B Hathi
email: b.hathi@open.ac.uk

A J Ball

M Banaszkiewicz

P M Daniell

J R C Garry

A Hagermann

M R Leese

R D Lorenz

P D Rosenberg

M C Towner

J C Zarnecki

In situ Thermal Conductivity measurements of Titan's Lower Atmosphere

Keywords: ATMOSPHERES, COMPOSITION, ABUNDANCE, TITAN, INSTRUMENTATION

), were made during the descent of the Huygens probe through the atmosphere of Titan below the altitude of 30 km.

The measurements are broadly consistent with reference values derived from the composition, pressure and temperature profiles of the atmosphere; except in narrow altitude regions around 19 km and 11 km, where the measured thermal conductivity is lower than the reference by 1% and 2% respectively. Only single data point exists at each of the two altitudes mentioned above; if true however, the result supports the case for existence for molecules heavier than nitrogen in these regions (such as: ethane, other primordial noble gases, carbon dioxide, and other hydrocarbon derivatives).

The increasing thermal conductivity observed below 7 km altitude could be due to some liquid deposition during the descent; either due to condensation and/or due to passing through layers of fog/cloud containing liquid nitrogen-methane. Thermal conductivity measurements do not allow conclusions to be drawn about how such liquid may have entered the sensor, but an estimate of the cumulative liquid content encountered in the last 7 km is 0.6% by volume of the Titan's atmosphere sampled during descent.

Introduction

Titan's dense and extended atmosphere, retained by a small gravitational force equivalent to only a seventh of the Earth's gravity, has been and continues to be studied by various remote observation techniques. The Huygens probe [START_REF] Lebreton | An overview of the descent and landing of the Huygens probe on Titan[END_REF] provided the first opportunity to make in situ measurements of Titan's atmosphere during its descent on 14 th January 2005. The atmospheric composition of Titan was resolved during the Huygens descent by mass spectroscopy, a part of the GCMS instrument suite, whose results are described in [START_REF] Niemann | The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe[END_REF] complemented by infrared spectroscopy measurements in the wavelength range 840 to 1700 nm from the DISR instrument [START_REF] Tomasko | Rain, winds and haze during the Huygens probe's descent to Titan's surface[END_REF]. The atmospheric structure of Titan, in terms of its vertical pressure, temperature and density profiles, were resolved by measurements from the HASI instrument suite [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF].

Given this background of accurate knowledge of Titan's atmosphere acquired from such high fidelity in situ measurements, the purpose of measuring a vertical thermal conductivity profile, rather than inferring from our present knowledge, seems to yield no extra information on Titan at first sight. However, none of the above measurements were able to distinguish the physical state of the atmosphere, in terms of how much liquid, if any, was encountered along the path of the probe's descent.

Compositional measurements such as the mass/charge (m/z) ratio measurements of the ions from GCMS , or methane absorption bands in the IR spectra from DISR are unable to detect any liquid that may either be present in the form of 'methane rain on Titan' [START_REF] Toon | methane rain on Titan[END_REF], or liquid accumulated from condensation.

In addition to complementing the above in situ measurements, thermal conductivity is a highly sensitive parameter to the physical state of the constituents; for instance, the ratio of liquid to gas thermal conductivity is > 20 (NIST14 1993) The thermal conductivity profile presented in this manuscript should contribute to the debate of some important, but as yet unresolved, issues pertaining to Titan, such as: the regions containing methane super saturation [START_REF] Samuelson | Gaseous abundances and methane supersaturation in Titan's troposphere[END_REF] ) and more recently, the inferred 'methane drizzle on Titan' [START_REF] Tokano | Methane drizzle on Titan[END_REF]. Later in this paper, we estimate the mean molecular mass of Titan's atmosphere from the thermal conductivity measurements under the assumption that the constituents exist only in gaseous state.

Thermal conductivity measurements were carried out by a dedicated Thermal properties (THP) sensor, within the Surface Science Package (SSP) payload [START_REF] Zarnecki | Huygens' Surface Science Package[END_REF]. The THP sensor measures thermal conductivity by monitoring the heat flow between a heat source; a platinum wire enclosed by a cylinder in this case (see Fig. 1), and the surrounding medium; a fluid sample from Titan's atmosphere. The sensor operates on the principle of 'transient hot wire [START_REF] De Groot | Instrument to measure the thermal conductivity of gases[END_REF], whereby, changes in temperature (dT) relative to the initial temperature of the wire are recorded after applying a step heat input over a preset time interval (15 seconds in the case of THP during descent).

Details pertaining to the THP sensor in terms of its design, operation and the technique used to calculate thermal conductivity are described in [START_REF] Hathi | Thermal Conductivity Instrument for measuring planetary atmospheric properties and data analysis technique[END_REF] <insert Figure 1 and caption 1 here> Although the THP sensor started operating above 100km altitude, the combination of measurement duration (15 seconds) and the low atmospheric pressure ( < 0.02 MPa) , are deemed to be unsuitable conditions to allow sufficient heat exchange between the medium and the source, hence we present data below 30 km. Data from the Huygens

Measurements

The process of calculating thermal conductivity, upon which the results in Fig. 3 are based, is described in [START_REF] Hathi | Thermal Conductivity Instrument for measuring planetary atmospheric properties and data analysis technique[END_REF]. In summary, an initial estimate of thermal conductivity is obtained from a gradient of raw measurements (see 'Raw data' points in Fig. 2) and is used to generate a new temperature profile after applying various correction factors (see 'corrected data' points in Fig. 2). The iterative process generates a corrected data curve for each gradient calculation from raw data until the thermal conductivity values from the raw and corrected data sets converge. The method yields two values (minimum and maximum) at each altitude step; the actual thermal conductivity value may lie anywhere within the boundary defined by these minimum and maximum values.

The measurements presented here cover the last 30 km of the Huygens descent and vary in altitude resolution from 1 km per sample at higher altitudes, to 0.5km. Under stable calibration conditions, the thermal conductivity calculations were accurate to within 1% for the three gaseous media: methane, ethane, and nitrogen. However, under descent conditions, where continuously changing pressure and internal-external temperature gradients determine gas flow rates through the THP sensor, the errors may be greater than the 1% encountered during calibration.

The errors (or the spread in values) in general decrease with decreasing altitude; in some regions the errors are well confined by a narrow range (see data around 11 to 10 km, and closer to surface below 5 km). The relatively large error bars in the upper atmosphere are due to poor convergence in the iterative method resulting from illconfined residuals (see Fig. 2d) which in turn might be a result of the atmosphere sample within the measuring cell having a combination of either thermal gradients or

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 7
a more turbulent gas flow. A constant eddy diffusion coefficient of 5000 cm 2 /s has been estimated below 90km [START_REF] Barth | Microphysical modeling of ethane ice clouds in Titan's atmosphere[END_REF] however, the eddy size of Titan's lower atmosphere is unknown and therefore it is not possible to compare turbulence length with those observed in high altitude THP measurements.

<insert Figure 2 and caption 2 here> Data in Appendix 1, summarised in Fig. 3 (below) describe Titan's vertical atmospheric structure in terms of its thermal conductivity. The measurements show a general trend of increasing thermal conductivity closer to the surface. The THP sensor measurements are time stamped, so the average altitude during a measurement can be correlated from the Huygens descent profile in Lebreton et al. 2005 (i.e. time-altitude profile).

The present analysis assumes that the gas sample in the THP sensor during a measurement is approximately similar to the external atmosphere sample (i.e. no gas flow lag between the THP sensor and the external atmosphere is considered). This assumption is based on the qualitative argument of increasing atmospheric pressure during the descent should result in some internal-external pressure differential ensuring that gas sample is similar to the external atmosphere sample.

<insert Figure 3

and caption 3 here>

In order to identify regions of interest (i.e. regions of the atmosphere where measurements differ from our present understanding of the atmosphere gained during the Huygens descent), we compare the measured thermal conductivity values to the reference values, shown in Fig. 3 by the "Titan reference λ" line.

A C C E P T E D

M A N U S C R I P T ACCEPTED MANUSCRIPT 8
The reference thermal conductivity, shown by "Titan reference λ" in Fig. 3, is constructed at a given altitude, from temperature and pressure measurements made by the atmospheric structure instrument during the descent [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF]) and the binary nitrogen-methane composition measured by GCMS [START_REF] Niemann | The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe[END_REF].

The reference thermal conductivity is calculated using the above measured parameters and the NIST database (NIST14 1993). Since the input parameters used to calculate the reference thermal conductivity are based on Titan measurements made by other independent instruments, it is reasonable to assume that the reference atmosphere, based on reference thermal conductivity, takes our current understanding of Titan's atmosphere into account.

The succeeding analysis focuses on the ratio of measured thermal conductivity relative to Titan reference (Titan λ / Titan reference λ). If the ratio is close to unity, then the measurements agree well with the reference. The regions where the thermal conductivity measurements are lower than reference (i.e. ratio < 1), suggest a presence of gas with heavier constituents than the nominal nitrogen-methane expected in the atmosphere at a given altitude.

<insert Figure 4 and caption 4 here> Using thermal conductivity to infer Titan's atmospheric composition at 19 km and 11 km region Thermal conductivity as a stand alone parameter cannot yield a unique solution to determine composition of an atmosphere (or gas mixing ratios), however it is possible to deduce the ratio of mean molecular mass of an atmosphere relative to the reference atmosphere by comparing thermal conductivity values (see Appendix 2 for details).

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

9 Also if we assume that the atmosphere consists of predominantly two constituents, then it is possible to infer composition in terms of mole fraction.

Since each thermal conductivity measurement in Fig. 3 is confined by a minimum and a maximum value, a balanced analysis at first sight might appear to be the one that compares both values versus its reference counterpart. However, we only consider the ratio of maximum thermal conductivity relative to the reference atmosphere (Titan max λ / Titan reference λ), as this approach helps in two ways: (1) in identifying regions of the atmosphere that most likely contain liquid, (2) in defining the minimum limit of other constituents present that are heavier than the reference atmosphere.

The thermal conductivity measurement around 19km is below the reference value and this observation is coincident with the Huygens imaging spectrometer [START_REF] Tomasko | Rain, winds and haze during the Huygens probe's descent to Titan's surface[END_REF]) detection of a cloud/haze layer at 20 km. At the time of writing this paper, we are not aware of any observations just above 11 km.

From thermal conductivity ratios, the lower limit for the mean molecular mass μ of the cloud/haze layer (around the 19km region) is 28.7 atomic mass units (i.e. 2.5% higher than nitrogen) . Nothing further can be deduced solely from thermal conductivity measurements but the observation is consistent with, but not limited to, the hypothesis: 'ethane in smog particles' [START_REF] Hunten | The sequestration of ethane on Titan in smog particles[END_REF], as the cloud layer could consist of a mixture of several constituents whose average μ is 28.7 .

The region around 11 km gives a slightly higher μ of 29.3 atomic mass units. Estimating the liquid content in Titan's atmosphere below 7 km to the surface Our current knowledge of constant methane abundance of 4.92 % (+/-0.25 %) below the altitude of 7km comes from GCMS measurements [START_REF] Niemann | The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe[END_REF]), yet the thermal conductivity measurements in this region (Fig. 3), show a gradual increase in thermal conductivity relative to the reference values. There are two ways of interpreting the thermal conductivity data in this region: one is to assume that the conduction of heat occurs in a pure gaseous medium and the other is to assume an additional component of thermal conductivity is due to some liquid accumulated during the last 7 km of the probe's descent.

On using the pure gas conduction assumption, the molecular mass implies methane abundance of up to 30% below 2.5 km. This is clearly a significant departure from our present knowledge of approximately 5% methane abundance in this region. Therefore, the latter assumption (i.e. assuming some liquid deposition) is more likely to be valid in explaining the apparent high thermal conductivity. Liquid deposition might have occurred either due to condensation, or if the probe had descended through a cloud/haze layer containing liquid. The analysis outlined below attempts to derive the volumetric liquid content encountered by the THP sensor during the descent.

Assuming any liquid that may exist in the lower atmosphere of Titan also consists of the nominal nitrogen-methane mix (0.95-0.05 by molar fraction) , found in the gaseous state of the atmosphere, then its thermal conductivity can be calculated using NIST to be 0.19 W/m.K . The last measurement of 0.0113 W/m.K lies within the boundaries set by the gas thermal conductivity of 0.0102 W/m.K and that of liquid at

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 11 0.
19 W/m.K; simple interpolation places a maximum limit of 6 % liquid to exist within the THP sensor. In effect, the measurement implies 6 % of the THP wire's (of 5 cm length and 10 μm diameter) surface to be covered in liquid; this could mean as little as few drops covering 6% of the wire's surface area, to 6 % of the THP's cylindrical volume of 45.4 cm 3 (i.e. 2.7 cm 3 ) . In the last 7 km of the descent, the sensor must have traversed through a column of atmosphere of ~ 6.4 m 3 (THP's external cylindrical enclosure is of 3.4 cm diameter, therefore: 7 km x π.(1.7 cm) 2 ~ 6.4 m 3 ).

The significance of a maximum of 2.7 cm 3 liquid accumulated during the last 7 km of descent remains open to debate.

The embedded assumption in the above figure of 2.7 cm 3 is that the heat pulse, active for the duration of the measurement (delivering ~ 0.035 Watts for 15 seconds), does not vaporise any liquid during a thermal conductivity measurement. The latent heat of vaporisation for liquid nitrogen-methane mixture at conditions encountered in Titan's lower atmosphere is ~ 3 x 10 5 J/kg and density ~ 670 kg/m 3 (NIST14 1993).

Therefore, the heat energy required to evaporate such a liquid mix is ~ 450 J; with the THP heat pulse delivering ~ 0.5 J per measurement, the above assumption should be valid.

Estimating the mean molecular mass profile of Titan's atmosphere from thermal conductivity measurements.

Hot wire based thermal conductivity sensors have been used for many years [START_REF] Daynes | Gas Analysis by Measurement of Thermal Conductivity[END_REF] in the field of Gas Chromatography to detect (unknown) gas components relative to a (known) reference gas. Since the THP sensor works on the same underlying principle (i.e. measuring thermal conductivity by using a hot wire sensing conductivity measurements, we need to first quantify the contribution of the heat injected by the THP sensor against a background of general heat from the probe.

Appendix 1 -Thermal conductivity measurements of Titan's atmosphere <insert Table 1

here> <insert Table caption here>

Appendix 2 -Thermal conductivity and mean molecular mass An atmosphere (or a closed system) tries to reach equilibrium by minimising temperature and pressure gradients. One of the mechanisms for achieving equilibrium is through transport of energy (heat).

If we assume the heat flux to be isotropic (i.e. same in all directions x, y, and z) and consider the heat flux equation in one dimension, then the rate of heat flow (dQ/dt) in an atmosphere (of area = A) is proportional to the temperature gradient (dT/dx) over a vertical distance dx. The relationship quoted in Eq.2 from Holman 1980, is for a gas containing n molecules (where molecules are assumed to be rigid spheres), with heat capacity C v , confined in area A,

) ' , ( ] 2 [ 3 1 3 1 number s Avogadro N velocity molecular mean where A N C C N n A A v v A = = ⋅ ⋅ = ⋅ ⋅ ⋅ = ν ν ν λ
From Maxwell-Boltzmann's probability distribution, several versions of 'average' molecular velocities can be derived (Hirschfelder, Curtiss, and Bird 1954 1 ).

M kT mean M kT square mean root M kT probable π ν ν ν 8 , 3 , 2 = = - - =
In all cases, the mean molecular velocity is proportional to square root of temperature and inversely proportional to square root of molecular mass (M). Therefore, at a given temperature, the thermal conductivity is also inversely proportional to the square root Heat capacity C v can be approximated by the product of the number density n and Boltzmann constant K B (in the limit that Titan's atmosphere can be approximated by ideal gas).

The thermal conductivity ratio ( λ Titan / λ Ref ) can be used to deduce atmospheric mean molecular mass M Titan (in atomic mass units) if the reference mass M Ref is known.

f f Ti Ti M M Re 2 Re tan tan 1 ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ≈ λ λ
Detailed studies of thermal conductivity consider the effects from the contributions of rotational and vibrational energy components (also known as Eucken correction) in the case of polyatomic gases. Readers wishing to seek further details should refer to Hirschfelder, Curtiss, and Bird 1954 2 , and Bird, Stewart, and Lightfoot 1960. Tables Table I ( trend of increasing λ towards the surface. The final measurement before landing is taken at 100m above the surface. The two reference lines show differences in λ due to instantaneous differences in internalexternal temperatures. If the gas sample is at similar temperature to that of the Huygens probe at THP sensor location, then the thermal conductivity will follow the "internal reference λ", alternatively if one assumes gas flow (i.e. incoming gas sample is approximately at Titan's atmosphere temperature), then the reference value will follow the path shown by "Titan reference λ".

Caption 4

  in conditions similar to those found in Titan's atmosphere below 20km (i.e. for a binary mix of 0.95 N 2 -CH 4 (in mole fraction) at temperature of ~ 80 K and pressure of ~ 0.07x10 6 Pa.).

  are being made available on NASA's PDS archive at the time of this publication for further analysis by the wider planetary science community.

  These measurements do not confirm or rule out the existence of methane clouds in the 3σ error range around 28 to 26 km (i.e. the region where[START_REF] Tokano | Methane drizzle on Titan[END_REF] suggest a probable existence of 'solid methane cloud'). However, there is no evidence for the lower liquid methane/nitrogen cloud between 15 to 10km suggested in[START_REF] Tokano | Methane drizzle on Titan[END_REF]

  . If we take the ratio of measured thermal conductivity with reference gas, then we should get a good estimate of the molecular mass.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure captions

Figure 4 .Figure 5 .

 45 Figure4. Thermal conductivity ratio suggests that there maybe a presence of heavier gas around 19km and 11km regions, but lack of data with ratio < 1 limits confidence. The increase in ratio below 7km maybe attributed to the THP sensor having encountered some moisture during the lower descent, or due to higher methane mole fraction. Nothing can be inferred from the values above 22 km due to large range of possible thermal conductivity values.

  Figures

Table caption Table I .

 captionI Thermal conductivity measurements of Titan's atmosphere during Huygens descent below 30 km. The reference atmosphere's thermal conductivity is derived using Nist database (NIST14 1993) by feeding compositional and physical parameters (at corresponding altitude ) measured independently during the descent (i.e. nitrogen and methane mixing fractions measured by Niemann et al. 2005 and Titan's atmospheric properties (i.e. temperature and pressure) measured by Fulchignoni et al. 2005).

Acknowledgements

The thermal conductivity instrument (THP) is a part of the Surface Science Package (SSP) on board the Huygens probe. The SSP project has been predominantly funded by the Particle Physics and Astronomy Research Council (PPARC), with support from the Polish Academy of Sciences.

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

12 element and comparing to the reference), we can estimate the mean molecular mass of Titan's atmosphere by using the method outlined in Appendix 2.

<insert Figure 5 and caption 5 here>

Summary and future work

The thermal conductivity measurements are broadly in line with the expected values derived from the reference model. There are two regions at 19 km and 11 km, where the measured values depart from reference suggesting possible existence of ethane and/or other heavier (than nitrogen) constituents. The minimum molecular mass is 28.7 and 29.3 atomic mass units respectively but lack of data supporting the case for heavier mass relative to nitrogen limits confidence. The region below 7km (particularly below 2.5km), must contain some liquid mix of nitrogen-methane for the measurements to be plausible; either due to condensation or from the probe descending through a liquid layer, with some liquid entering the THP sensor.

Vertical error bars, though not shown in Fig. 3, must exist in terms of altitude resolution; some further work to improve our understanding of the gas flow within the THP sensor, should improve the altitude aspect of the altitude-thermal conductivity profile. However, such work requires a model based on gas dynamics, experiments and simulations to verify the gas flow rates (not available at the time of this publication).

Thermal conductivity is a useful property in modelling atmospheres and is one of the parameters used in general circulation atmosphere models. The data set from Titan is still being analysed to recover post-landing thermal conductivity and, if possible, to extend the upper atmosphere range. In order to evaluate the Titan's surface constituents (and volatiles) that maybe present in the post-landing thermal


M Cournil

J.-M Herri

ASYMPTOTIC MODELLING OF CRYSTALLISATION IN TWO-LAYER SYSTEMS. APPLICATION TO METHANE HYDRATE CRYSTALLIZATION

The problem of gas-liquid crystallization is re-visited in the framework of a two-film model. The moments of the crystal size distribution can be derived from a differential equation system. Instead of a numerical solution, we present here a general procedure to express analytically the asymptotic behaviour of the physical system. Thanks to this formulation, influence of different parameters can be easily identified and validated on experimental data which mainly concern methane hydrate crystallization.

INTRODUCTION

Gas-liquid crystallization can be described by the overall reaction:

A 1(gas) + pA 2 aq → qA 3 (solid) [R1] in which A 2aq is dissolved in an aqueous solution, p and q are stoichiometric coefficients. This is for instance the case of carbonatation of lime water (Wachi and Jones, 1991 a,b;Jones et al., 1992). Gas hydrate crystallization can be also represented by a [R1]-type reaction in which A 2aq denotes water and A 3 gas hydrate (Englezos et al., 1987 a,b;[START_REF] Skovborg | [END_REF]Herri et al.,1999). Models generally assume a two-layer configuration which consists of:

i) a thin film at the gas-liquid interface in which absorption and diffusion of the gas into the liquid phase take place (possibly accompanied by reactions between dissolved species); this zone, of both high supersaturation and high concentration gradient in dissolved gas, is favourable to crystal primary nucleation;

ii) a bulk zone in which crystals develop by growth; this is a region of lower concentration values and nearly zero gradients particularly if the medium is stirred. Models take into account: a) equations for the gas-liquid mass transfer (film theory) accompanied with kinetic models of chemical reactions; b) equations for the crystal population and dissolved gas mass balances; c) crystallization kinetic laws.

The associated problem is a partial derivative equation problem (Wachi and Jones, 1991ab) or an ordinary differential equation problem when simplifying assumptions or procedures can be applied (Englezos et al. 1987 a,b;Herri et al, 1999).

In this paper, we re-visit several aspects of gas-liquid precipitation in the framework of the two-layer model. We propose a general model of crystallization and discuss some possible simplifications particularly at later stages of the process. The main originality, however, is to propose analytical laws for the system asymptotic behaviour; these predictions can be easily compared to experimental results and give quantitative estimation of the model parameters. This general approach is supported and validated by the experimental context of both calcium carbonate precipitation and above all methane hydrate crystallization for which we have many results.

MODELS

System configuration

We consider a vertical cylindrical stirred reactor filled with water. Liquid height and volume are respectively denoted by H and V. z is the vertical co-ordinate (the gas-liquid interface is located at z = 0); t is the time.

Processes -gas absorption

Gas absorption rate per unit volume r(t) is expressed by (Mehta and Sharma, 1971):

r(t) = k L a (C ext -c b (t)) (1)
a is the mass transfer surface area per volume of liquid and k L the mass-transfer coefficient. In the experiments reported here, k L a ranges between 10 -4 and 5 x 10 -3 s -1 .

-mass transport in the interfacial layer In the two-film theory, the interfacial layer thickness is obtained from the relation :

a k a D L G = δ (2)
D G is the dissolved gas diffusivity. For instance, δ ranges between 44 µm an 126 µm in (Wachi and Jones, 1991b) and between 10 and 50 µm in (Herri et al, 1999). Thus, the interfacial layer is very thick compared to the usual height of the reactor(0.2 m).

Concentration is maintained at value C ext by the gas-liquid equilibrium at the external interface. Crystallization occurs because C ext is greater than C eq , the equilibrium concentration in presence of crystals. In the bulk, c b , is proved to be close to C eq , at least, at late stages of the crystallization process. Thus, supersaturation sharply decreases throughout the film layer. Visual observations show that nucleation mainly takes place in the interfacial film. Nucleated crystals are then transferred to the bulk where they go on growing. According to the authors, this transfer process is differently described: Stokes-Einstein diffusion in (Wachi and Jones;1991 a), instantaneous transfer to the bulk of newly nucleated crystals in (Englezos et al;1987 a,b). However, so far, the authors neglected considering the role of settling for dense particles or floating.

From quantitative estimation of these different processes (Herri and Cournil, 2002), it appears that, once a crystal is nucleated in the interfacial film, it rapidly reaches a size for which diffusion is negligible; thus, its motion is essentially ruled by sedimentation or flotation. Most crystals are nucleated at the gas-solid boundary where supersaturation is maximum. Crystals denser than water fall downwards and leave the interfacial layer to enter the bulk (after a residence time in the film of 152 s and a size of 0.72 µm for calcium carbonate). Gas hydrate crystals, however, float and rise to the gas-liquid interface where they go on growing. Their transfer to the bulk is due to entrainment by the bulk flow, however should occur only beyond a minimum size.

-crystallization processes Rates of the crystallization processes are presented in Table 1 (Garside, 1985).

G = k g σ p (linear rate) ) 1 ( ln 1 2 e σ β + - ∝ B or B 1 = k 1 σ n B 2 = k 2 σ m m 2
In these expressions, σ , (σ = c/C eq -1) is the relative supersaturation; m 2 is the 2 nd order moment of the crystal diameter distribution. k g , β, k 1 , k 2 are positive constants. For lack of space, agglomeration is not envisaged here (see Herri et al., 2002).

Model dynamic equations

In this section we present the general equations which describe the time evolution of concentration in dissolved gas and crystal density and possible simplifications.

-mass balance bulk zone:

( ) b mol b v b ext L b G v m k c C a k dt dc 2 - - =
(3)

interfacial layer

As commonly in the framework of the film model [START_REF] References Beek | Transport phenomena[END_REF], comparison between the gas absorption flow-rate and the gas amount actually consumed by crystallization in the interfacial layer can suggest simplifications (see details in Herri et al., 2002). Actually, crystallization generally weakly affects mass transfer in the interfacial layer; thus, a linear profile of concentration ranging between C ext and C b can be assumed in the interfacial layer at the steady state.

-crystal population i. interfacial layer: Due to the film small extension and the crystal low residence time, the interface layer is assumed to be at steady state as said before with only primary nucleation as relevant crystallization process. Thus the interfacial film role is reduced to an external source of nuclei which feeds the reactor bulk. Mean nucleation rate 1 ' B is calculated from integration of local nucleation term (Table 1, 3 rd column) over the film:

b ext n b n ext n k B σ σ σ σ - - + = + + 1 1 1 1 1 ' ( 4
)
σ ext and σ b are the respective supersaturation levels at the film boundaries.

ii) bulk zone Population balance is expressed by [START_REF] Randolph | Theory of Particulate Processes[END_REF]:

0 ' ) , ( ) , ( 2 1 1 = - - - + b b b b b B B B H D t D n G t t D n δ ∂ ∂ ∂ ∂ (5)
iii) moment equations Partial derivative equation ( 5) results in the following moment equations:

b b b B B B H t m 2 1 1 0 ' d d + + = δ (6) b b b m G t m 0 1 d d = (7) b b b m G t m 1 2 2 d d = (8)
m 0b , m 1b , m 2b are respectively the zero, first and second order moments of the crystal diameter distribution in the bulk. Possibility of nuclei of non zero size and of agglomeration is envisaged in (Herri et al, 2002).

Asymptotic solution to the problem

Solving Equations ( 3), (6-8) requires numerical integration which presents no particular difficulty, however is not straightforward (Englezos et al. 1987 ;Wachi and Jones, 1991, a,b;Herri et al.,1999). Sensitivity to the system parameters clearly appears in these results, however cannot be described in simple words. We will prove here that asymptotic analytical solutions to the problem can be easily found.

-mathematical procedure As, at a given temperature, external pressure is fixed at a value P ext higher than the equilibrium value P eq (or equivalently C ext > C eq ), the system continuously absorbs gas to create new crystals. Thus, m 2b continuously increases. It is assumed to be asymptotycally proportional to : t α where α is a positive exponent. As, in Equation ( 3

G = K t -α (9)
Putting these asymptotic values into (3) gives:

α σ t Kk v aC k m v mol ext eq L b = 2 (10)
The following steps of the procedure consist of : i) putting m 2b and G b into Equation ( 8) and deriving m 1b ; ii) putting m 1b and G b into Equation ( 7) and deriving m 0b ; iii) putting m 0b into Equation ( 6) and identifying α and K; iv) expressing the different moments, total number N b and mean diameter b D of the bulk crystal population.

-typical cases

Previous procedure is applied to different situations of relevant crystallization processes and gives the following asymptotic results (Table 2).

( ) ( ) t n a k S ak D L n ext G 1 1 + σ ( ) 3 1 1 1 2 1 2         + - n ext v G mol eq L k n ak D H v C a k σ f film nucleation, bulk growth, secondary nucleation       + = p m 2 3 α ; m < p ( ) [ ] ( ) 2 3 1 2 3 2 1 2 2 2 - -         - - α α α α α α σ t k HS v aC k k k p m G v mol ext eq L ( ) ( ) α α α α α α - - - -        1 3 1 3 2 1 2 2 3 2 t k k p m G

COMPARISON WITH EXPERIMENTAL DATA

Agreement between theory and experiments are now examined in the framework of the two already mentioned experimental studies : calcium carbonate precipitation and above all methane hydrate crystallization. In Fig. 1, experimental results (Herri et al., 1999) on methane hydrate crystallization are recalled. Time evolution of asymptotic crystal density and mean diameter are analyzed and interpreted in the framework of the previous model (Table 3). (Herri et al., 2002) Results from Wachi and Jones (1991 b) also show a slight increase in the crystal mean diameter to a possible maximum. No data on particle number are available. This behaviour is quite consistent with a mechanism of film nucleation and bulk crystal growth perturbed by agglomeration (which is actually mentioned by the authors).

Influence of stirring rate on the crystal mean diameter

We consider only experiments in which primary nucleation and crystal growth are preponderant, that is to say with constant asymptotic mean diameter b D .

From 2 (2 nd line, 3 rd column). In this expression, the mo st dependent factor on stirring rate is k L which is known to be an increasing function (Wachi andJones, 1991b, Herri et al., 1999). This is quite consistent with the experimental results.

  finite values, G b tends to zero (thus c b tends asymptotycally to C eq and σ b to zero) , thus G b is of the form:

Fig. 1 :

 1 Fig.1: Time evolution of crystal mean diameter (a) and number per unit volume (b) at different stirring rates during methane hydrate crystallization at 30 bars and 1°C

Figure 1 ,

 1 it appears that b D increases with the stirring rate in the range [350 rpm-450 rpm] for which b D is nearly independent of time. The same conclusions can be derived from the results of Jones et al. (1992) on calcium carbonate. b D predicted value is given in Table

Table 1 :

 1 Crystallization process rates versus supersaturation level.

	Process Crystal growth	Primary nucleation.	Secondary nucleation
	Rate

Table 2 :

 2 Asymptotic time variation of crystal total number and mean diameter

	Relevant processes	Crystal total number	Crystal mean diameter
	film nucleation; bulk growth

Table 3 :

 3 Comparison between experimental data and theoretical predictions

	Stirring rate	Mean diameter ≈ t β	Particle number ≈ t ε	Relevant processes (according to Table 2)
	500 rpm	β < 0	ε > 1	film nucleation, bulk crystal growth and
				secondary nucleation : m/p = 1/2 (Table 2)
	400 rpm	β = 0	ε = 1	film nucleation and bulk crystal growth
				(Table 2)
	250 rpm	β > 0	ε < 1	film nucleation, bulk crystal growth
				and agglomeration


Michel Cournil

Frédéric Gruy

Patrick Cugniet

Pascal Gardin

Hubert Saint

H Saint-Raymond

Model of aggregation of solid particles in nonwetting liquid medium

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In spite of many complex aspects, aggregation dynamics is relatively well understood (De Boer et al., 1989). However, some physical situations were little studied and deserve further works. This is the case of aggregation in non wetting liquid media. An important application of this problem is found in the processing of liquid steel. Solid inclusions-typically alumina (Al 2 O 3 ), 3 to 20 µm particles-are present in the baths and gather to form clusters of 50 to 300 µm. For lack of systematic studies -due to the conditions of a molten bath (2000 K)-many aspects of the phenomenon still remain obscure. Importance of non-wetting of the solid particles by the liquid phase was acknowledged as essential element of understanding in (Kozakévitch and Lucas, 1968). According to these authors, the liquid phase is spontaneously drained off from the contact zone between two solid inclusions; this results in the formation of a gaseous bridge which ensures a stronger cohesion of the particle doublet. In several points, this situation suggests analogies with the hydrophobic interactions which have been known for many years, however in different physical contexts. Many experimental works, indeed, have definitely proved the existence of very strong and long range attractive forces between hydrophobic surfaces in water or more generally surfaces separated by non-wetting medium (Yaminsky et al., 1983, Yushchenko et al., 1983, Parker et al., 1994). This hydrophobic interaction was measured and proved to be much larger than the van der Waals forces. Several works mention the existence of gas cavities between particles in close interaction. After a long period of controversies, it seems that the interpretations of hydrophobic forces a re now convergent. Hydrophobicity results in reducing the solvent density down to possible local evaporation near the solid surface (Forsman et al.,1997). Ruckenstein and Churaev (1991), Yaminski and Niham (1993), and Ruckenstein (1997) calculated interactions between surfaces covered with gaseous gaps, however separated by a liquid layer.

To our knowledge, aggregation dynamics of solid particles in non-wetting medium has never been studied extensively in spite of the interest of some experimental works (Zhou et al, 1996;Song and Lopez Valdivieso, 1999) on particular points. The aim of this work is to re-examine and, if need be, to adapt or modify several elements of aggregation modelling in case of non-wetting. The main static and thermodynamic aspects of aggregation are presented first, then, dynamic aspects are studied; in particular, the aggregation kernel factors (collision frequency and efficiency) are calculated and principles of fragmentation kernel determination are given.

STATIC ASPECTS OF AGGREGATION IN NON-WETTING MEDIA

In case of non-wetting, equilibrium of the contact line between the three phases gasliquid-solid (when it exists) imposes the Young relation between the respective interfacial tensions γ (G = gas phase; L = liquid phase; S = solid phase):

γ SG -γ SL = γ LG cosθ (1)
where θ is the contact angle. Larger than 90° θ values correspond to non-wetting situations. In the case of the alumina -liquid steel -air system, θ =140° (2.44 radians).

Possibility of existence and development of different gas-liquid-solid configurations can be judged from the sign and variations of their Gibbs enthalpy of formation ∆G n :

∆G n = n (µ G (T, P ext ) -µ L (T, P ext )) + γ LG ∆S LG + γ SG ∆S SG + γ SL ∆S SL (2)
T is the temperature, P ext , the pressure in the liquid phase, n, the vapour mole number; µ G and µ L are respectively the chemical potentials of the gas and the liquid; ∆S LG , ∆S SG and ∆S SL , the changes in liquid-gas, solid-gas and solid-liquid interfacial areas.

From these criteria, we find the following results: § gas cavities in pores Gas cavities can spontaneous appear and grow in most of the pores, holes or crevices of the inclusion surface and fill them to reach the external surface. Thus, the surface of a solid particle immersed in a non-wetting liquid is partially covered with a gas layer which consists of the top of different cavities filled with gas (Figure 1). Thus, surface bridging via pores filled with gas is spontaneous and constitutes a quite plausible mechanism. Gas is either vaporized liquid or gas desorbed from liquid.

Fig.2: Spontaneous evolution of a gas bridge between two flat interfaces § forces between particles in a non-wetting medium

Hydrophilic particles in interaction in a fluid medium are submitted to the well-known DLVO forces (De Boer et al., 1989). In a non-wetting and non-aqueous medium, van der Waals forces are still active, whereas electrochemical forces are irrelevant. Presence of gas bubbles or cavities at or between the particle surfaces results in attractive forces: i) van der Waals force:for two plane surfaces, force f W per unit area is given by:

f W = 3 6 h A π (3)
A is the Hamaker constant, h the separation between the surfaces.

ii) hydrophobic force (absence of gaseous bridge): (Ruckenstein, 1997) evaluated the interaction force f R due to the hydrodynamic interaction force between pulsating gas bubbles located on hydrophobic surfaces in water:

f R 3 1 h ≈ (4)
Dependence of f w and f R against separation h is the same (≈1/h 3 ). Numerical comparison is difficult because of unknown parameters in (4). However, experiments prove that coefficient of 1/h 3 is much larger in f R than in f w .

iii) forces due to the gaseous bridge: Problem of determination of forces due to the presence of a mass bridge between solid particles was studied in (Simmons et al., 1994;Yaminski et al., 1983). Capillary binding forces F G can be compared to van der Waals force F w , for alumina in liquid steel (Cournil et al., 2002): F w / F G = 1.4 x 10 -10 /r 1 2 where r 1 , radius of the gas bridge, is expressed in µm. Thus, van der Waals forces are negligible, once the gas bridge is established and cohesion force of the doublet of particles is considerably higher than in case of aggregation in wetting conditions.

DYNAMICAL ASPECTS OF AGGREGATION IN NON-WETTING MEDIA

In this section, we will successively examine the effect of non-wetting and connected phenomena on the aggregation and fragmentation kernels.

Aggregation kernels

We consider solid grains of typical size 5 µm in a turbulent medium of Kolmogorov scale of about 50 µm. At the eddy scale, the solid particles can be considered as submitted mainly to a local laminar flow characterised by a velocity gradient γ& .

In a suspension consisting of classes of particles or aggregates (mean radius R i and density by number n i ), the collision frequency of particle i can be calculated as follows (Saffman and Turner, 1956):

( ) j j i ij n a a J 3 . 0 3 4 + = γ & with 2 / 1       ≈ µ ρε γ &
; ε is the turbulent energy dissipation rate per unit mass, ρ, the liquid density, and µ the dynamic viscosity. Aggregation models should take into account the effects of the interaction forces between particles. Some of them also exist in motionless system; others appear only with motion (fluid drainage). These effects modify the collision frequency as follows:

0 ij ij ij J J α = (5)
where α ij is the collision efficiency coefficient. In case of wetting liquid, when no-slip condition is fulfilled, α ij is calculated from (Highashitani, 1982). In case of non-wetting, presence of gas pockets at the interface may result in slip of the liquid. Slip conditions have been already considered in the vicinity of solid interfaces (Vinogradova, 1995).

Collision efficiency between two particles in non-wetting media has been calculated by us in (Cournil et al., 2002). For common values of the energy dissipation rate (10 -3 m 2 .s -3 <ε < 1 m 2 .s -3 ), γ& is ranging between 18.9 and 598 s -1 . For particles radius of 5 µm and van der Waals -like interactions, α ij is little sensitive to the Hamaker constant (2). For instance, for hundred or thousand times as large Hamaker constants, α ij values would not change. As interaction forces due to the presence of gas cavities (3) are of the same form as van der Waals forces, previous α ij calculations are valid in this case too.

In the common case of wetting, α ij = 0.15; in case of non-wetting α ij = 0.38. Thus, nonwetting results in an increase of the collision efficiency, thus of the aggregation rate.

Fragmentation

The occurrence of break-up depends on the balance between the disaggregation effects due to the action of the fluid and the overall cohesion of the aggregate due to the interactions between primary particles. In case of non-wetting, the situation of fragmentation is quite new because the different particles are linked by gas bridges. This problem has not been studied yet. Here, we only examine the fragmentation conditions of a doublet of identical spherical particles just after the collision between the particles and later when the gas bridge is built up.

Particle "sticking": we assume that gas cavities pre-exist at or under the surface of the solid particles. Building up of a gaseous bridge requires that the two colliding particles stay close to each other for a minimum time. Similar situations have been envisaged for agglomeration from supersaturated solutions ( David et al., 1991, Mumtaz et al., 1997, Hounslow et al., 1998). Models generally consist in comparing time t b needed to form the bridge and time t p spent by the particles in close proximity. For particles smaller than Kolmogorov microscale, t p is currently taken

equal to -1 γ & , thus: t p ≈ ( ) 2 / 1 ε ν . t b ,
is the drainage time of the liquid film located in the slit between the two inclusion surfaces. Motion of the liquid gas meniscus is due to the difference of pressure between the gas and the liquid phase. For the system of reference, t b ≈ 8 x 10 -7 s and t p ≈ 10 -2 s (see details in (Cournil et al., 2002)). As the time needed to build up a gas bridge is considerably shorter than the duration of the contact, the sticking probability of the two inclusions is close to 1.

Doublet rupture

Competition between the disaggregation and the cohesion effects can be judged from the value of ratio E c /E t ; E c and E t are respectively the aggregate cohesion energy and the turbulent energy acting on this aggregate. Breakage rate is

proportional to γ . t c e E E -
. From analogy with rupture of pendular (liquid) bridges between particles (Simmons et al., 1994), energy e c per unit volume of the doublet is : found equal to: 2.53 x 10 4 J.m -3 . This value can be compared to the turbulent energy e t dissipated per unit volume during action time: t p . e t ranges between 0.35 and 12 J.m -3 . This fluid turbulent energy is much lower than the required breakage energy and gaseous bridge fragmentation by the liquid flow is highly unlikely. Thus, very large aggregates can be met in aggregation in non-wetting media.

Experimental aspects

The previous theoretical approach is qualitatively confirmed in the case of alumina inclusions in liquid steel. Another validation comes from the experimental study of aggregation of hydrophobic silica in water. Aggregation is followed in situ and continuously using a turbidity probe. Turbidity of a suspension depends indeed on the number, the size and the morphology of the particles it contains and therefore may be very sensitive to a process such as agglomeration. In Fig. 3, we present an example of turbidity evolution with time during aggregation for two silica samples of same weight: one of them has been made hydrophobic by grafting of silanol groups at the surface of the grains (1.5 µm in diameter), the other consists of unprocessed silica In (Saint-Raymond et al, 1998), we explain how to interpret this sort of curves. Initial decrease in turbidity is due to aggregation whereas the final unprocessed silica hydrophobic silica plateau height strongly depends on the fragmentation intensity. The higher this plateau, the more intense the aggregate fragmentation. From Figure 3, it appears that initial aggregation is a little weaker for unprocessed silica than for hydrophobized silica. The effect of hydrophobicity on fragmentation is however much stronger. The near zero asymptotic value of turbidity reached for hydrophobized silica proves that large aggregates have been formed. On the contrary, in the absence of hydrophobizing process, the aggregates remain small, probably because their size is reduced by fragmentation. These two features of the aggregation process exactly correspond to the predictions of the previous discussions. In the same hydrodynamic conditions, non-wetting slightly increases the collision efficiency, thus the aggregation rate, whereas it practically suppresses fragmentation.

CONCLUSION

From preliminary thermodynamic study, conditions of aggregation of solid particles in a non-wetting medium are defined: presence and role of gaseous cavities are justified as well as the expressions of interaction forces, whether the particles are in contact or not. From theoretical and experimental studies of aggregation processes, it appears that, in the same hydrodynamic conditions, non-wetting affects both aggregate formation and fragmentation, however much more the latter than the former phenomenon.

Fig. 1 :

 1 Fig.1: Gas cavity in a crevice; solid-liquid interface with gas cavities § gas bridge between two solid surfaces In Fig.2is shown a gas bridge between two close flat surfaces. From thermodynamic criteria, it appears that this bridge can spontaneous appear only if the surfaces are in contact, otherwise, an activation is necessary. Once gas bridge is formed, it can

Fig. 3 :

 3 Fig. 3: Comparison of aggregation in water of two silica samples : unprocessed silica and hydrophobic silica (monitoring by turbidimetry)


Charlotte Vinchon
email: c.vinchon@brgm.fr

Anne Laurence Angenais

Emmanuelle Berthelier
email: emmanuelle.berthelier@arteliagroup.com

Manuel Garcin

Marianne Grisel

Cécile Hérivaux

Laure Kuhfuss

Laure Maton

Catherine Meur-Ferec
email: meurferec@univ-brest.fr

Hélène Rey-Valette
email: helene.rey-valette@univ-montp1.fr

Vinchon Charlotte

Agenais Anne Laurence

Baron-Yelles Nacima

Berthelier Emmanuelle

Garcin Manuel

Grisel Marianne

Hérivaux Cécile

Kuhfuss Laure

Maton Laure

Meur-Ferec Catherine

Rey-Valette Hélène

Balouin Yann

Charles Jean Christophe

Delvallée Etienne

Flanquart Hervé

Hellequin Anne Peggy

Krien Yann

Lecacheux Sophie

Le Cozannet Goneri

Mazeiraud Vincent

Nathan Fabien

Pedreros Rodrigo

Poisson Blanche

Romieu Emmanuel

Rulleau Benedicte
email: benedicte.rulleau@reeds.uvsq.fr

Serrand Maud

Evolution of coastal zone vulnerability to marine inundation in a global

come   L'archive ouverte pluridisciplinaire

The coastal system is likely to suffer increasing costal risk in a global change context. Its management implies to consider those risks in a holistic approach of the different vulnerability components of the coastal zone, by improving knowledge of hazard and exposure as well as analyzing and quantifying present day and future territory vulnerability. The ANR/VMC2007/MISEEVA project (2008)(2009)(2010)(2011) has applied this approach on Languedoc Roussillon region in France.

MISEEVA approach relies on several scenarios for 2030 and 2100, in terms of meteorology (driver of coastal hazard), sea level rise, and also considering further trends in demography and economy, and possible adaption strategies Hazard has been modeled (SWAN, MARS and SURFWB), on the base of the presentday situation, sea level rise hypotheses, and existing or modeled data, of extreme meteorological driving f. It allowed to assess the possible surges ranges and map coastal zone exposure to:

-a permanent inundation (considering sea level rise in 2030 and 2100, -a recurrent inundation (considering sea level rise and extreme tidal range) -an exceptional inundation (adding extreme storm surge to sea level rise and tidal range). In 2030, exposure will be comparable to present day exposure. In 2100, extreme condition will affect a larger zone.

Present days social and economic components of the coastal zone have been analyzed in terms of vulnerability and potential damaging. Adaptation capacity was approached by public inquiries and interviews of stakeholders and policy makers, based on existing planning documents The knowledge of the present day system is then compared to the possible management strategies that could be chosen in the future, so to imagine what would be the evolution of vulnerability to marine inundation, in regards to these possible strategies. Le milieu littoral sera vraisemblablement soumis à une aggravation des risques côtiers dans le contexte du changement climatique. Sa gestion nécessite d'appréhender ces risques de façon holistique, en considérant les différentes composantes de la vulnérabilité du système côtier, tant en améliorant la connaissance de l'aléa et de sa propagation qu'en analysant et quantifiant la vulnérabilité, actuelle et future du territoire exposé à l'aléa. C'est cette démarche qu'a suivi le projet ANR/VMC2007/MISEEVA (2008)(2009)(2010)(2011), sur le territoire du Languedoc Roussillon.

La démarche de MISEEVA se fonde sur un certain nombre de scénarios pour 2030 et 2100, en termes de climat (forçage des aléas côtiers) et d'élévation du niveau de la mer (« E.N.M »), de poursuite des tendances démographiques et économiques et de stratégies possibles de réponse (actuelle ou future) au changement.

L'aléa a été modélisé (SWAN, MARS et SURFWB), sur la base de la situation actuelle, des hypothèses d'élévation du niveau de la mer, et des données existantes ou modélisées de conditions extrêmes de forçage météorologique. Cela a permis d'évaluer l'amplitude des surcotes possibles et de cartographier l'exposition du système côtier à l'aléa de submersion en considérant dans le futur une submersion permanente (ENM), récurrente (ENM et niveau max des marées) ou exceptionnelle (ELM, Marée, surcotes). En 2030 la submersion sera peu différente de la situation actuelle. En 2100, l'emprise de la submersion sera plus importante.

Les enjeux actuels ont été analysés, dans l'emprise de cette exposition à 2100, en termes de vulnérabilité, et de dommages potentiels La capacité d'adaptation, à ce jour, a été approchée par des enquêtes de perception auprès du public et des pouvoirs publics et l'analyse des documents stratégiques.

Cette connaissance du système actuel est confrontée aux différentes perspectives de stratégie de gestion du risque dans le futur, afin d'imaginer quelles serait l'évolution de sa vulnérabilité dans le futur au regard des différentes stratégies possibles.

Evolution de la vulnérabilité du système côtier à la submersion marine dans le contexte du changement global, selon les choix stratégiques d'adaptation. Application au Languedoc Roussillon

Vinchon Charlotte 1 , Agenais Anne Laurence 1, Baron-Yelles Nacima 2 , Berthelier Emmanuelle 3 , Garcin Manuel 1 , Grisel Marianne 3 , Hérivaux Cécile 1 , Kuhfuss Laure 4 , Maton Laure 1 , Meur-Ferec Catherine 5, Rey-Valette Hélène 4 , Balouin Yann 1, Charles Jean Christophe 4 , Delvallée Etienne 1 , Flanquart Hervé 5 , Hellequin Anne Peggy 5 , Krien Yann 1 , Lecacheux Sophie 1 , Le Cozannet Goneri 1 , Mazeiraud Vincent 3 , Nathan Fabien 3 , Pedreros Rodrigo 1 , Poisson Blanche 1 , Romieu Emmanuel 1 , Rulleau Benedicte 6 , Serrand Maud 1 1 BRGM/RIS/RIC BP 36009, 45018 Orléans Cedex 2, c.vinchon@brgm.fr 2 LVMT EA3582-Université de Marne la vallée-19 rue Alfred Nobel-Cité Descartes-77455 Marne La vallée-Cedex 2, n.baron@univ-mlv.fr 3 SOGREAH, 6 rue de Lorraine 38130 Echirolles, emmanuelle.berthelier@sogreah.fr 4 LAMETA, Faculté de sciences économiques-Avenue de la Mer-Site Richter 34 960 Montpellier Cedex 2,helene.rey-valette@univ-montp1.fr 5 MESHS, UBO, Géomer -LETG -UMR 6554, Institut Européen d'Etudes Marines Place Nicolas Copernic, Technopôle Brest Iroise, 29 280 PLOUZANE, 6 REEDS, Université de Versailles-Saint Quentin en Yvelines,Bâtiment Vauban,47 boulevard Vauban,78280 Guyancourt,benedicte.rulleau@reeds.uvsq.fr Le milieu littoral sera vraisemblablement soumis à une aggravation des risques côtiers dans le contexte du changement climatique. Sa gestion nécessite d'appréhender ces risques de façon holistique, en considérant les différentes composantes de la vulnérabilité du système côtier, tant en améliorant la connaissance de l'aléa et de sa propagation qu'en analysant et quantifiant la vulnérabilité, actuelle et future du territoire exposé à l'aléa. C'est cette démarche qu'a suivi le projet ANR/VMC2007/MISEEVA (2008)(2009)(2010)(2011), sur le territoire du Languedoc Roussillon.

La démarche de MISEEVA se fonde sur un certain nombre de scénarios pour 2030 et 2100, en termes de climat (forçage des aléas côtiers) et d'élévation du niveau de la mer (« E.N.M »), de poursuite des tendances démographiques et économiques et de stratégies possibles de réponse (actuelle ou future) au changement.

L'aléa a été modélisé (SWAN, MARS et SURFWB), sur la base de la situation actuelle, des hypothèses d'élévation du niveau de la mer, et des données existantes ou modélisées de conditions extrêmes de forçage météorologique. Cela a permis d'évaluer l'amplitude des surcotes possibles et de cartographier l'exposition du système côtier à l'aléa de submersion en considérant dans le futur une submersion permanente (ENM), récurrente (ENM et niveau max des marées) ou exceptionnelle (ELM, Marée, surcotes). En 2030 la submersion sera peu différente de la situation actuelle. En 2100, l'emprise de la submersion sera plus importante.

Les enjeux actuels ont été analysés, dans l'emprise de cette exposition à 2100, en termes de vulnérabilité, et de dommages potentiels La capacité d'adaptation, à ce jour, a été approchée par des enquêtes de perception auprès du public et des pouvoirs publics et l'analyse des documents stratégiques.

Cette connaissance du système actuel est confrontée aux différentes perspectives de stratégie de gestion du risque dans le futur, afin d'imaginer quelles serait l'évolution de sa vulnérabilité dans le futur au regard des différentes stratégies possibles.

Titre auteurs 1. Titre 1

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	normal normal normal normal normal normal normal normal.
	Normal normal normal normal normal normal normal normal normal normal normal
	normal normal normal normal normal normal normal normal normal normal.

Evolution de la vulnérabilité du système côtier à la submersion marine dans le contexte du changement global, selon les choix stratégiques d'adaptation. Application au Languedoc Roussillon Vinchon

  Charlotte 1 , Agenais Anne Laurence 1, Baron-Yelles Nacima 2 , Berthelier Emmanuelle 3 , Garcin Manuel 1 , Grisel Marianne 3 , Hérivaux Cécile 1 , Kuhfuss Laure 4 , Maton Laure 1 , Meur-Ferec Catherine 5, Rey-Valette Hélène 4 , Balouin Yann 1, Charles Jean Christophe 4 , Delvallée Etienne 1 , Flanquart Hervé 5 , Hellequin Anne Peggy 5 , Krien Yann 1 , Lecacheux Sophie 1 , Le Cozannet Goneri 1 , Mazeiraud Vincent 3 , Nathan Fabien 3 , Pedreros Rodrigo 1 , Poisson Blanche 1 , Romieu Emmanuel 1 , Rulleau Benedicte 6 , Serrand Maud 1 1 BRGM/RNSC/RIC BP 36009, 45018 Orléans Cedex 2, c.vinchon@brgm.fr 2 LVMT EA3582-Université de Marne la vallée-19 rue Alfred Nobel-Cité Descartes-77455 Marne La vallée-Cedex 2, n.baron@univ-mlv.fr 3 SOGREAH Groupe ARTELIA, 6 rue de Lorraine 38130 Echirolles, emmanuelle.berthelier@arteliagroup.com 4 LAMETA, Faculté de sciences économiques-Avenue de la Mer-Site Richter 34 960 Montpellier Cedex 2,helene.rey-valette@univ-montp1.fr 5 MESHS, UBO, Géomer -

	LETG -UMR 6554, Institut Européen d'Etudes Marines, Place Nicolas Copernic,
	Technopôle Brest Iroise, 29 280 PLOUZANE, 6 REEDS, Université de Versailles-
	Saint Quentin en Yvelines, Bâtiment Vauban, 47 boulevard Vauban, 78280
	Guyancourt, benedicte.rulleau@reeds.uvsq.fr


Thanh Thuy

Nguyen Tu
email: ttnguyen@snv.jussieu.fr

Céline Egasse

Bernd Zeller

Gérard Bardoux

Philippe Biron

Jean-François Ponge

Brigitte David

Sylvie Derenne

Early degradation of plant alkanes in soils: A litterbag experiment using 13 C-labelled leaves

Keywords: leaf litter decomposition, stable carbon isotopes, lipids, soil organic matter, n-alkanes

 specific isotope composition

Introduction

The carbon isotope composition of organic matter in soils and sediments has proven useful in documenting past environments, carbon dynamics and the sources of organic matter. However, the isotope composition of bulk organic matter may be altered during decomposition and/or by diagenesis. Indeed, the isotope composition of bulk organic matter corresponds to the weighted mean comprised by the isotope composition of each of its individual constituents. Therefore, the isotope composition of bulk organic matter can be disproportionately altered if the constituents lost by degradation have an isotope composition which differs substantially from that of the preserved constituents [START_REF] Deines | The isotopic composition of reduced organic carbon[END_REF][START_REF] Balesdent | Site related  13 C of tree leaves and soil organic matter in a temperate forest[END_REF]. Consequently, the isotope analysis of specific compounds having high preservation potential may minimize degradation biases and is becoming increasingly favoured [START_REF] Wiesenberg | Source and turnover of organic matter in agricultural soils derived from n-alkane/ncarboxylic acid compositions and C-isotope signatures[END_REF][START_REF] Yamamoto | Paleoenvironmental significance of compound-specific 13C variations in nalkanes in the Hongyuan peat sequence from southwest China over the last 13 ka[END_REF]. Among such biomarkers, long-chain fatty lipids such as n-alkanes and n-acids are the most commonly investigated molecules for specific compound isotope analyses. Indeed, these typical plant components exhibit a rather high preservation potential and are relatively easy to analyse. However, these long-chain lipids may not be completely resistant to degradation and their relative distribution may be modified in the early phases of organic matter degradation [START_REF] Cranwell | Diagenesis of free and bound lipids in terrestrial detritus deposited in a lacustrine sediment[END_REF][START_REF] Buggle | Is there a possibility to correct fossil n-alkane data for postsedimentary alteration effects?[END_REF]. Previous investigations on the effects of degradation on the isotope composition of these specific lipids led to contrasting results: either the 13 C-content of these compounds was unaffected over time or it exhibited a trend towards 13 C-enrichment of specific molecules [START_REF] Stahl | Compositional changes and 13 C/ 12 C fractionation during the degradation of hydrocarbons by bacteria[END_REF][START_REF] Huang | Absence of carbon isotope fractionation of individual n-alkanes in a 23-year field decomposition experiment with Calluna vulgaris[END_REF][START_REF] Mansuy | Source identification of oil spills based on the isotopic composition of individual components in weathered oil samples[END_REF][START_REF] Mazéas | Absence of stable carbon isotope fractionation of saturated and polycyclic aromatic hydrocarbons during aerobic bacterial biodegradation[END_REF][START_REF] Nguyen Tu | Diagenesis effects on specific carbon isotope composition of plant n-alkanes[END_REF][START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF]. The observed 13 C-enrichment of fatty lipids was suggested to have two possible causes: (i) an isotope discrimination effect had occurred during degradation and/or (ii) the fatty lipids were contaminated by longchain lipids derived from microbes. In the absence of categorical evidence, neither of these two alternatives could be favoured or excluded by the previous authors [START_REF] Nguyen Tu | Diagenesis effects on specific carbon isotope composition of plant n-alkanes[END_REF][START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF].Nevertheless, the disparity in the reported 13 C-content trends is likely to be related to differences in the environments investigated: i.e., oxic vs. anoxic, well-drained vs. stagnant water, soil organic matter vs. oil spills, etc. Such a disparity calls for complementary studies in other environments, to better constrain the potential for bias in the isotope record of (paleo)environments.

The present study aimed to determine the precise effects of early degradation on the isotope composition of specific alkanes. A major challenge to investigating the degradation of organic matter is the multiplicity and diversity of its sources. Indeed, it can be difficult to distinguish the actual effects of decomposition from those related to variations in the relative contributions of its sources. An alternative approach is to study materials that are precisely identified, such as the plant leaves that provide the main source of long-chain alkanes in soils and sediments [START_REF] Eglinton | Leaf epicuticular waxes[END_REF]. Litterbag experiments constitute a prime technique to monitor the fate of leaves through litter decomposition. Indeed, this method allows plant debris to be sampled at specific ages, even at high levels of decomposition [START_REF] Bocock | The disappearance of leaf litter under different woodland conditions[END_REF][START_REF] Smith | Litter quality impacts on grassland litter decomposition are differently dependent on soil fauna across time[END_REF]. The present study was thus based on a decay experiment in which beech leaves were enclosed in litterbags. European beech (Fagus sylvatica L.) was chosen as a source because it is a common inhabitant of temperate forests.

Monitoring the fate of 13 C-labelled molecules has proven useful to unravel biogeochemical processes in ecological studies [START_REF] Crossman | The use of 13 C labelling of bacterial lipids in the characterisation of ambient methane-oxidising bacteria in soils[END_REF][START_REF] Bahri | Lignin degradation during a laboratory incubation followed by 13 C isotope analysis[END_REF]. Therefore, our experiment was carried out using 13 C-labelled leaves in order to trace the original plant alkanes and to test for possible contamination by microbial alkanes. Stable isotope labelling of plants generally led to 13 C-enrichment in the order of several hundred-fold per mil [START_REF] Angers | Fate of carbon and nitrogen in water-stable aggregates during decomposition of 13 C 15 N-labelled wheat straw in situ[END_REF][START_REF] Zeller | Decomposition of 15 N-labelled beech litter and fate of nitrogen derived from litter in a beech forest[END_REF][START_REF] Bahri | Lignin degradation during a laboratory incubation followed by 13 C isotope analysis[END_REF]. However, it may be technically difficult to measure small isotope effects when dealing with such intense labelling. Limited labelling (i.e. lower than 50‰) provides the opportunity to detect even minor microbial contribution. We thus used slightly 13 Cenriched beech leaves to monitor the effects of decomposition during a four-year experiment in natural forest soil. To our knowledge, this study represents the first time 13 C-labelled leaves have been used to investigate, in the field, the effects of degradation on the isotope composition of specific lipids. Our data provide a better understanding of the sources of potential bias related to degradation effects, and hence will allow specific compound isotope analysis in (paleo)environmental studies to be used with greater accuracy and significance.

Material and methods

13 C-labelling of beech leaves

Beech seeds were germinated at the end of May 2004. Young seedlings were transferred at the cotyledon stage to a controlled chamber at the beginning of June 2004. In order to minimize isotope effects linked to soil respiration, plants were grown on vermiculite and fed three times per week with a previously described nutritional solution [START_REF] Coïc | Cultures hydroponiques[END_REF]. The pCO 2 and  13 C atm were maintained at 380 ppmv and +40‰, respectively. Climate conditions in the chamber were held constant during the five months of labelling: 70% relative humidity and 20°C day temperature.

Four Osram HQI/D Daylight lamps (400 W/D) provided a light intensity of approximately 350 µmol/m 2 •s of photosynthetically active radiation during a 15 hr period per day (i.e. 7h-20h). The chamber is described in detail elsewhere [START_REF] Girardin | A method for 13 C-labeling of metabolic carbohydrates within French bean leaves (Phaseolus vulgaris L.) for decomposition studies in soils[END_REF]. Three weeks before the end of the experiment, the conditions were modified in order to induce leaf senescence. The temperature was reduced to 18°C, the daylight range was reduced to 8 hr (9h-17h) and nutritional solution was provided only once per week. The leaves thus obtained exhibited a mean  13 C value of +25.0‰ and ranged between +16.3‰ and +35.3‰.

Degradation experiment

Experimental site

The degradation experiment was established in the "Breuil-Chenue" experimental forest site located in Burgundy, France (47°18'10"N, 4°4'44"E). This forest is part of the "Parc Naturel Régional du Morvan", a protected area where urban pollution is minimal. The field is situated on a shelf at 650 m above sea level and exhibits a slight northwest-facing slope. Mean annual temperature and precipitation at the site are 9°C and 1,280 mm, respectively. The bedrock is the alkaline granite of "La Pierre qui Vire" covered by a thin layer of eolian silt. Soils are classified as dystric cambisol [START_REF] Wrb | IUSS Working group[END_REF] with a thick moder on top (~10 cm). They are acidic soils with pH values of 4-4.5 and have a poorly saturated cation exchange complex. More information on the experimental site is available elsewhere [START_REF] Moukoumi | Effect of tree species substitution on organic matter biodegradability and mineral nutrient availability in a temperate topsoil[END_REF][START_REF] Andrianarisoa | Control of Nitrification by Tree Species in a Common-Garden Experiment[END_REF]. The incubation took place in a stand planted with 30 year-old European beech trees (Fagus sylvatica L). Unlabelled senescent leaves were also incubated as reference material. They were harvested in October 2004, in the stand where the incubation took place. The leaves were collected at the same height (~1.5 m) from the branches of several different trees in order to obtain mean composition and to minimize biases linked to intrapopulational variability.

Selection of senescent leaves

After harvesting, leaves were rinsed with distilled water to remove extraneous particles and dried at 45°C until they attained a constant weight. Leaves were then examined under a dissecting microscope to monitor morphological changes. One milligram was removed from each leaf for elemental and isotope analyses (see section 2.3.1) to determine the main biochemical characteristics of the leaves at the initial stage of degradation. Each batch was composed of 10-15 leaves and corresponded to approximately one gram of organic matter. Batches were assembled using leaves from as many different trees/plants as possible to obtain equivalent batches. 13 C-enriched leaves were selected to constitute batches having isotope variabilities similar to those of natural leaves (i.e. a standard deviation ≤0.8 ‰). The mean isotope composition of the batches of labelled leaves varied within a rather large range (i.e. +16.3 ‰ to +36.8 ‰) that precluded direct comparison between batches. Moreover, labelled and unlabelled leaves were grown in different conditions and exhibited slightly different biochemical characteristics. Therefore, to avoid biases linked to differences between the 13 C-enriched leaf batches and the wild leaf batches at the initial stage, the following discussion will be based primarily on the comparison of degradation trends (i.e.  13 C degradation =  13 C degraded - 13 C initial ).

Litterbag incubation

Preliminary investigations showed that in contrast to aluminium nets, the nylon and polypropylene nets generally used for litterbags may release substantial amounts of contaminants that could be potentially extracted with the leaf lipids.

Accordingly, the litterbags (9.5  14.5 cm) were made of aluminium wire. The mesh size was 1.4  1.8 mm and was small enough to contain small leaf litter debris yet large enough to permit aerobic microbial activity and free entry of small soil animals. Indeed, soil fauna at the experimental site was dominated in biomass by enchytraeids, and contained to a lesser extent, mites and springtails, as it is generally the case in moders [START_REF] Swift | Decomposition in terrestrial ecosystems[END_REF][START_REF] Ponge | Soil fauna and site assessment in beech stands of the Belgian Ardennes[END_REF]. Before being enclosed in litterbags, the leaves were weighed and then re-moistened with distilled water to recreate the natural moisture conditions of leaf fall in autumn. The litterbags were placed in the field at the end of autumn 2004, on the surface of the existing forest litter layer, akin to leaves falling naturally in autumn. Samples were retrieved from the field at 5, 10, 15, 20, 30, 40, 52, 79, 129 and 207 weeks (four years). At each sampling date, two bags of natural leaves and two bags of labelled leaves were taken.

Analyses

The recovered material was first rinsed with distilled water to remove obvious extraneous particles such as mosses, roots or arthropods. Leaves were then scanned, dried to constant weight at 45°C, weighed and examined under a dissecting microscope. Samples were stored dark in aluminium foil at 5°C until analysis. All the leaves of each litterbag were then combined and ground fine enough to pass through a 500 m mesh. An aliquot of the so-obtained powder (~1 mg) was taken for bulk elemental and isotope characterization (see 3.2.1.) and the rest was submitted to the extraction procedure.

Isotope and elemental analyses of bulk leaves

Stable isotope ratios were measured using an automated unit that combines an elemental analyser with an isotope ratio mass spectrometer. The samples were combusted in a Carlo-Erba CHN elemental analyser connected to a VG-SIRA 10, isotope ratio mass spectrometer. After flash combustion with copper oxide at 1000°C, CO 2 was cryogenically distilled, purified and introduced on-line into the mass spectrometer to determine carbon isotope ratios [START_REF] Girardin | Analyse isotopique du 13 C en abondance naturelle dans le carbone organique : un système automatique avec robot préparateur[END_REF]. The  13 C values were measured with a precision of 0.1‰ (1).

Lipid extraction and alkane fractionation

Leaf powder was ultrasonically extracted for 20 min with 30 ml dichloromethane/methanol (2/1; v/v). The mixture was centrifuged (10 min at 4,000 rpm) and the extracted lipids were recovered in the supernatant. The extraction procedure was repeated six times with the centrifugation residue (pellet). The combined extracts were concentrated by rotary evaporation and then dried under nitrogen gas. The extract yield was determined by weighing the dried combined extracts. The total extract was then fractionated on an alumina column (1 g alumina per 10 mg dry extract, Sigma-Aldrich 507C ~150 mesh) deactivated to Brockmann grade IV by adding 0.1% by weight of distilled water. Alkanes were recovered in the apolar fraction after elution with heptane (4 ml for 1 g of alumina). A known amount of an internal standard (i.e. tetratriacontane) was introduced in the fraction for quantification purposes.

Alkane-specific isotope analyses

Alkanes were identified by gas chromatography using a an Agilent 6890N gas chromatograph (GC) equipped with a split/splitless injector and fitted with a fused silica capillary column, coated with VF5-MS (50 m  0.32 mm i.d., 0.12 m film thickness). For GC the temperature was increased from 80°C to 100°C at 10°C/min, then increased to 325°C at 4°C/min, then held at 325°C for 30 min. Helium was used as carrier gas at a constant flow of 2 ml/min. The splitless injector and flame ionization detector temperatures were held at 350°C. Compound-specific  13 C values of the dominant alkanes were determined with a Micromass IsoChrom III coupling, comprised by an IsoChrom isotope ratio mass spectrometer coupled to a GC via a Micromass combustion interface (CuO combustion furnace at 850°C and cryogenic trap at -100°C).  13 C values were measured with a precision (1) of 0.5‰. Each sample was run in triplicate. To enable comparison between leaves that exhibited a rather large range of isotope variability, the isotope compositions of specific alkanes were expressed relative to the bulk isotope composition of undegraded leaves according to:  13 C alkane =  13 C alkane - 13 C undegraded leaves .

Results and discussion

Bulk degradation patterns

Microscopic examination of the leaves revealed traces of epiphytic microflora beginning at the initial/senescent stage. Indeed, fungal fructifications (Fig. 1a) and mycelia (Fig. 1b) were detected on several leaves. During the experiment, the leaves exhibited progressive degradation patterns. The first evidence of grazing by soil fauna, in which the lower cuticle was missing between the tertiary/quaternary veins, was detected after five weeks of decomposition in the field. The lower cuticle of leaves degrades more easily than the upper cuticle and the veins are much thicker and decay more slowly. These grazing patterns are typical of litter-consuming fauna, notably the enchytraeids that are very abundant in moders [START_REF] Ponge | Horizons and Humus Forms in Beech Forests of the Belgian Ardennes[END_REF]. These grazing marks became frequently observed after 10 weeks of decomposition (Fig. 1c). After one year, the upper cuticle of leaves showed evidence of grazing, leading to complete holes between veins (Figs. 1d and1e) and to a progressive skeletonization of the leaves (Fig. 1f). After decomposing for four years, the only original material remaining consisted of bundles of skeletonized leaf fragments (Fig. 1f). Exogenous material also accumulated on the leaves during the experiment.

Fungi progressively invaded the leaf surfaces (Fig. 1d); on leaves exposed to light, micro-algae colonized the gaps left by grazing fauna (Fig. 1d); faecal material was deposited by soil fauna (Fig. 1e); and conifer pollen grains probably originating from adjacent stands were also deposited (Fig. 1e and1f). Labelled and unlabelled leaves exhibited similar degradation patterns upon microscopic examination.

After four years of decomposition in the field, the litter leaves had lost 50-90% of their initial dry weight (Fig. 2a). A rather large weight loss was observed during the first several days followed by slower decomposition rates afterwards. This decomposition trend is in agreement with other studies that reported the decomposition patterns of beech litters under similar conditions [START_REF] Cortez | Field decomposition of leaf litters: relationships between decomposition rates and soil moisture, soil temperature and earthworm activity[END_REF][START_REF] Ono | Organic carbon accumulation processes on a forest floor during an early humification stage in a temperate deciduous forest in Japan: Evaluations of chemical compositional changes by 13 C NMR and their decomposition rates from litterbag experiment[END_REF]. 13 C-labelled leaves appeared to degrade slightly more quickly than natural leaves during the first three years (Fig. 2a). Nevertheless, both leaf types eventually lost equivalent weights after four years (Fig. 2a). The difference in initial decomposition rates of the natural and the labelled leaves probably reflected differences in initial leaf quality. Among other factors, the C/N ratio was lower in labelled leaves than in natural leaves at the initial stage (with means of 19.6 and 26.9 for labelled and unlabelled leaves, respectively). This lower C/N ratio probably contributed significantly to the difference in decomposition rate, and has been suggested previously [START_REF] Melin | Biological Decomposition of Some Types of Litter From North American Forests[END_REF][START_REF] Witkamp | Decomposition of Leaf Litter in Relation to Environment, Microflora, and Microbial Respiration[END_REF][START_REF] Taylor | Nitrogen and Lignin Content as Predictors of Litter Decay Rates: A Microcosm Test[END_REF]. Litter quality differences may be attributed to growing conditions that were probably more favourable in the labelling chamber than in the field. To avoid potential bias linked to this difference in litter quality, we based our discussion on degradation trends calculated relative to the initial/undegraded stage of each batch, rather than on direct comparisons between the two crude datasets. Regardless of the dataset, no specific trends were evident with respect to the carbon content or the C/N ratio, both of which remained relatively constant during the experiment (~450 mg/g and ~20, respectively; data not shown). These values agree with those previously reported for beech leaves and litter found at the experimental site [START_REF] Zeller | 13 C and 15 N isotopic fractionation in trees, soils and fungi in a natural forest stand and a Norway spruce plantation[END_REF]. Lipids of senescent leaves (i.e. at the initial stage of degradation) accounted for ~11 wt.% and ~16 wt.% of the dry material for unlabelled and 13 C-labelled leaves, respectively. Here again, the higher lipid content of the labelled leaves compared to that of the natural leaves was probably due to differences in growing conditions. Nevertheless, both leaf types exhibited similar degradation patterns for lipids (Fig. 2b). Lipid content decreased sharply during the first month of the experiment, reaching ~6 wt.% of dry material. Leaf lipid content then progressively decreased to become >1 wt.% after four years of degradation (Fig. 2b). Final lipid loss was greater than 99 wt.% of the initial lipid content, which was much higher than the bulk weight loss (i.e. ~80 wt.% of initial leaves). Accordingly, lipids were degraded to a greater extent than were the non-lipidic constituents of the leaves. The chemical composition of lipids from senescent beech leaves has been reported previously [START_REF] Nguyen Tu | Chemotaxonomical investigations of fossil and extant beeches. I. Leaf lipids from the extant Fagus sylvatica L[END_REF]: most n-alkanes consisted of between 16 and 29 carbon atoms and were markedly dominated by the C 27 homologue. The initial alkane content present in senescent leaves decreased substantially during the four year decomposition, as illustrated by the amount of the C 27 homologue (Fig. 2c).

Isotope degradation patterns

The bulk isotope composition of unlabelled leaves remained nearly constant during decomposition, whereas that of the 13 C-labelled leaves exhibited a significant decrease over time (i.e. 13 C-depletion, Fig. 3a). This 13 C-depletion reached 12‰ after the four-year decomposition period. In agreement with previous reports [START_REF] Collister | Compound-specific  13 C analyses of leaf lipids from plants with differing carbon dioxide metabolisms[END_REF][START_REF] Chikaraishi | Carbon and hydrogen isotopic fractionation during lipid biosynthesis in a higher plant (Cryptomeria japonica)[END_REF], specific alkanes appeared to be 13 C-depleted compared to the bulk leaves. The 13 C-content of specific alkanes exhibited degradation patterns similar to that of bulk leaves. For example, the 13 C-content of the C 27 homologue (Fig. 3b) remained nearly constant in the unlabelled leaves but exhibited a decrease ~20‰ in the 13 C-enriched leaves. The C 25 and C 29 homologues exhibited degradation patterns similar to that of C 27 (data not shown). At the bulk leaf scale, as well as at the molecular scale, previous authors observed either increasing  13 C values or unchanging isotope content during organic matter degradation [START_REF] Balesdent | Site related  13 C of tree leaves and soil organic matter in a temperate forest[END_REF][START_REF] Connin | Isotopic discrimination during long-term decomposition in an arid land ecosystem[END_REF]. These studies dealt with unlabelled material and reported 13 C-enrichments of up to 6‰. 13 C-depletion in the context of unlabelled organic matter decomposition was reported in only one early study of bulk Spartina rhizomes decaying in salt marsh sediments [START_REF] Benner | Depletion of 13 C in lignin and its implicatons for stable carbon isotope studies[END_REF]. The observed variability in the trends of 13 C content that has been documented in the literature is likely due to the wide range of environments employed to investigate decomposition. In a recent experiment dealing with highly 13 C-enriched (i.e.  13 C  166‰) poplar leaves, Rubino and colleagues (2010) reported a decrease of 41‰ in  13 C after one year of litter degradation.

Disproportionate changes in isotope content during degradation may reflect either contributions from exogenous material having different isotope compositions or an "isotope effect" [START_REF] Natelhoffer | Controls on natural nitrogen-15 and carbon-13 abundances in forest soil organic matter[END_REF][START_REF] Balesdent | Site related  13 C of tree leaves and soil organic matter in a temperate forest[END_REF]. The latter phenomenon describes the selective degradation of chemical compounds having  13 C values deviating from that of bulk leaves and/or kinetic discrimination during metabolism of leaf constituents by degrading microorganisms (i.e. preferential metabolism of the material that is 13 C-depleted). Kinetic discrimination would be expected to generate similar patterns for a given species in a given environment.

This explanation can thus be ruled out in our experiment since 13 C-labelled and unlabelled leaves exhibited different isotope depletion patterns. The preferential degradation of the lipids noted in section 3.1 did not likely account for the observed isotope trends because lipids corresponded to only between 1 and 15% of the bulk leaf weight. Moreover, lipids are 13 C-depleted compared to the bulk leaves [START_REF] Park | Carbon isotope fractionation during photosynthesis[END_REF][START_REF] Monson | Carbon isotopic fractionation in the biosynthesis of bacterial fatty acids. Ozonolysis of unsaturated fatty acids as a means of determining the intramolecular distribution of carbon isotopes[END_REF]. Selective degradation of 13 C-enriched molecules such as carbohydrates may partly explain the isotope content trends detected in bulk leaves. Indeed, 13 C-labelled leaves were grown in optimal conditions which may have led to them having higher carbohydrate content than the unlabelled leaves. Since carbohydrates can be 13 C-enriched up to 5‰ with respect to bulk leaves (Ehleringer, 1991), this may have played a role in the different behaviours of the isotope content in labelled and unlabelled leaves. Nevertheless, the depletion observed here for bulk labelled leaves reached 12‰ after four years of degradation. A complementary explanation is thus necessary to fully explain the observed isotope patterns, especially with respect to those observed for specific alkanes. Accordingly, this is most likely due to a contribution from exogenous organic matter that is of a  13 C value lower than that of the labelled leaves. Such an exogenous contribution may be linked to the progressive invasion and/or accumulation of algae, faeces and fungi which were revealed upon microscopic examination. Although such soil-derived microbial biomass is generally considered to be devoid of long chain lipids such as nalkanes, microbes such as fungi or algae may contain long-chain lipids [START_REF] Jones | Major paraffin constituents of microbial cells with particular references to Chromatium sp[END_REF][START_REF] Rezanka | Rapid method for the enrichment of very longchain fatty acids from microorganisms[END_REF][START_REF] Volkman | Microalgal biomarkers: A review of recent research development[END_REF].

The isotope composition of the exogenous organic matter that may have contributed to the decaying leaves is likely similar to or slightly enriched in 13 C with respect to the original unlabelled material, whether at the bulk leaf level or the molecular level. Indeed, soil microbial biomass is generally considered to be 13 C-enriched by 1-3‰ compared to soil organic matter (Werth and Kuzyakov, 2010;and reference therein). Fungi can be either slightly 13 C-depleted or 13 C-enriched relative to the 13 C content of the substrate, depending on the fungus taxon and on the substrate [START_REF] Gleixner | Correlation between the 13 C content of primary and secondary products in different cell compartments and that in decomposing basidiomycetes[END_REF][START_REF] Hobbie | Mycorrhizal vs Saprotrophic Status of Fungi: The Isotopic Evidence[END_REF][START_REF] Abraham | Isotope fractionations in the biosynthesis of cell components by different fungi: a basis for environmental carbon flux studies[END_REF][START_REF] Ruess | Carbon stable isotope fractionation and trophic transfert of fatty acids in fungal based soil food chains[END_REF][START_REF] Cowie | Carbon isotope fractionation in phospholipid fatty acid biomarkers of bacteria and fungi native to an acid mine drainage lake[END_REF]. The sporophores of the saprophytic fungi from our experimental site were shown to be 13 C-enriched by ~4‰ with respect to their substrate [START_REF] Zeller | 13 C and 15 N isotopic fractionation in trees, soils and fungi in a natural forest stand and a Norway spruce plantation[END_REF]. Specific lipids from heterotrophic microorganisms have been shown to be either 13 C-enriched or 13 C-depleted by a few per mill, with respect to their total biomass, according to the taxon and to the environment [START_REF] Teece | Isotopic fractionation associated with biosynthesis of fatty acids by a marine bacterium under oxic and anoxic conditions[END_REF][START_REF] Abraham | Isotope fractionations in the biosynthesis of cell components by different fungi: a basis for environmental carbon flux studies[END_REF][START_REF] Cowie | Carbon isotope fractionation in phospholipid fatty acid biomarkers of bacteria and fungi native to an acid mine drainage lake[END_REF]. The carbon isotope composition of faeces relative to diet is poorly known for soil fauna and seems to vary among taxa for small metazoans [START_REF] Deniro | Influence of diet on the distribution of carbon isotopes in animals[END_REF][START_REF] Tamelander | Fractionation of stable isotopes in the Arctic marine copepod Calanus glacialis: Effects on the isotopic composition of marine particulate organic matter[END_REF]. Specific compounds of faeces from soil fauna may reflect that of their diet as shown for copepod sterols [START_REF] Grice | Effects of zooplankton herbivory on biomarker proxy records[END_REF]. Therefore, the exogenous contribution to the original plant material probably had an isotope composition similar to or slightly higher than that of the unlabelled leaves. This implies that fungi, other microbes and the animals that produced the faeces in the litter likely derived mostly their diet from unlabelled organic matter that was the main substrate in the experimental site.

By comparing degradation patterns in 13 C-labelled and unlabelled leaves, this study provides evidence for microbial contributions to decaying litter at the level of bulk organic material and at the level of specific alkanes. This exogenous contribution was probably substantive but relatively small when compared to the bulk mass of the leaves in our samples. In this way, no isotope trend would be expected for unlabelled leaves while 13 C-enriched leaves would be expected to exhibit decreasing  13 C values throughout the decay period. While contribution from microbial organic matter to bulk plant organic matter has been well established previously, this has not been reported for long-chain alkanes. These molecules have been generally considered to be typical of plants, although recent studies suggested that microbial alkanes may contribute to degrading plant alkanes in soils and sediments [START_REF] Buggle | Is there a possibility to correct fossil n-alkane data for postsedimentary alteration effects?[END_REF]. The present study thus provides direct isotope arguments in favour of microbial contribution rather than isotope discrimination effects to explain the 13 C-enrichment trends previously reported for plant alkanes in soils [START_REF] Nguyen Tu | Diagenesis effects on specific carbon isotope composition of plant n-alkanes[END_REF][START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF]. Although microbial contribution appeared to be relatively limited for unlabelled/natural litter for this four-year-incubation, results from other studies suggest that it may lead to a 13 Cenrichment of up to 4‰ [START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF]. This result was actually based on lipids extracted from bulk soils sampled from the horizon underlying the litter layer (i.e. 2-10 cm in depth). Therefore, it may be suggested that the high 13 Cenrichment detected by [START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF] corresponded to the accumulation over time of an increase in 13 C-content that was negligible at first but that led to a measurable effect in the long-term. [START_REF] Chikaraishi | Carbon and hydrogen isotope variation of plant biomarkers in a plant-soil system[END_REF] found that long-chain n-alkanols and n-alkanoic acids can also undergo significant 13 C-enrichment during leaf degradation in soils. We may therefore generalize our findings to other long-chain fatty lipids, which may also be contaminated by microbial lipids. Thus, circumspection is called for when considering long-chain fatty lipids as unaltered record of organic carbon isotope composition.

Figure captions Figure 1 .Figure 2 .

 captions12 Figure captions

Figure 3 .

 3 Figure 3. Changes in isotope composition. Solid symbols: unlabelled leaves; open symbols: 13 C-labelled leaves. a. 13 C-content of bulk leaves ( 13 C =  13 C degraded - 13 C initial ). b. Specific 13 C-content of heptacosane ( 13 C =  13 C heptacosane - 13 C bulk undegraded leaves ).

  Figure

Acknowledgements

We are indebted to Thierry Bariac for access to the controlled chamber and to Patricia Richard for technical support during the labelling experiment. Thanks are also due to Jacques Ranger for access to the experimental site of Breuil-Chenue forest and Dominique Gelhaye and Jean-Pierre Calmet for their assistance in the field. We are grateful to Christelle Anquetil, Nicolas Péchot and Valérie Pouteau for mass spectrometry facilities as well as Stéphane Lemettre and Florent Zanetti for help in lipid preparation. We also thank Jorge Cubo, Yongsong Huang and Gladys Loranger for helpful discussions along with Stéphane Peigné and Son Nguyen Tu for technical assistance. Thanks are due to the two anonymous referees who provided constructive reviews and to Kurt Liittschwager for correction of the English of the manuscript. This work was funded by a grant from Fond National pour la Science (ACI JC 10051 -notification 035214) which was greatly appreciated.


Hubert Saint

Frédéric Gruy

Michel Cournil

Study of the agglomeration of alumina powders using in situ turbidimetry

teaching and research institutions in France or abroad, or from public or private research centers.