heating[END_REF], a general understanding of such transitional process between steady axisymmetric laminar plumes and turbulent plumes is still missing probably because the destabilization mechanisms at stake strongly depend on the details of the configuration (geometry and boundary conditions). These configurations fall broadly into two categories.

In the first case, the plume is generated by a buoyant jet with a fixed rate of buoyancy. This is for example the case of a helium round jet in air, as studied experimentally by [START_REF] Subbarao | Investigation of a co-flowing buoyant jet: experiments on the effect of reynolds number and richardson number[END_REF], [START_REF] Cetegen | Experiments on stability and oscillatory behaviour of planar buoyant plumes[END_REF] and [START_REF] Cetegen | Experiments on the oscillatory behavior of buoyant plumes of helium and helium-air mixtures[END_REF]. The jet becomes unstable with respect to an axisymmetric puffing (varicose) instability whose frequency varies as Ri 0.38 (where the Richardson number Ri is based on the density difference and the jet diameter and velocity). These observations were corroborated by the DNS results of [START_REF] Jiang | Direct numerical simulation of the puffing phenomenon of an axisymmetric thermal plume[END_REF] and of [START_REF] Satti | Flow structure in the near-field of buoyant low-density gas jets[END_REF]. This is also consistent with the recent theoretical analysis of [START_REF] Chakravarthy | Global stability of buoyant jets and plumes[END_REF] based on global modes. However, the local stability analysis by [START_REF] Chakravarthy | Local linear stability of laminar axisymmetric plumes[END_REF] found that the dominant and only absolutely unstable perturbation is helical rather than axisymmetric. 2D experiments have also been performed by [START_REF] Pesci | Inertially driven buckling and overturning of jets in a Hele-Shaw cell[END_REF] in a Hele-Shaw cell where a salted water jet is injected from a point source into a stably stratified environment. They observed an asymmetric sinuous instability rather than a varicose instability. Pesci's first interpretation of this buckling instability relied on a 2D Kelvin-Helmholtz scenario while subsequent works by [START_REF] Lombardi | Growth and instability of a laminar plume in a strongly stratified environment[END_REF] provide a quite different explanation of Pesci's experimental observations based on vorticity enhancement by horizontal density gradient effects. In these studies, the high values of the Schmidt number is a key ingredient of the instability. [START_REF] Lombardi | Growth and instability of a laminar plume in a strongly stratified environment[END_REF] also observed a subdominant varicose mode similar to the instability that we observe in three dimensions. However, the buoyant jet is injected into a pre-existing stratified environment whereas, in our study, stratification builds up as the carbon dioxide dissolves into the tube. Furthermore, in these 2D experiments, the buoyancy flux is fixed and steady whereas in our experiments the buoyancy flux increases with the fluid velocity and thus oscillates in the unsteady regime.

Alternatively, the plume can be generated without recourse to any jet by a simple condition of buoyancy at the boundary. For instance thermal plumes are classically created by imposing a fixed temperature at a point source (the spatial extent of which is often poorly known). The boundary conditions of thermal buoyancy experiments are thus closer to the configuration studied in this paper (despite the smaller values of the Prandtl number). Torrance et al. (1969) performed an experimental study of a confined thermal plume generated in water by a localized source (with a Prandtl number equal to 7). Corresponding numerical simulations were presented by Torrance & Rockett (1969) in a companion paper. Experiments and numerics revealed the presence of axisymmetric varicose instabilities, while simulations failed to accurately compute the critical Rayleigh number. Later, [START_REF] Torrance | Natural convection in thermally stratified enclosures with localized heating from below[END_REF] added a background stratification ; he observed a quasi-steady regime but could not reach the unstable regime. [START_REF] Lopez | Instability of plumes driven by localized heating[END_REF] performed numerical simulations without background stratification and with a small radial dimension of the buoyancy source in a confined geometry (inside a finiteheight cylinder) with a Prandtl number equal to 7. They observed an axisymmetric varicose instability above a critical height-based Rayleigh number equal to 5.4×10 7 . This instability was followed by a subsequent breaking of the axisymmetry at larger Rayleigh numbers. [START_REF] Kimura | Mechanism for transition to turbulence in buoyant plume flow[END_REF] did similar (but unstratified) experiments in air (where the Prandtl number is equal to 0.7) in a larger container. They found that the instability is not axisymmetric and occurs as a buckling of the plume rather than a varicose puffing sequence. These asymmetric instabilities were later explained theoretically by [START_REF] Yang | Buckling of a thermal plume[END_REF]. Despite the apparent strong similarities between these configurations and our experimental study, there are still major differences. First, they impose the temperature on all boundaries (leading to a stationary base state) whereas we have no flux of buoyancy on the sides and the bottom wall (leading to a filling-box process). Second, their source of buoyancy is much smaller in size than the diameter of the tube whereas it spreads over the entire tube in our case. Finally, their Prandtl number is equal to 0.7 or 7, whereas it is equal to 700 in our experiments, the latter value leading to an almost z-invariant laminar plume.

The present article focuses on the destabilization of a chemical plume, which is created by the convection of the heavy layer of dissolved CO 2 at the free surface of water (see figure 1a). This set-up, which is described in detail in the next section, corresponds to the case of a distributed source (since CO 2 injection occurs over the entire free surface) and to the case of a purely buoyant plume (no initial momentum). It should be noted that the experiment is done at large Prandtl/Schmidt number, which is difficult to achieve numerically. Materials and methods are depicted in section 2. Section 3 is devoted to the description of the experimental instability and its numerical counterpart. The main features of the laminar steady plume are first briefly recalled. The rest of the section deals with the exponential growth of the periodic instability in the linear regime and the subsequent saturation in the non-linear regime. A simplified model is proposed in section 4 as an attempt to explain the mechanism underlying the destabilization process. As the model is essentially qualitative, analytical details are relegated to appendix A. In the concluding section 5, a possible explanation concerning the predominance of the axisymmetric mode of destabilization (in the present study and similar previous works) is proposed.

Materials and methods

Experimental setup

A detailed description of the experimental setup used to characterize the flow induced in a vertical glass tube by a time step of the partial CO 2 pressure is given in [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF]. We recall in the following the main components of the setup. A centimetre-sized glass cylinder of internal radius R c ranging from 4 to 8 mm and thickness 2 mm (Optik-C, France) is filled with water (density ρ 0 , viscosity ν) up to a height H (H is measured from the bottom of the cylinder to the bottom of the meniscus) as shown on figure 1(a).

The tube is immersed in a square optical tank full of water (not drawn in figure 1), in order to reduce radial distortions of the images. There are no vertical distortions of the images because the tube is cylindrical. The whole (optical tank + cylinder) is placed at the center of a pressure cell (drawn in figure 1b). Four lateral sides of the pressure cell are closed by 1 cm thick quartz windows for visualisations. Flat rubber gaskets located between the quartz plates and the steel body ensure the airtightness of the cell. Carbon dioxide is brought into the cell by a PVC millimetric diameter pipe (Legris, France) connected to the top of the pressure cell (CO 2 inlet in figure 1b). The inlet jet (of the order of a few meters per second during the pressure increase) is deviated at 90 degrees toward the wall in order to prevent the forcing of disturbing motions inside the water. The 200 bar bottle (Air liquide, France) provides a 99.9% pure carbon dioxide, the pressure of which can be adjusted using a pressure reduction valve [0-50 bars] (ref. Air liquide,France). For each run, the pressure is measured with a 25 bar manometer (Wika, USA) and a high precision differential 25 bar pressure sensor (Vega, Germany) connected to the top of the pressure cell (pressure in figure 1b). Once the valve is opened, the total pressure P rises from P 0 = 1 bar up to its final value P 1 in a few tens of seconds. The partial pressure of CO 2 increases from 0 to P + = P 1 -P 0 (which is directly read on the differential manometer since P 0 is the pressure outside the cell).

The temperature is measured using a high speed response thermocouple (TC Direct, France) located on the axis of the cylinder 4-5 mm above the meniscus through a gas-proof connection on the top of the pressure cell (temperature on figure 1b). Both signals are recorded using a HP 34970A data logger (Hewlett Packard, USA) at a frequency of 5 Hz. During the pressurization, the temperature rises up to 325-330 K (∆T ∼ 30 K), due to the nearly-adiabatic compression of the gas. This temperature increase damps over a period of 100s. This temperature increase is larger for faster pressurizations. Although this effect could not be neglected for the study of the initial set-up of the plume [START_REF] Vreme | Gravitational instability due to the dissolution of carbon dioxide in a hele-shaw cell[END_REF], we made sure by varying the duration of the initial pressure transient that it had no effect on the characteristics of either the stationary or the unstable regimes. A fourth pipe connected to the top of the pressure cell permits to purge the system (purge in figure 1b).

Particle image velocimetry measurements (PIV) are performed by seeding the fluid with 5 µm diameter polystyrene spheres (Polyscience, USA). About 0.2 µl of the original colloidal suspension has to be diluted in 1 cm 3 of solution, in order to obtain enough particles to perform PIV analysis. These particles are slightly denser than water, but their characteristic time of sedimentation is always much greater than the saturation time of the solution. So, these particles are considered as good tracers. The seeded solution is periodically illuminated following a diametral plane, by a red diode laser (average power 250 mW at 670 nm) sheet 150 µm thick (see figure 1b). The latter is triggered at the PIV frequency of 8 Hz by a Hewlett Packard 34970a Data Acquisition Unit and each flash lasts 4 milliseconds, in order to avoid heat convection flows.

Governing equations and dimensionless numbers

Governing equations and boundary conditions will be first used to introduce the dimensionless parameters and second to present the numerical method.

Using the cylindrical coordinates, the Overbeek-Boussinesq approximation of the Navier-Stokes (NS) equations can be made dimensionless by non-dimensionalizing lengths by the radius R c , times by R 2 c /D, velocities by D/R c and pressures by ρ 0 D 2 /R 2 c (D referring to the diffusivity of carbon dioxide in pure water). The saturation concentration at thermodynamic equilibrium C + = K H P + (where K H = 3.4 10 -2 mol l -1 atm -1 denotes the Henry's constant of carbon dioxide in water) is naturally chosen as the typical concentration. Using lowercase letters for dimensionless quantities, the NS and diffusion equations can be rewritten

1 S ∂u ∂t + (u • ∇)u + ∇p = Ra c k + ∇ 2 u, (2.1) ∇ • u = 0, (2.2) and ∂c ∂t + (u • ∇) c -∇ 2 c = 0. (2.3)
In equation (2.1), S and Ra refer to the Schmidt and Rayleigh numbers, which are defined as follows

S = ν D and Ra = gαK H P + R 3 c Dν , (2.4)
where g refers to the acceleration of gravity and α refers to the chemical expansion coefficient (1/ρ)(∂ρ/∂C). The experimental constants are known accurately (D = 1.8 × 10 -9 m 2 s -1 , ν varies in the range [0.88; 1] × 10 -6 m 2 s -1 depending on the room temperature which was measured within half a degree), except for the coefficient α which is difficult to measure because the density difference is small (of the order of 0.1%) at the concentrations considered in this paper. In the literature, the product αK H has been measured by [START_REF] Hebach | Density of water+carbon dioxide at elevated pressures: measurements and correlation[END_REF] but the results of their measurements is marred by a large uncertainty (αK H = 0.004 ± 0.001 MPa -1 ), which leads to a large uncertainty (of the order of 25%) in the experimental determination of the Rayleigh number. The density gradient due to the heat of the CO 2 dissolution can be neglected because it is about two orders of magnitude smaller than the density gradient due to the presence of CO 2 . Indeed, the ratio between these two density gradients is of the order of (α H /α)(∆H sol /C p ) D/D H where α H = 2.07 × 10 -4 K -1 is the heat expansion coefficient, ∆H sol = 20500 J mol -1 is the heat due to the CO 2 dissolution, C p = 4180 J kg -1 K -1 is the volumetric heat capacity and D H = 0.143 × 10 -6 m 2 s -1 is the heat diffusivity of water.

The problem must be completed by a suitable set of boundary conditions for the hydrodynamic velocity field and the gas concentration. The hydrodynamic no-slip boundary conditions at the solid walls, can be expressed as follows

u = 0 at r = 1 for z ∈ [-h, h m ] z = -h for r ∈ [0, 1] , (2.5)
where h = H/R c and h m = H m /R c denote the aspect ratio of the fluid cylinder and the dimensionless depth of the meniscus respectively (see figure 1). The thermal dilatation of the water due to the ingestion of CO 2 modifies by less than 1.5% the height of the fluid and has been neglected. The hydrodynamic boundary condition at the meniscus is much more tricky to write. Whereas the most obvious would be to consider the vanishing of the tangential constraint at the surface (free slip), some experimental and numerical evidences tend to prove the nearly-solid nature of the meniscus. Due to the contamination by surfactants and other substances, water molecules at the interface are not able to flow anymore and behave as a solid wall [START_REF] Ybert | Stabilisation des mousses aqueuses par des protéines[END_REF]. So, the last no-slip hydrodynamic boundary condition can be written u = 0 at the surface defined by z = z s (r).

(2.6)

In the previous condition, z s (r) is the solution of the dimensionless equation [START_REF] Concus | Static menisci in a vertical right cylinder[END_REF] 1 r d dr r dz s /dr

1 + (dz s /dr) 2 = Bo z s , (2.7)
which satisfies the condition d z s /dr = cot θ c at r = 1. The contact angle θ c of the meniscus has been measured from video images and is fairly constant in the interval [25 • , 35 • ] so that we took θ c = 30 • in the simulations. In equation (2.7), the Bond number is defined by Bo = ρ 0 gR 2 c /γ, where γ = 72 mN m -1 is the surface tension of the interface (which does not depend on the carbon dioxide concentration, see e.g. [START_REF] Akutsu | Interfacial tension between water and high-pressure CO 2 in the presence of hydrocarbon surfactant[END_REF]. We checked that residual gas flow (due to CO 2 intake) and convective flow in the liquid are not strong enough to alter the shape of the interface by more that 0.1% in altitude.

Finally, one must formulate a relevant boundary condition at the surface for the gas concentration or flux. There is no reason here to consider a resistive relation between the mass flux at the interface and the deviation from the gas concentration at saturation [START_REF] Cussler | Diffusion : mass transfer in fluid systems[END_REF]. So, we make the assumption that the thermodynamic equilibrium is immediately reached at the liquid/gas interface, namely c = 1 at the surface defined by z = z s (r).

(2.8)

Numerical results presented throughout the article are obtained by solving equations (2.1), (2.2) and (2.4) completed by the boundary conditions (2.5), (2.6), and (2.8) using a finite element method. The simulations are axisymmetric and the surface shape z s (r) is entered for each Bond number after solving (2.7) using Matlab. The mesh which contains 20000 elements is refined at the surface with 10 additional layers of elements having a stretching factor of 1.2. This makes the thickness of the first layer equal to 0.5% of the tube's radius i.e. much smaller than the thickness of the diffusive layer of CO 2 (of the order of 2.5% of the radius at the largest Rayleigh number). The software uses biquadratic polynomials for the velocity, bilinear polynomials for the pressure and a bicubic discretization for the CO 2 concentration. This leads to 200,000 degrees of freedom for an aspect ratio of 3. Simulations are initiated with u = 0, c = 0 inside the fluid and are usually completed in a couple of weeks on a 64bits PC with 2 processors at 2.4 GHz.

The Reynolds number of the plume can be defined as Re = wl/S using the (non-dimensional) velocity w and radius l of the plume (S being the Schmidt number). Using the results of [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] for the laminar plume, the Reynolds number is found to range from 0.2 to 1.2 when the Rayleigh number ranges from 3 × 10 5 to 5 × 10 6 as in the experiments. 1). The chronology of the flow can be divided into four distinct phases, referred to as I, II, III and IV in the following. The nature of the observed phenomena and the way they are sequenced is the same for all experiments although regimes III and IV (linear and non linear phases of the instability) appear sooner or later depending on the dimensionless numbers of the problem (aspect ratio, Rayleigh and Bond numbers).

Instability of the steady plume

Regimes I and II : a quasi-steady base flow

Once the inlet is open (t = 0), the carbon dioxide creates a diffusive gas enriched layer of dense fluid at the surface, which is unstable from a gravitational point of view. A plume is formed, which propagates downwards to the bottom of the cell. This transient plume is followed by a few others (typically 3 or 4) at a frequency of about 1 Hz, which corresponds to about 1000 in non-dimensional frequency units. This first transient regime (I) is very short (of the order of 0.003 dimensionless time units). After this period of time, the rapid oscillations of the velocity disappear completely in the numerics and remain weak in the experiments. A nearly-stationary regime (II) settles in the tube.

The velocity of the plume slowly decreases by 25% during stage II. It can be noted that the velocity amplitude is 20% smaller in the experiments than in the numerics. This could be due to small oscillations and asymmetries on the base flow in the experiment (especially visible at large Bond numbers).

At the beginning of stage II, the plume is composed of a stem with streamlines parallel to each other. The stem fills the whole height of the cylinder (see experimental and numerical velocity shown in figures 3a,c) and the amplitude of the velocity is independent of z along the axis from z = -0.5 to z = -3.5. By contrast, figures 3(b,d) show that at the end of stage II the vertical velocity is smaller at the bottom of the plume (around z = -3) than at the top (around z = -1). This is due to the gradual filling of the tube by the saturated solution which reduces the buoyancy difference between the plume and the surrounding medium. For example, the density fields obtained numerically (figures 3e,f ) indicate that the difference of buoyancy c between the axis and the outer part of the plume (at the bottom of the cylinder) is equal to about 0.6 at the beginning of stage II and equal to about 0.3 at the end of stage II. This filling-box effect decreases the velocity of the plume at the bottom of the tube, and has an overall effect on the streamlines. The "rotation center", i.e. the elliptic stagnation point at the center of the smallest streamlines (highlighted by a white dot in figures 3c-f ) is located at z = -1.5 at the beginning of stage II. It gets closer to the free surface as time evolves and reaches the altitude z = -0.5 at the end of stage II. After a long period of time, the amplitude of the oscillations resumes growing (stage III), indicating that the slowly evolving plume has become suddenly unstable. The nearly-stationary plume is considered as the base flow of the instability depicted in the following.

Regimes III and IV : a sudden destabilization of the flow

After a long period of time t i , the vertical velocity of the plume is subject to rapidly growing oscillations which characterize the linear instability (regime III). The onset time seems to correspond to the instant when the altitude of the rotation center is close to z = -1. The velocity oscillations correspond to an axisymmetric varicose mode in which broadenings are advected down to the bottom of the cell (regime III, see supplementary materials movie1.avi). In the first oscillatory regime (period τ , frequency = 2π/τ ) the velocity amplitude grows rapidly during few tens of periods (10 to 20 typically). The amplitude of the oscillations then saturates and the period of the instability switches to a slightly larger value τ NL > τ . In the latter non linear regime (IV), the broadenings of the varicose instability evolve towards dissociated blobs which periodically pour from the meniscus, as shown on figures 4(a-d). The puffs are less visible in the numerical simulations (figures 4e-h) since the instability saturates at a lower amplitude (possibly due to numerical diffusion). Then, the period of the non-linear regime slowly keeps increasing in time. In some rare experimental cases a second frequency steps in, leading to a quasi-periodic flow. The next paragraphs are devoted to a quantitative description of the instability (regimes III and IV).

Frequency of the perturbation

To determine the characteristics of the instability accurately, the perturbation is separated from the base flow by taking the temporal Fourier transform of the vertical velocity over a sliding window. The vertical velocity w(r, z, t) obtained from PIV measurements is first multiplied by exp i 0 t, where 0 is manually tuned once for each experiment to get as close as possible to the experimental frequency , then averaged over a period τ 0 = 2π/ 0 leading to a complex velocity ŵ(r, z). The integration over a period τ 0 allows us to eliminate the stationary component of the flow. At the same time, if we assume that the vertical component of the perturbation is of the form w(r) exp i(kz -t)+c.c. (where c.c. corresponds to the complex conjugate) the previous operation provides the spatial structure of the perturbation since ŵ(r, z) = 1 τ 0 t+τ0 t w(r) e i(kz-t ) e i 0t dt = w(r) e ikz for 0 = .

(3.1)

The amplitude | ŵ| of the perturbation is displayed in figure 5(a). In the stable regime (stage II), the amplitude of the 0 -Fourier component remains weak and stationary; it is due to the noise in the measurements. At the end of the stable regime, the amplitude of the 0 -Fourier component grows by about one order of magnitude (stage III). The amplitude then saturates when the system enters the non-linear regime IV.

Clearly, this process relies on the choice of the Fourier frequency 0 which is tuned once for each experiment in order to get stationary iso-phases during the linear stage. Figure 5(b) shows the temporal evolution of the phase φ = arg( ŵ) of the 0 -Fourier component on the axis of the plume. Before t = 0.06, the instability is too weak such that the argument has no physical meaning (noise). Between t = 0.06 and t = 0.085, the iso-phases are nearly stationary for the Fourier frequency 0 has been chosen as close as possible to the frequency of the instability. After t = 0.08, the iso-phases of the 0 -Fourier component are no longer stationary: they are translated in the positive z-direction since the period of the oscillations in the non-linear regime is slightly larger than in the linear regime (by about 20%). The error on is of the order of 5 to 10% since the linear stage only lasts for 10 to 20 periods. It should be noted that the determination of the frequency is deduced from velocity measurements along the whole axis rather than at a single point.

The frequency of the instability in the linear regime is plotted in figure 6 as a function of the aspect ratio (a) and Rayleigh number (b). Figure 6 shows that the experimental data is practically independent of the Bond number. The frequency obtained in this configuration (with a meniscus) can thus be extrapolated to flat free surfaces (without meniscus) which correspond to infinite Bond numbers. Figure 6(a) also indicates that the frequency is independent of the aspect ratio within the experimental range. (3.2) with a small uncertainty in the measurements. Numerical results overestimate the experimental values by about 20%, but are still consistent in order of magnitude (the overestimate is less visible in figure 6(b) due to the logarithmic scale of the vertical axis).

Wavenumber and phase velocity of the perturbation

In order to obtain the wavenumber of the perturbation, the phase φ = arg( ŵ) is fitted by a linear function φ = kz during stage III when φ is stationary in time (i.e. around t = 0.067 in figure 5a). Indeed, if the frequency 0 is equal to the frequency of the mode, equation (3.1) indicates that k is the wavenumber of the perturbation.

The wave number is plotted as a function of the Rayleigh number for h = 3 in figure 7(a), and as a function of the aspect ratio for Ra = 10 6 in figure 7(b). Due to the noise in the measurements of the vertical velocity, the evaluation of the wavenumber is marred by a large uncertainty (∼ 45%). However, the mean wavenumber (averaged over the Rayleigh number and the aspect ratio) does not vary by more than 15% when the Bond number increases from 2 to 9. This tends to indicate that these results may be extrapolated to the cases of flat free surfaces. More surprisingly, no clear dependence on the Rayleigh number or aspect ratio can be identified. Consequently, the experimental wave number is considered as independent of any dimensionless number. The value k = 1.5, (3.3) (in non-dimensional form) which corresponds to the best fitting value of the experimental data is plotted as dashed lines in figures 7(a,b). It has also been observed that the phase φ was not always linear in z : φ may increase faster at the bottom than at the top. This means that the wave number is larger at the bottom than at the top. The values reported here correspond to the mean value of the wavenumber (evaluated between z = 1 -h and z = -1 in order to remove the noisy PIV measurements at the top and the bottom).

The phase velocity of the instability, which can be deduced from the frequency and wavenumber of the instability via the relationship w φ = /k, is plotted in figure 8. As observed for the frequency and the wavenumber, the experimental phase velocity of the instability is independent of the Bond number. As deduced from the measurements on and k, no clear dependence of the phase velocity w φ on the aspect ratio can be identified (see figure 8a), at least in the limit of the measurement uncertainty (due to the large dispersion observed on k).

As obtained for the frequency, the phase velocity strongly depends on the Rayleigh number. It can be fitted by the power law has a velocity given by the intrinsic (parameter free) modified power law w = 0.17 Ra 2/3 (log Ra) 1/3 .

(3.5)

This expression of the plume velocity is plotted as a solid line in figure 8. It is very close to the experimental results for the phase velocity of the instability (despite the absence of adjustable parameters). It means that the instability is mostly advected by the base flow in the linear regime and does not propagate relative to the fluid. This result will be a key point in the qualitative model presented in section 4 and appendix A.

It can be noted that the local phase velocity is actually smaller at the bottom than at the top (because the wavenumber is larger at the bottom than at the top). This is again in agreement with the assumption that the perturbation is advected at the fluid velocity of the plume. Indeed, the vertical velocity of the plume is smaller at the bottom than at the top due to the background stratification (as stated in §3.1).

Finally, using the relation w φ = /k, the theoretical value of the plume velocity (3.5) and the empirical value of the wavenumber k = 1.5, the frequency of the plume can be given semi-theoretically as = 0.255 Ra 2/3 (log Ra) 1/3 .

(3.6)

This prediction plotted in solid lines in figure 6 is again fairly close to the experimental and numerical values.

Onset time

In every experimental run, the instability appeared at a fairly reproducible time t i , strongly depending on the aspect ratio and Rayleigh number. Furthermore, contrary to what is observed for other quantities (frequency, wave number, phase velocity), the onset time does depend on the Bond number: the plume destabilizes later for smaller Bond numbers, indicating that the meniscus has a stabilizing effect. Such an effect can be intuitively understood as follows. The slope of the meniscus induces solutal baroclinicity underneath the free surface which tends to force the heavy fluid towards the axis. The baroclinic CO 2 enriched fluid located underneath the interface near the contact line is advected fast enough towards the bottom of the meniscus to prevent the growth of any fingering instability (other than the main central plume).

Since the Bond number characterizes the degree of flatness of the meniscus, this effect is expected to saturate at large Bond numbers, where the radius of the cylinder is larger than the capillary length l c = (γ/ρ 0 g) 1/2 . In an attempt to make all the results collapse onto a single curve, the onset time t i has been rescaled by a function f (Bo) = (1+Bo -1 ) β which tends to 1 in the limit of large Bond numbers. The rescaled onset time ti = f (Bo) t i is plotted in figure 9 with an exponent β adjusted to -3.5. Figure 9(a) shows that the rescaled onset time ti is proportional to the height of the cylinder, at fixed Rayleigh number. As mentioned at the beginning of paragraph 3.2, the destabilization seems to occur as soon as the streamlines are confined to a region of vertical extension 1 (R c in dimensional units) or equivalently, when the "rotation center" of the streamlines is located around z = -1. So, considering that the flow becomes unstable once the background stratification has filled the cylinder up to a specific height and recalling that the dimensionless buoyancy flux Sh (Sherwood number) of a steady laminar plume scales as Sh ∼ Ra 1/3 (see [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF]) leads to a scaling of the form ti ∼ h Ra -1/3 . Such an interpretation is consistent with the scenario proposed in section 4, where the instability is triggered by what is called a "filling box" effect by [START_REF] Lopez | Instability of plumes driven by localized heating[END_REF]. The linear scaling between the onset time and the height of the cylinder is well recovered experimentally, as shown in figure 9(a).

That being said, the real flow and stratification are not that simple and the above explanation is only an idealized view of the problem. The scaling on the Rayleigh number is thus slightly different in the experiments. Figure 9(b) shows that the decrease of the rescaled onset time with the Rayleigh number can be roughly rendered by a power fitting

Stability diagram and non-linear saturation amplitude

The instability described above only occurs for large enough values of the Rayleigh number. Below a critical Rayleigh number, the plume remains nearly steady until the end of the experiment -i.e. the total dissolution of CO 2 in water (thermodynamic equilibrium). The stability of the quasi-steady base flow has been investigated in the plane (h, Ra) for two different Bond numbers. As shown on figure 10(a), the critical Rayleigh number Ra c depends on both the aspect ratio h and the Bond number. The critical Rayleigh number has a minimum at h 2, so that the flow is unconditionally stable for 2.5 × 10 5 . The critical Rayleigh number increases by a factor 2 (resp. 4) when the aspect ratio h increases from 2 to 6 at Bo = 2.2 (resp. Bo = 4.8). It seems that the meniscus (which is more curved at smaller Bond number) tends to stabilize the flow, which is consistent with the interpretation provided in section 3.5. Unfortunately, the stability diagram could not be obtained experimentally at higher Bond numbers, due to residual motions (a long wavelength asymmetric circulation) which perturbed the onset of the instability.

A bifurcation diagram is presented in figure 10(b) for the particular values of the parameters Bo = 2.2 and h = 3. For this purpose, the non-linear amplitude of the oscillations ∆w is extracted in the experiments as the mean amplitude over 5 periods around the maximal amplitude (i.e. at the beginning of stage IV). The square of the saturation amplitude ∆w is then plotted as a function of the Rayleigh number. Despite the few experimental points and the quite large uncertainty on the measurements, the bifurcation appears to be supercritical. Close to the critical Rayleigh number Ra c , the amplitude ∆w is proportional to (Ra -Ra c ) 1/2 (Hopf bifurcation).

Possible origin of the instability -Heuristic model and discussion

We propose an interpretative scenario in which the progressive filling of the cylinder by the CO 2 -enriched heavy fluid triggers the destabilization. Such an interpretation is supported by a model with reduced number of degrees of freedom, which has some similarities with the Lorenz' waterwheel [START_REF] Kolář | Theory for the experimental observation of chaos in a rotating waterwheel[END_REF]. The waterwheel corresponds to the streamline located beneath the free surface and inside the plume (see figure 11a). This streamline is rectangular since the meniscus is assumed to be flat (i.e. the Bond number is assumed to be infinite).

When the fluid flows below the free surface (from r = 1 to r = 0) at the velocity u s , carbon dioxide diffuses into the liquid, creating a thin layer with a thickness δ(r, t) increasing as r decreases (see figure 11a). An equation for δ (and alternately for the linear density λ, see fig 11b) can be obtained from the advection-diffusion equation for c and from the incompressibility condition. Once the fluid reaches the axis of the cylinder, it sinks down to the bottom of the cell under the effect of gravity without loss of buoyancy. The CO 2 -enriched fluid forms a dense vertical shaft, which is subject to a viscous force from the surrounding fluid as it travels down towards the bottom wall. Unlike heat [START_REF] Lopez | Instability of plumes driven by localized heating[END_REF], the carbon dioxide is confined in the cylinder and can not escape through the walls. Carbon dioxide is advected again upwards to the free surface once it has reached the bottom wall. A cylindrical annulus of CO 2 -enriched heavy fluid then builds up close to the lateral wall (labeled heavy fluid torus in figure 11), which exerts a counter force on the axial shaft and slows down the central plume. The differential equation for the velocity of the plume w is obtained by calculating the momentum balance on the plume (inertia, adverse pressure gradient, buoyancy and viscous drag). This axial velocity governs the recirculation of the flow and thus governs the radial velocity at the free surface u s .

The destabilization of the flow can be understood as follows. Once the downward flow is slow enough, the boundary layer located beneath the free surface becomes overloaded. This excess of buoyancy then re-accelerates the fluid when it reaches the axis of the cylinder, thereby feeding the upward flowing zone and so on. The details of the derivation of the model and the subsequent linear stability analysis are given in appendix A. The model generally captures the essential features of the experimental phenomenology and yields reasonable trends and orders of magnitude for the frequency, phase velocity, wave number and onset time. We list in the following the main results which are obtained from a direct numerical integration of the system of equations (A 5) and (A 7 -A 10) and from a linear stability analysis of these equations.

(i) the system switches from stable to unstable at a specific onset time t i , after a quasi-stationary regime where the velocity decreases. The time at which the change of regime occurs can be identified in the model by applying a small perturbative step just before the onset time. The oscillatory response is first damped and then grows again as soon as t > t i (see figure 11c). The so-determined value of the onset time is robust regarding the amplitude of the perturbation and the time at which the perturbation is applied.

(ii) The destabilization of the flow in the model can be predicted analytically in the Quasi-Steady State Approximation by calculating the growth rate using a linear stability analysis (see appendix A.4). This prediction is in excellent agreement with the direct numerical integration of the theoretical model;

(iii) the dependence in Rayleigh number of the frequency, phase velocity, wavenumber and onset time are in very good agreement with the experimental observations : the scaling exponents provided by the model are very close to their experimental counterparts. For instance the frequency and the phase velocity scale as Ra 3/4 in the experiments whereas they scale as Ra 0.67 in the model for the range of Rayleigh numbers considered here (see § §A.5). The onset time scales as Ra -0.55 in the experiments close to the model which predicts a scaling as Ra -0.67 in the range of the experiments. It can be noted that the model predicts different scalings for larger Rayleigh numbers (equal to Ra ±2/5 for infinite Rayleigh numbers);

(iv) the model predicts a very small dependence of the frequency, phase velocity and wavenumber with the aspect ratio h. This is consistent with the experiments where their variations are smaller than the uncertainty in the measurements.

(v) the model predicts that the onset time t i is almost proportional to the aspect ratio h. This is again in excellent agreement with the experimental results;

(vi) the order of magnitudes for the frequency , phase velocity w φ , wavenumber k and onset time are consistent with those experimentally observed (again, see §A.5) despite an underestimation of a factor 2 to 6 for , w φ and k.

Conclusion

This paper presents experimental and numerical results on the destabilization of a negatively buoyant plume created by an extended source at high Schmidt number. Such a configuration usually generates several plumes which interact in a complex way. Here, the presence of a meniscus confines the buoyant fluid into a unique axisymmetric plume, the stability of which can thus be analysed through reproducible experiments. After a long onset time, the quasi-steady plume destabilizes through an axisymmetric puffing instability with an amplitude which saturates and decreases slowly at very late stages. Fortunately, most characteristics of the instability (frequency and wavenumber) are found to be independent of the size of the meniscus allowing for an extrapolation of the results to a flat surface (Bo → ∞).

The instability is related to the feedback of the global flow on the injection rate of buoyancy and to the presence of a background stratification. First, the feedback mechanism is due to the boundary condition of constant buoyancy at the surface (rather than a steady injection rate of buoyancy). A deceleration of the global flow within the container allows for a larger accumulation of buoyant fluid at the surface. When this added buoyancy reaches the axis of the cylinder, it brings on an increase of the buoyant force and thus an acceleration of the global flow half a period later. This feedback mechanism sets the wavelength of the instability which is proportional to the radius of the cylinder. The perturbation is then advected by the flow at the velocity of the base flow which has been shown by [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] to be proportional to Ra 2/3 (log Ra) 1/3 . Therefore, the frequency of the instability is proportional to Ra 2/3 (log Ra) 1/3 as well. Second, the background stratification builds up within the container due to the no-flux boundary conditions at the bottom and on the sides of the container. The time for the stratification to reach the buoyant surface is proportional to the height of the cylinder such that the onset time of the instability is also proportional to the height of the container. A simple heuristic model has been derived where the buoyant fluid is advected by the flow as in a water-wheel model. This model supports the idea that the background stratification is a key ingredient for the instability.

As discussed in the introduction, the nature of the instability has been found to be very different depending on the configuration of the system. In our case, the instability is a varicose puffing rather than a sinuous buckling. This is similar to what has been obtained for Helium jets by [START_REF] Subbarao | Investigation of a co-flowing buoyant jet: experiments on the effect of reynolds number and richardson number[END_REF], [START_REF] Cetegen | Experiments on the oscillatory behavior of buoyant plumes of helium and helium-air mixtures[END_REF] and [START_REF] Cetegen | Experiments on stability and oscillatory behaviour of planar buoyant plumes[END_REF]. However, their scaling of the frequency as a function of the Richardson number cannot be extrapolated to our study since our configuration corresponds to an infinite Richardson number. The axisymmetric puffing instability observed in our study is also similar to the instability observed experimentally by Torrance et al. (1969) and numerically by [START_REF] Lopez | Instability of plumes driven by localized heating[END_REF] for a point source of thermal buoyancy in a confined geometry. In both studies, the background stratification and the feedback mechanisms are present although not highlighted. It is thus natural to infer that the varicose nature of the instability is related to these two key ingredients. However, despite the presence of a background stratification, [START_REF] Pesci | Inertially driven buckling and overturning of jets in a Hele-Shaw cell[END_REF] observed a sinuous instability for a 2D buoyant jet. Likewise, despite the natural feedback mechanism, [START_REF] Kimura | Mechanism for transition to turbulence in buoyant plume flow[END_REF] observed a sinuous instability for a heat point source. Furthermore, in our configuration (with stratification and feedback), preliminary results for large aspect ratios (h > 6) have revealed the presence of a weak sinuous instability. It thus seems that the nature of the instability is not related to these ingredients. A possible explanation may lie in the vertical confinement of the plume. Indeed, the varicose instability has mostly been obtained in vertically confined containers (Torrance et al., 1969;[START_REF] Lopez | Instability of plumes driven by localized heating[END_REF] whereas sinuous instabilities have been obtained in open configurations [START_REF] Pesci | Inertially driven buckling and overturning of jets in a Hele-Shaw cell[END_REF][START_REF] Kimura | Mechanism for transition to turbulence in buoyant plume flow[END_REF]. In our experiments, the plume is confined vertically for moderate aspect ratios, which is consistent with the observed axisymmetric varicose instability. For large aspect ratios (h > 6), the sinuous instability has a wavelength larger than for the varicose instability. Thus, the sinuous instability may be stabilized by the vertical confinement because its wavelength does not fit within the container.

thickness of the viscous boundary layer is much smaller than the thickness of the diffusive layer of concentration. This is counter-intuitive in our case because the Schmidt number is very large (S = 550). However, [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] found numerically that the viscous layer is 2 to 3 times smaller than the diffusive chemical layer (see their figure 15b).

As shown in the steady case by Whittaker & Lister (2006b), a self-similar solution exists, of the form

c(r, z, t) = 1 -erf z δ(r, t) (A 2)
with a thickness δ of the diffusive layer depending on r. This result can be extended to an unsteady velocity profile with a thickness δ(r, t) depending on r and t by introducing (A 2) into (A 1). The thickness must then satisfy:

∂δ 2 ∂t + 1 r 2 u s ∂(ru s δ) 2 ∂r = 4. (A 3) It is possible to define the linear density of CO 2 concentration λ(r, t) = ∞ 0 2πrc(r, z, t) = 2πrδ(r, t)C with C = ∞ 0 [1 -erf(x)]dx = 0.5642. (A 4)
Introducing this definition into (A 3) gives an equation for λ at the free surface

∂λ 2 ∂t + 1 u s ∂(u 2 s λ 2 ) ∂r = 16π 2 r 2 C 2 . ( A 5)
For a steady plume, [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] showed using a matched asymptotic expansion that the velocity at the surface u s is proportional to the plume velocity w and can be approximated by :

u s (r) = -κw(1 -r) (A 6)
with the constant κ ∼ 0.25 around Ra = 10 6 . This formula is valid theoretically in the limit of large aspect ratios h for a steady plume. Experimentally, it was found to be independent of h for h > 3. We will keep this profile of radial velocity at the free surface which is valid for a nearly parallel plume, in the limit of low wavenumber of the perturbation and in the case of free-slip boundary conditions at the free surface.

A.2. Equations inside the plume

When reaching the axis of the cylinder, the linear density of CO 2 is then advected at the velocity of the plume w(t) which is supposed to be invariant in z. The equation for λ(z, t) inside the plume is thus

∂λ ∂t + w ∂λ ∂z = 0. (A 7)
The continuity condition between the free surface and the vertical plume is found by equating the incoming flux at the free surface with the downward flux at the top of the plume:

[λ(r, t)u s ] r=0 = [λ(z, t)w] z=h . (A 8)
It should be noted that the exact downward flux at z = h can be calculated in a more rigorous way by taking into account the Gaussian profile of concentration c(r) and its associated profile of axial velocity. It modifies only by 20% the value of the flux, since the profile of velocity is much thicker than the profile of concentration. Taking into account this effect would modify by 15% the frequency and the velocity of the instability. It has been neglected here for simplicity.

Finally, the velocity of the plume is subject to different forces which correspond to the different terms of Eq.(2.1). They can be found by integrating r times Eq.(2.1) from z = 0 to z = h and from r = 0 to r = r 0 (which corresponds to the radius where the flow is reversed).

To estimate the coefficients we have assumed that the velocity profile is close to the profile of a steady plume. [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] showed numerically (see their figure 11a) that for a steady plume at large Prandtl number, the concentration is Gaussian (of size l) in the radial direction and nearly uniform in the axial direction . Assuming that there is no axial flux, the velocity profile can be calculated as wF l (r)/F l (0) where

F l (r) = 1/l r/l 1 -e -x 2 x dx + (r 2 -1)(1 -l 2 ). (A 9)
It can be noted that this profile depends logarithmically on the thickness of the plume l. In our model, l was chosen equal to 0.1, which is characteristic of the range of Rayleigh numbers found in the experiment. The value of the reversing radius r 0 was chosen as r 0 = 0.3 since it varies from 0.4 down to 0.2 during an experiment. This value has almost no influence on the characteristics of the instability (wavenumber, frequency) but it slightly modifies the value of the onset time of the instability.

(i) the first term of Eq.(2.1) gives the inertia of the plume h(I/S)(dw/dt) where the coefficient I = r0 0 2πrF l (r)dr/F l (0) is close to 0.124 ;

(ii) the second term vanishes for a parallel plume ;

(iii) the third term corresponds to the mean adverse pressure gradient which is due to the CO 2 filling of the outer part of the cylinder (from r = r 0 to r = 1). This term can be estimated as BRa It should be noted that the weight of the heavy layer underneath the free surface is neglected compared to the weight of the plume. This approximation is valid in the limit of large cylinder's height h since the weight of the plume is proportional to h. In our experiments, this assumption seems to be justified since the laminar velocity of the plume was measured to be independent of the Bond number (see [START_REF] Nadal | Stationary plume induced by carbon dioxide dissolution[END_REF] whereas the forcing due to the heavy layer is proportional to the tilt of the free surface which depends on the curvature of the meniscus, i.e. on the Bond number. It can be derived asymptotically that for large Rayleigh numbers the wavenumber k is independent of the Rayleigh number whereas the frequency and the plume velocity w 0 (t i ) scale as Ra 2/5 . Indeed, (A 23) indicates that A i tends to 0 because A r and ˜ must be finite (since ˜ = 0 is not a solution and since |A r | < |A| < 1). Assuming A i = 0 fixes the value of ˜ as independent of the Rayleigh number, since it is solution of

Im

-12(1 -e -κi ˜ h ) (i ˜ + 2)(i ˜ + 3)(i ˜ + 4) = 0,

where Im stands for imaginary part. The scalings of w 0 and then are thus obtained directly from (A 24).

A.5. General trends and orders of magnitude

The frequency, wavenumber, phase velocity and onset time produced by the model are plotted in figure 12 as a function of the aspect ratio and the Rayleigh number. First, the analytical predictions (A 23,A 24) using the linear stability analysis (plotted as solid lines) are in excellent agreement with the results obtained through a numerical integration of the model (plotted as symbols). Second, the general trends observed on the frequency, the wave number, the phase velocity and the onset time are consistent, although not in exact numerical accordance with the experiment.

The frequency is an increasing function of the Rayleigh number in both the model and in the experiments. In the model, it scales as Ra 0.67 (see figure 12b), close to the experimental scaling equal to Ra 3/4 . It should be noted that these scalings are obtained by fitting the theoretical predictions in the range where the experimental results have been obtained. However, the model predicts that the exponent is smaller at larger Rayleigh numbers (equal to 2/5 in the limit of large Rayleigh numbers). In the model, the frequency is a slightly decreasing function of the aspect ratio h (by a factor 2 over one decade), whereas it appears almost independent from h in the experiments. Finally, the orders of magnitude predicted by the model are correct for the frequency despite an underestimation by a factor 6.

At the onset of the instability, the phase velocity (which is equal to the plume velocity w 0 (t i )) is an increasing function of the Rayleigh number (scaling as Ra 0.67 in the range of the experiments) whereas its experimental counterpart scales as Ra 3/4 (see figure 8b). As mentioned above, the model predicts a smaller scaling exponent equal to 2/5 in the limit of large Rayleigh numbers. In the model, the phase velocity is a slowly increasing function of the aspect ratio (by 20%). Even if not obvious in figure 8(a), such a trend is not inconsistent with that of the experimental phase velocity, the latter being marred by a large uncertainty. Finally, the orders of magnitude predicted by the model are correct for the phase velocity despite an underestimation by a factor 2.

The wavenumber is a decreasing function of the aspect ratio (by 50%) and a slightly decreasing function of the Rayleigh number (by 10% over two decades) while its experimental counterpart seems to be independent from both parameters. However, the large uncertainty in the experimental measurements (of the order of 30%) may explain this apparent disagreement. Again the order of magnitude produced by the model for the wavenumber k is consistent with the experimental one despite an underestimation by a factor 2.

Finally, the onset time is very well rendered by the model. In the model, it increases nearly proportionally to the aspect ratio h as in the experiments (see figure 9a). It is a decreasing function of the Rayleigh number (scaling as Ra -0.67 ) as in the experiments (where t i ∝ Ra -0.55 in figure 9b). Furthermore, there is a quantitative agreement (within 30%) between the experiments and the model.

Figure 1 .

 1 Figure 1. Experimental set-up containing a cylindrical tube (a) filled with water and located in a pressure cell (b) filled with CO2. The fluid is seeded with PIV particles and the CO2 enriched water creates a sinking plume (drawn in grey).

Figure 2 .

 2 Figure 2. Experimental (a) and numerical (b) z-component w of the velocity one radius below the meniscus (z = -1, point A in figure 1a) as a function of time for Bo = 2.2, Ra = 10 6 and h = 4 (Rc = 4 mm, P + = 6.4 bar). Phenomenology of regimes I (transient plumes) and II (quasi-steady plume) are recalled in paragraph §3.1. The linear instability (regime III) and its non-linear saturation (regime IV) are detailed in paragraphs §3.2.

Figure 2

 2 Figure2(a) and 2(b) show generic experimental and numerical time series of the vertical component of the velocity w as a function of time, measured one radius below the meniscus (z = -1, point A in figure1). The chronology of the flow can be divided into four distinct phases, referred to as I, II, III and IV in the following. The nature of the observed phenomena and the way they are sequenced is the same for all experiments although regimes III and IV (linear and non linear phases of the instability) appear sooner or later depending on the dimensionless numbers of the problem (aspect ratio, Rayleigh and Bond numbers).

Figure 3 .

 3 Figure 3. Experimental and numerical z-component w of the velocity at the beginning of the dissolution process (a, c: t = 0.01) and just before the instability onset (b,d: t = 0.055) for Bo = 2.2, Ra = 10 6 and h = 4 (Rc = 4 mm, P + = 6.4 bar). Corresponding numerical concentration fields are shown on (e) and (f). Streamlines (white solid lines) are superimposed to numerical fields. White dots show the position of the elliptic stagnation points.

Figure 4 .

 4 Figure 4. (a-d) Experimental and numerical (e-h) z-component of velocity at t = 0.1 (a,e), t = 0.1 + τNL/4 (b,f), t = 0.1 + τNL/2 (c,g), t = 0.1 + 3 τNL/4 (d,h), where τNL = 0.0015 is the period of the instability in the non-linear regime. Ra = 10 6 , h = 4, Bo = 2.2.

  Figure 5. (a) Time evolution of the amplitude of ŵ averaged in the domain [|r| < 0.15, -3.5 < z < -0.5]. (b) Spatio-temporal diagram of the argument of the 0-transform (3.1), averaged for |r| < 0.15. Here Bo = 2.2, Ra = 10 6 and h = 4.

  Finally, figure 6(b) reveals that the frequency strongly depends on the Rayleigh number. It can be fitted by the power law = 0.165 Ra 3/4

Figure 6 .

 6 Figure 6. Frequency of the instability (linear growth) as a function of (a) the aspect ratio h and (b) the Rayleigh number Ra. The Bond number is equal to 2.2 (circles, Rc = 4 mm), 3.4 (diamonds, Rc = 5 mm), 4.8 (squares, Rc = 6 mm) and 8.6 (triangles, Rc = 8 mm).Experimental results (open symbols) are compared to the numerical results (solid symbols). The dashed line is the best power fit (3.2) of the experimental data. The theoretical prediction (solid line) corresponds to the the fluid velocity in a stationary plume (w φ = 0.17 Ra 2/3 (log Ra) 1/3 ) times a constant empirical value of the wave number k = 1.5 (see equation (3.6)). The error in the experimental determination of is smaller than 10%.

Figure 7 .Figure 8 .

 78 Figure 7. Wavenumber of the instability as a function of (a) the aspect ratio, for Ra = 10 6 and (b) the Rayleigh number for h = 3. The Bond number is equal to Bo = 2.2 (circles), Bo = 3.4 (diamonds), Bo = 4.8 (squares) and Bo = 8.6 (triangles). The dashed line corresponds to the best fitting value given by (3.3). The error in the experimental determination of k ranges from 20 to 30%.

Figure 9 .

 9 Figure 9. Rescaled onset time of the instability ti = (1 + Bo -1 ) -3.5 ti as a function of (a) the aspect ratio h and (b) the Rayleigh number Ra. The Bond number is equal to 2.2 (circles), 3.4 (diamonds), 4.8 (squares) and 8.6 (triangles). Dashed lines correspond the best fit of the experimental data by the power law (3.7). Experimental and numerical data are plotted with open and solid symbol respectively. The error in the experimental determination of ti is of the order of 20%.

  Figure 10. (a) Stability diagram in the (h, Ra) space for Bo = 2.2 (Rc = 4 mm, red circles) and Bo = 4.8 (Rc = 6 mm, black circles). The points corresponding to a stable (resp. unstable) situation are plotted as solid (resp. open) symbols. Stable and unstable domains are separated by a solid line. (b) Bifurcation diagram showing the saturation amplitude as a function of the Rayleigh number for Bo = 2.2 and h = 3. The dashed line corresponds to a Hopf bifurcation with ∆w = 3.65 (Ra -Rac) 1/2 . The error on (∆w) 2 is of the order of 30%.

Figure 11 .

 11 Figure 11. (a) Explanatory sketch of the model (see text for explanations). (b) Zoom of the fluid zone beneath the free surface. (c) Typical evolution in time of the velocity when a perturbative step (black arrow) is applied at t = 0.008. The resulting oscillations amplitude first decay then grow again as soon as t > ti ≈ 0.027.

t0

  λwdt where the coefficient B = r 2 0 /(1 -r 2 0 ) is close to 0.1 ;(iv) the fourth term gives the weight of the plume and is equal to Ra h 0 λ(z)dz ;(v) the last term gives the drag -Dhw where the coefficient D = 2π(1 -2r 2 0 )/F l (0) is close to 3.24.

Figure 12 .

 12 Figure 12. Frequency (a,e), phase velocity (b,f), wave number (c,g) and onset time (d,h) at the beginning of the instability predicted by the model for (h, Ra) in the range [2, 8]×[2×10 5 , 7×10 5 ]. Symbols are obtained by solving numerically the model (A 5-A 10). Solid lines correspond to the linear stability analysis where the frequency and velocity at onset are given by (A 23,A 24).

Acknowledgements

The Agence Nationale de la Recherche (ANR) under the grant CO2-3D and the Labex MEC are acknowledged for financial support.

Appendix A. Axisymmetric Model

A.1. Equations at the surface

As shown on the schematic drawing of figure 11, the velocity u s of the fluid at the free surface creates a thin layer of CO 2 enriched fluid, whose thickness becomes larger close to the center. The concentration of CO 2 is governed by (2.3) which can be transformed into a radial equation at the free surface:

subject to the boundary condition c = 1 at z = 0 and c = 0 at z = -∞. This equation is valid for a free-slip boundary condition at the free surface since the velocity u s is uniform inside the diffusive layer. The model has thus been derived for free-slip boundary conditions. Surprisingly, this equation is also valid for a no-slip boundary condition at the free surface because the This leads to a differential equation for the velocity w of the plume:

The model can be solved numerically by integrating the equations for λ at the surface (A 5) and along the plume (A 7) with the continuity condition (A 8) between the two domains. The velocity of the plume is found numerically by integrating Eq.(A 10) and is in fair agreement with the experimental and numerical results. After a rapid acceleration of the plume velocity, the plume enters a quasi-stationary regime where the plume velocity gradually diminishes due to the fill-up of the cylinder. After a long onset time, the plume becomes unstable (see the plot of the plume velocity in figure 11(c) where the perturbations are damped and then grow again after the onset time). The perturbations grow in amplitude, but do not saturate as in the experiment and in the numerics.

In the following, we will try to give analytical predictions of the wavenumber, frequency and onset time of the instability.

A.3. Base flow (QSSA)

We first try to find the stable solution, obtained in the quasi-steady state approximation (QSSA). Assuming that the variables evolve on a slow time, the temporal derivative in Eq. (A 5) can be neglected such that the solution for the linear density at the free surface can be calculated as:

Here the index 0 refers to the QSSA regime. Inside the plume, the linear density of scalar is constant, as found by integrating (A 7) and equal to

Introducing this expression in the balance of momentum (while neglecting the time derivative) leads to an equation for the plume velocity in the QSSA

This can be solved by differentiation and gives the time as a function of the velocity:

A.4. Linear stability analysis A small perturbation is then added to the flow of the QSSA:

w = w 0 1 + w 1 e σt (A 16)

Introducing this expansion into the equation for the linear density at the free surface (A 5) gives at order O( ) an equation for λ 1 (r):

The homogeneous solution of this equation is equal to

from which the full solution can be found by varying the constant, leading (after integration from r = 0 to r = 1) to the value of the linear density on the axis:

Here, the growth rate has been re-dimensionalised as

Inside the plume, the equation for the linear density (A 7) at order O( ) indicates that the linear density λ 1 is advected by the base flow:

This is indeed what is observed experimentally (see section 3.4). The linear density at order O( ) in the plume can be calculated by using the continuity condition (A 8) at order O( ) and the value (A 18) of the linear density at the center of the free surface:

Introducing this expression in the balance of momentum (A 10) at order O( ) leads to the dispersion relation for the growth rate σ: 22) This equation has first been analysed numerically. It was found that the real part is always negative when the velocity w 0 is equal to its initial velocity obtained before the build-up of the stratification. This clearly proves that the background stratification is a necessary condition for the destabilization of the system. In the QSSA, the velocity w 0 evolves slowly such that the real part of the growth rate increases slowly with time. The instability starts at the onset time when the real part of the growth rate reaches 0, i.e. when the growth rate is purely imaginary (σ = i ˜ ), which leads to two real equations by taking the real part and imaginary part of the dispersion relation (A 22). Eliminating w 0 from these equations permits to calculate the frequency ˜ at the onset of the instability. It is found as the root of

where A r and A i denote the real part and imaginary part of A defined in (A 22) in which σ is replaced by i ˜ . The velocity of the plume at onset can then be calculated by taking the imaginary part of (A 22):

We recall here that the frequency has been rescaled as = ˜ κw 0 . The wavenumber of the instability is simply obtained as k = /w 0 . The onset time can then be calculated by introducing the previous expression of w 0 into (A 14).


Cellulose Gum: a new additive for wine tartaric stability. Tentative of structures determination involved in the haze formation after CMC addition in wine C. Bliard, P-y Bournerias, M. Luigi, Bertrand

Cellulose Gum: a new additive for wine tartaric stability. Tentative of structures determination involved in the haze formation after CMC addition in wine. CMC is known to have a high e ciency for potassium bitartrate and calcium tartrate crystallization inhibition in white and sparkling wines. Hypotheses suggest an inhibition of the nuclei growth at the beginning of their formation. However some problems remain, such as the formation of a low increase of the turbidity in white wine (from 0,1 to 0,4 NTU at room temperature) requiring a ltration step and the formation of a high lumps volume when CMC is used in some red wines.

The goal of the following experiments was to determine which molecules are involved in the haze formed in white or red wines.

1. On white wines: A unique Sauvignon wine is treated from 0 up to 600mg/L of activated bentonite. After ltration, each batch was added (or not) with 100mg/L of CMC previously dissolved in tap water (conc.:50g/L). After 1 week of storage at 13°C, samples were heated at 80°C during ½ h and then stored at RT during 24h before running turbidity.

2. On red wines: 1L of red wine (blend of Cinsault, Merlot and Cab. Sauvignon) was added with 100mg/L of CMC (see above) and stored at -4°C for 4 days. After this time, the wine showed a high level of red clouds. At negative temperature, the deposit was ltered on 0.2 µm nitrocellulose lter membrane and extensively washed with a hydro-alcoholic solution (12% ethanol v/v -pH: 3,5/HCl) kept at -4°C. The membrane was then dried under vacuum and the deposit was collected and exchanged 3 times with D2O for H1-NMR study (HRMAS).

On white wines

Depending on the bentonite content, the turbidity decrease whatever the CMC level after heating. This highly indicates that the haze formed with CMC in wine is concentration-dependent of the proteins. Even at room temperature (without heating / blue bar) we can notice a slight but signi cant decrease of the turbidity as a function of the bentonite increase (protein decrease).

Using CPMAS, we can qualify all organic molecules participating to the deposit coming from the reaction between CMC and other wine molecules. In this experiment CMC appears to be the main component with other peaks attributed to proteins and a broad band to polyphenols compounds. Organic acids are also present in this deposit. The quantitative composition can be estimated as:

-CMC: 80-90% -Proteins: 5-10% -Organic acids: 5-10% -Polyphenols: <5%

On red wines

For both white and red wine, proteins seem to be involved in the haze formed after CMC addition. At wine pH, CMC is partially negatively charged at the opposite of the proteins, essentially positively charged. These ionic interactions can explain -at least in part -the adducts formed after CMC addition and subsequently haze formation in white or red wine.

  UMR 6229 Gpe PFR Eq. Oligo-Polysaccharides Bât 18 Univ. de Reims -URCA BP 1039 F-51687 Reims Cedex 2 2 Institut Oenologique de Champagne, Z.I. de Mardeuil BP 25 51201 EPERNAY France. Corresponding author: b.robillard@institut-oenologique.com Cellulose gum (or sodium carboxymethylcellulose / CMC) is a new additive permitted by the European Community for tartaric stabilization (maximum dosage: 10g/HL).