Marcel Bourgade
email: mbourgade@hotmail.com

History of Squamate Lizard Dactyloidae from the Eastern Caribbean Origins of Anolis from Martinique, Zanndoli Matinik (Dactyloa roquet) by

Keywords: Eastern Caribbean, Eocene, geology, Martinique, phylogeny, history, origin, center of dispersion, Herpetofauna, Squamates, Lizard, Anolis, Dactyloidae, Dactyloa .roquet

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

INTRODUCTION

Geological history and geosciences are key to understanding the general evolution of biodiversity. The herpetofauna of the islands of the eastern Caribbean and particularly the small amphibians and squamates were among the first occupants of land surfaces. And so the geological evolutiontectonic and volcanic -of Martinique and the Caribbean archipelago is decisive for the process of dispersions and therefore of speciations of this herpetofauna originating in the area of the current Orinoco basin. But also these processes of dispersions and speciations, must be analyzed in a logic of conjunctions of this geological evolution of the Eastern Caribbean with phenomena of great upheavals or climatic changes impacting the entire planet; periods of glaciation with the formation of ice caps at the poles leading in bathymetric terms to significant drops in sea level. With advances in genetics, research in molecular systematics makes species of this micro herpetofauna in particular indicators allowing revelation and precision of dating of geological phenomena and events. A phylogeny of a herpetofauna which is therefore revealing of a geological history of the Eastern Caribbean where Martinique stands out as exceptional and central on the scale of this Grenadian basin where it is located; playing a main role as a refuge island from -25 My, then from center of dispersion towards -12 My for an endemic herpetofauna older than previously thought. A proto-Martinique island refuge in this almost unique Grenadian basin (with proto-Barbados) maintained not submerged from -25 My, which was quite naturally center of dispersion, first towards a proto-Saint Lucia in geological phase re-emergence around -12 My.

Research in herpetology and particularly the first results of work in molecular systematics [START_REF] Hedges | Molecular phylogeny and biogeography of West Indian frogs of the genus Leptodactylus (Anura, Leptodactylidae)[END_REF][START_REF] Surget-Groba | Journal of Biogéography n°40 -School of Biological sciences , College of Natural Sciences, Bangor University -UK -Supporting information A likelihood framework analysis of an island radiation: comparative phylogeography of the Lesser Antillean gecko Sphaerodactylus vincenti[END_REF][START_REF] Hedges | Tree of Life Reveals Clock-Like Speciation and Diversification[END_REF] relating to this Martinican herpetofauna are shaking up the geosciences and obliging a revision of the historical scenario of the basically tectonic geological formation and evolution of the Eastern Caribbean with emerged land (forming an isthmus since the Eocene, well over -45 My), then almost all submerged around -25 My. This isthmus at the top of '' a cordillera (volcanic arc), located on the southeastern edge of the so-called Caribbean plate, at the junction of the three lithospheric films (or plates), Caribbean, North America and South America, formed one of the two bridges, with that of the Aves ridge, between the Orinoco basin and the Greater Antilles. (See Fig. 2 and Fig. 3)

The history of biological endemism on the surface of land that has emerged since then does not begin there in the Miocene at "-24 My" as it is generally accepted. It is in such a context that the Dactyloïdés of Martinique (Zanndoli, in Martinique language), are like the Spherodactyles (Ti-Mabouya), and Tétrachéilostomes (Ti-Sèpan Tè) emblematic of this evolution of biodiversity in a logic of cause and effect with the geological history of Martinique, obviously intrinsic to that of the eastern Caribbean, and in conjunction with climate change.

The base of Martinique consists of a fragment of the Aves wrinkle located east of the Caribbean tectonic film which evolved 120 My ago in the Pacific Ocean. This Aves wrinkle, with its two consecutive folds of the west to east displacement of the Caribbean lithospheric film encrusted between the two most important American lithospheric films, is part of a set called the Caribbean Mesozoic Arc . [START_REF] Stephan | Paleogeodynamic maps of the Caribbean[END_REF].

Martinique is the only island in the eastern Caribbean to present three phases of volcanic activity juxtaposed with a regular displacement of these activities from east to west since 25 My (Fig. 4 This contribution relating to the history of the Dactyloidae lizards of the Eastern Caribbean is based on field observations on the current Martinican country, and therefore concerning lines of the Dactyloa roquet species, by evoking origins and phylogeny of the species, and therefore by making reference to recent but also very old publications, dealing with biogeography, geology, biology and systematics : [START_REF] Dumeril | Etude sur les Reptiles[END_REF][START_REF] Dumeril | Etude sur les Reptiles[END_REF][START_REF] Barbour | A contribution to the zoogeography of the West Indies, with especial reference to Amphibians and Reptiles[END_REF][START_REF] Barbour | Memoirs of the Museum of Comparative Zoology at Harvard College[END_REF][START_REF] Barbour | A list of Antillean reptiles and amphibians[END_REF][START_REF] Barbour | A second list of Antillean reptiles and amphibians[END_REF][START_REF] Kl | Third list of Antillean reptiles and amphibians[END_REF][START_REF] King | Systematics of Lesser Antillean lizards of the genus Sphaerodactylus[END_REF][START_REF] Schwartz | A review of Sphaerodactylus vincenti in the southern Windward Islands[END_REF][START_REF] Schwartz | A new subspiecies of the gecko Sphaérodactylus microlepis[END_REF], Westerkamp 1975[START_REF] Lliboutry | Traité de Glaciologie[END_REF][START_REF] Lopez-Ramos | Geological summary of the Yucatan Peninsula[END_REF][START_REF] Schwartz | A check-list of West Indian Amphibians and Reptiles[END_REF], Andreieff, Baubron, Gardner et al. 1987[START_REF] Andreieff | Histoire géologique de la Martinique[END_REF][START_REF] Stephan | Paleogeodynamic maps of the Caribbean[END_REF][START_REF] Hedges | The origin of West Indian amphibians and reptiles. Contributions to West Indian herpetology: a tribute to Albert Schwartz[END_REF][START_REF] Malhotra | Reptiles & Amphibians of the Eastern Caribbean[END_REF][START_REF] Breuil | Atlas des amphibiens et reptiles de la Martinique : illustration et cartographie provisoires (IVème partie) -Histoire géologique et différenciation géologique des populations de sphérodactyles de la Martinique (Sphaerodactylus vincenti) -Laboratoire des Reptiles et Amphibiens Muséum national d'Histoire naturelle -France -Thorpe[END_REF], 2009, 2011, 2013[START_REF] Gradstein | A geologic time scale 2004[END_REF][START_REF] Schulte | Chicxulub impact ejecta fromthe Cretaceous-Paleogene (K-P) boundary in northeastern México, in Large Meteorite Impacts III[END_REF] The ancestors of the Anolis of the Eastern Caribbean (common ancestors of Dactyloa and Ctenonotus) are survivors, who evolved at the time on the geographical position of the proto basin of the Orinoco, north of the continental block South America, from the 5th great extinction which took place -66 My ago. This 5th great planetary extinction of species was consequence of the impact of the asteroid which occurred 66 MY ago in Chicxulub on the tip of the Yucatan peninsula (Gulf from Mexico). (Smit et al. 1994[START_REF] Smit | Coarse-grained, clastic sandstone complex at the K/T boundary around the Gulf of Mexico: Deposition by tsunami waves induced by the Chicxulub impact, in The Cretaceous-Tertiary Event and Other Catastrophes in Earth History[END_REF] This asteroid impact event caused major ecological changes to lower sea levels [START_REF] Gradstein | A geologic time scale 2004[END_REF].

The beginning of the formation of the Aves and Caribbean bridges, allowing inter-continental terrestrial biological connection, and therefore very ancient dispersion in this Caribbean geographical position of terrestrial flora and fauna species, would result from the conjunction of both geological phenomena ( tectonics, migrations of bedding), climatic (glaciations) and the consequences of the impact of the asteroid which occurred 66 My ago at Chicxulub on the tip of the Yucatan peninsula (Lopez-Ramos 1975).

The ancestors common to Dactyloa and Ctenonotus, squamates, were then able to disperse by almost terrestrial route, respectively on the most eastern Caribbean isthmus for Dactyloa, and on the Aves isthmus for Ctenonotus, isthmus formed since 65 My [START_REF] Stephan | Paleogeodynamic maps of the Caribbean[END_REF]).

These dispersions and separations between Dactyloa and Ctenonotus are attested by molecular biology and dated to -50 My in the Eocene (Prates et al. 2015).

At -50 My (early Eocene) the temperature of oceanic water masses is close to 15 ° C (Matthew et al. 2009). (see Fig. 2 and Fig. 3)

The ancestors of the Dactyloïdés installed on quasi isthmus of the Eastern Caribbean since -50 My, diverged from their South American congeners of the proto basin of the Orinoco around -37 My (Prates et al. 2015). At -35 My (late Eocene), it is the beginning during the Tertiary era of the glaciation period still current, the temperature of oceanic water masses dropped to 11 ° C at the surface and to 9 ° C in depth ; there is then a development of mountain glaciers on Antarctica (which has been at the south pole since -100 My) and there is again significant cooling which results in a decrease of about 6 ° C in the temperature of the bottom water [START_REF] Bennett | Glacial geology : ice sheets and landforms[END_REF]).

These ancestors of the Dactyloïdés, surviving on banks of islands of the proto Martinique remained emerged following the submersion of this Caribbean isthmus which proceeded from -40 My to -25 My, will evolve in isolation; then around -12 My, the Martinique proto will play a role as a center of dispersal of the Dactyloïdes towards banks of re-emerged islands in the south of Martinique: proto Saint Lucia, proto Grenada, proto Saint -Vincent, proto Barbados . Note the fact of a major new cooling of the planet towards -13 My with an increase in the Antarctic ice cap, and therefore a drop in sea level [START_REF] Bennett | Glacial geology : ice sheets and landforms[END_REF]. Thus there will be differentiation of Dactyloa, dispersed directly or indirectly, from the proto Martinique:

-to the prototype Saint Lucia, with the ancestor of D. luciae since around 17 My (probable age of re-emergence of island banks: Gros-Ilet and Ilets Maria)

-towards the island banks of Grenada, with the ancestor of D. richardii since 12 My [START_REF] Hedges | Tree of Life Reveals Clock-Like Speciation and Diversification[END_REF]. Then diversification towards the Grenadines, with the ancestor of D. aenea.

-towards the prototype Saint-Vincent, via Saint-Lucia, with the ancestors of D. griseus, and D.

trinitatis.

-to Blanquilla and Bonaire, via Ste-Lucie, with ancestors of D. blanquillana and D. bonairensis.

From proto Martinique and the old island of Sainte-Anne, the ancestors of Dactyloa roquet also dispersed over new areas as geological evolution and volcanic activity formed this proto Martinique (see Fig. 4 and Fig. 5), first towards banks of islets on the geographical position of the current Génipa Bay (Ducos, Lamentin), then towards the peninsula of south-west Martinique. Then as the geological evolution and the formation of volcanic massifs (Vauclin, Morne Pitault, ...), the Dactyloa roquet occupied the Martinican space of the center, between the peninsula of Sainte-Anne, that of the southwest and that of the Caravelle. And finally towards the north and north-west of Martinique with first the emergence of Le Morne Jacob, the Pitons du Carbet, then the island of Mont Conil (Prêcheur), and finally the Montagne Pelée. Unlike the Eleutherodactylid amphibians and spherodactyls, the Dactyloa did not cross the Dominica Canal. The phylogeny work of Thorpe et al. 2010 make it possible to distinguish, four (4) large lines within the Dactyloa roquet:

-the lineage of the Sainte-Anne peninsula; -the southwest line; -the center line; with a dispersion from the Atlantic coast to Barbados estimated at -4 My.

-and the north-west line, the most recent where Dactyloa have experienced last volcanic episodes and therefore for some have survived. The presence observed in 2019 by Christophe Auguste, of a line presenting a particular phenotype with a remarkable morphological character of development of their spiny dorsal crests (photograph 2), remains to be studied.

Dactyloa roquet are also present in Saint Lucia [START_REF] Daltry | The status and management of Saint-Lucia's forest reptiles and amphibians. National forest and bio-physical resource inventory project[END_REF], and are called "Zanndoli Babad" (Anolis of Barbados) by the population. Additional investigations should be carried out to confirm or deny the fact that this line observed in Saint Lucia comes from Barbados or directly from Martinique.

This historical scenario of evolution of the genus of the Dactyloa known as Anolis in the Eastern Caribbean whose ancestors knew as refuge the island banks of the Martinique proto remained emerged from -24 My (compared to the other island banks of this Eastern Caribbean which they were submerged), presents similarities to that declined for the genus Sphaérodactylus of Martinique. Moreover this historical scenario would be globally valid with chronological differences, for several genera of the micro herpetofauna the most formerly dispersed from the basin of the Orinoco towards the geographical position of the current banks of islands of the eastern Caribbean from the Eocene, for more than 45 My.

It is the particular configuration of the proto Martinique (South-East) geologically, that is to say the existence in the basement, of large limestone formations out of water, compared to that of the other islands of the Eastern Caribbean (including Barbados), to have found itself as the only possible refuge for fauna and flora, with banks of islands tectonically remained emerged between -24 My and -12 My. It is this situation which explains this scenario of which we have scientific certainty since 2008, of a Martinique center of dispersion on the scale of the eastern Caribbean, for the Anolis (Johansson, Surget-Groba, & Thorpe 2008), and for the Sphaérodactylus (Surget-Groba, & Thorpe 2013). This global scenario is presumed to become more precise as the work in molecular biology proceeds, and to be the same for Anurans, Amphibians of the genus Eleutherodactylus, as well as concerning the snake reptiles of the genus Tetracheilostoma.

This datum of the geological history of the Caribbean, history of islands linked to the existence of volcanoes certainly, but naturally also and above all history of tectonics, sediment bedding, existence of isthmus or bridges (Aves ride) to the geographical position of the eastern Caribbean from 100 My to 35 My, makes consistent the reading of data from research results in molecular systematics and phylogeny of reptiles and amphibians, and therefore for many species of the plant kingdom. Despite the results of molecular biology, the authors underestimate this existence of tectonically emerged lands and precisely of a Martinique proto that has remained emerged since the beginning of the Eocene -50 My; and remain frozen in an approach which turns out to be deceptive of Martinique as being an "oceanic island" and only "volcanically emerged", the first parts of which have "arisen from the ocean since -24 My". [START_REF] Dewynter | Atlas des Amphibiens et Reptiles de la Martinique[END_REF][START_REF] Bourgade | Sphaerodactyls Endemic to South-Eastern of Martinique and Geological History of the Eastern Caribbean. Demonstration of a 4 th species S. X sp. Presents on the peninsula of Sainte-Anne, supposed center of dispersion of the common ancestor of Sphaerodactylus microlepis[END_REF], interpreting the fact highlighted by the work in molecular systematics of [START_REF] Hedges | Tree of Life Reveals Clock-Like Speciation and Diversification[END_REF], of a differentiation of the Anolis of the Grenadines (Dactyloa richardii) with those of Martinique (Dactyloa roquet) since -12 My, implicitly suggest the thesis that the bank of islands of Dactyloïdes from the Eastern Caribbean, that therefore their geographic location of isolation of their South American congeners as of -37 My ago, would have been the proto Grenada and the Grenadines, and that the installation of the ancestor of Dactyloa roquet on the proto Martinique and old island de Sainte-Anne would be dated "-8 My" (p. 66 of Bull. Soc. Herp. Fr. (2019) 169). This thesis and interpretation of molecular biology results is, in our opinion, completely wrong ; indeed, the absence on these proto islands of Grenada and the Grenadines of the genera of Spherodactyls and Tetracheilostomes pleads in favor of a total submersion of these banks of islands to count between -25 My and -12 My. As also the absence of the genera of Spherodactyls and Tetracheilostomes endemic to the proto Saint-Vincent also pleads for a total submersion of this island from -25 My unlike the old island of Sainte-Anne. As still, the absence of the genera of Spherodactyls and Anolis (Dactyloa) endemic to the Barbados proto argues for the fact of an almost total submersion of the latter from -24 My, and this always unlike the bench Proto Martinique island and precisely the old island of Sainte-Anne.

The existence of the eastern Caribbean isthmus, most certainly from -50 My to -35 My, essentially linked to tectonic phenomena and climate change, comes to explain data from molecular research concerning species of reptiles and amphibians from the oldest present, originally refugees on proto Martinique. The residual islands of the Proto Martinique bench, Caravelle and Sainte Anne, have become centers of dispersal of species having survived the significant extinction between -35 My and -24 My of a biodiversity that had dispersed from the continent South American to the Caribbean isthmus since -50 My; isthmus all the more formed during glacial periods when the sea level is estimated at 130 meters compared to the current level [START_REF] Bennett | Glacial geology : ice sheets and landforms[END_REF]). See fig. 3, allowing a visualization of the context of isthmus or double bridge, of land emerged during this geological era.

IV. CONCLUSION

In the current state of knowledge, and since 2015, we can state the certainty of the fact that the ancestors of the Dactyloids of the eastern Caribbean settled there -50 million years ago on the tectonically emerged lands constituting this proto Caribbean; and singularly ancestors of the Dactyloa roquet on banks of islands of the Martinique proto -50 My ago. These Dactyloïdés of the Eastern Caribbean found themselves genetically isolated from their parents of the proto basin of the Orinoco from -37 My. From -25 My, the benches of islands of the proto Martinique, remained emerged, constituted the almost unique and exceptional refuge for these isolated Dactyloïdes, while in the north, as in the south of this proto Martinique, the benches of islands corresponding to the geographic positions to the north, Dominica, the Guadeloupe archipelago and islands further north (Antigua, Barbuda, banks etc.); in the south, from Saint Lucia to the island of Grenada, but also probably the island of Barbados, were all almost completely submerged.

The geographical position of the current Sainte-Anne peninsula in the south-east of Martinique corresponding with certainty to the refuge area and then the center of dispersal of the Dactyloïdes which dispersed in the Eastern Caribbean to the south of Martinique only (Sainte -Lucia, Saint, Vincent, Grenada, Barbados, even along the coasts of Venezuela, on the islands of Blanquilla, and Bonaire).

Fig

  Fig. 1 :

Fig. 2 :Fig. 3 :

 23 Fig. 2 : Extracts from cartographic works by Stephan, J.F. et al. (1990). Paleogeodynamic maps of the Caribbean. Bulletin n°6

  Fig. 7 : Current distribution (in green) of Dactyloid species in the south of the Eastern Caribbean

8

  Photographs of the author and data on : inaturalist.org/observations/m-bourgade-mkTwo males of the typical Dactyloa roquet species by their features and patterns of their bosses of the southern line of the Sainte-Anne peninsula obviously fighting for a territory.Two males of the Dactyloa roquet species observed by Christophe Auguste 2019, presenting particular phenotype within the line of northwest Martinique with a character remarkable morphological development of their spiny dorsal ridges.Young male Dactyloa roquet, present on islet of Génipa bay (Morne Doré) within of the lineage in central Martinique with a pattern coloring tending towards a bluish tint.

  the Sainte-Anne peninsula line, cradle of the D. roquet species. Female specimen within the line of central Martinique (Balata) with a patternless pattern . Male individual D.roquet observed on the North Atlantic coast of Martinique (Basse-Pointe, within the northwest line) with a black coloration of its head making it more visible its back crest. Male D. roquet observed within the northwest line (St. Pierre), with a crest spiny spine developed. (Photo by Myriam Bouaziz) Male individual observed on the Caravelle peninsula (lineage of central Martinique). Male specimen from the line of southwest Martinique (Anses-d'Arlet). Male specimen observed on Saint-Aubin islet on the North Atlantic coast of Martinique (Trinité) of the line of Dactyloa roquet distributed in the center of the country. Male specimen within the lineage of central Martinique (Balata). Female specimen within the line of southwest Martinique (Anses-d´Arlet) Female specimen within the line of southwest Martinique (Anses-d´Arlet) showing a reddish color, like that of the bark of the tree constituting its habitat, a Red Gum (Bursera simaruba). Male specimen of the Sainte-Anne peninsula line, cradle of the species. Male specimen from the line of southwest Martinique (Vatable, Trois-Ilets). Female specimen of the line from south-west Martinique (Vatable, Trois-Ilets). Male specimen within the lineage of central Martinique, here on the northern flank of the Vauclin Mountain. Female specimen within the lineage of central Martinique, here on the northern flank of the Vauclin Mountain. Females tending to present patterns with line patterns along the back. III. HISTORY OF A DISPERSION SINCE THE EOCENE (-50 My), FROM THE PROTO BASIN OF THE ORINOCO TOWARDS LANDS EMERGING FROM THE PROTO CARIBBEAN, FROM THE ANOLI GENUSES: COMMON ANCESTORS TO DACTYLOA AND CTENONOTUS

Acknowledgments -I warmly thank Ansèl Fong, and David Maceira, biologists from Santiago de Cuba, who since 2013 have encouraged me to persevere in my approach to herpetological and geological research. Thank you, to Christophe Auguste for his observations, and contributions (in prep.) For the highlighting of a particular phenotype of Dactyloa roquet within the line of northwest Martinique presenting a remarkable development of their spiny dorsal crest, as well as Myriam Bouaziz for photo 7. Many thanks also to David Belfan, passionate about nature who informs us and shares his great knowledge of Martinique's biodiversity. My thanks also go to Roger Mauvois for this fundamental information in terms of geology, as well as to Garcin Malsa for his readings and reviews of this manuscript.


Ion Lizarraga

Cédric Giraudet

Fabrizio Croccolo

M Mounir Bou-Ali

Henri Bataller

Mgep Mondragon Goi

Eskola Politeknikoa

Mass diffusion and thermal diffusivity of the decane-pentane mixture under high pressure as a ground-based study for SCCO project

Keywords: mass diffusion, thermal diffusivity, decane-pentane mixture, non-equilibrium fluctuations, high pressure, SCCO, SJ10

Thermodiffusion experiments on iso-massic binary mixture of decane and pentane in the liquid phase have been performed between 25°C and 50°C and for pressures from 1MPa until 20MPa. By dynamic analysis of the light scattered by concentration non-equilibrium fluctuations in the binary mixture we obtained the mass diffusion coefficients of the mixture at each temperature and pressure. For the first time we were able to apply similar analysis to thermal fluctuations thus getting a simultaneous measurement of the thermal diffusivity coefficient. While mass diffusion coefficients decrease linearly with the pressure, thermal diffusivity coefficients increase linearly. In principle the proposed method can be used also for measuring the Soret coefficients at the same time. However, for the present mixture the intensity of the optical signal is limited by the optical contrast factor. This affects our capability of providing a reliable estimate of the Soret coefficient by means of dynamic Shadowgraph. Therefore the mass diffusion coefficients measurements would need to be combined with independent measurements of the thermodiffusion coefficients, e.g. thermogravitational column, to provide Soret coefficients. The obtained values constitute the on-ground reference measurements for one of the mixture studied in the frame of the project SCCO-SJ10, which aims to measure the Soret coefficients of multicomponents mixtures under reservoir conditions. Microgravity experiments will be performed on the Chinese satellite SJ10 launched in April 2016.

Introduction

The precise modelling of the distribution of chemical species in oil and gas reservoirs remains a topical issue for the oil industry, especially now that the reserves of fossil fuels are getting more difficult to extract. It is known that not only gravitational segregation, but also thermodiffusion due to geothermal gradients, are two physical phenomena determining the vertical distribution of species in hydrocarbon reservoirs on Earth [START_REF] Lira-Galeana | Computation of compositional grading in hydrocarbon reservoirs. Application of continuous thermodynamics[END_REF][START_REF] Høier | grading-theory and Practice[END_REF][START_REF] Ghorayeb | Interpretation on the unusual fluid distribution in the Yufutsu gas-condensate field[END_REF][START_REF] Montel | Initial state of petroleum reservoirs: A comprehensive approach[END_REF]). Thermodiffusion, or Soret effect, is a phenomenon that couples heat and mass fluxes [START_REF] De Groot | Nonequilibrium Thermodynamics[END_REF] and can also lead to convective unstable conditions in particular cases [START_REF] Galliero | Understanding compositional grading in petroleum reservoirs thanks to molecular simulations[END_REF]). The contribution of thermodiffusion is difficult to quantify, mainly due to a lack of experimental data as well as accurate modeling for multicomponent mixtures. Although noticeable progresses have been made during the last twenty years, (Assael et al., 2014 and references therein) especially on ternary mixtures both theoretically [START_REF] Firoozabadi | Theoretical model of thermal diffusion factors in multicomponent mixtures[END_REF][START_REF] Kempers | A comprehensive thermodynamic theory of the Soret effect in a multicomponent gas, liquid, or solid[END_REF][START_REF] Galliero | On thermal diffusion in binary and ternary mixtures by non-equilibrium molecular dynamics[END_REF] and experimentally [START_REF] Leahy-Dios | Measurements of molecular and thermal diffusion coefficients in ternary mixtures[END_REF][START_REF] Larrañaga | Soret Coefficients of the Ternary Mixture 1,2,3,4-Tetrahydronaphthalene + Isobutylbenzene + N-Dodecane[END_REF][START_REF] Gebhardt | Soret, thermodiffusion, and mean diffusion coefficients of the ternary mixture ndodecane+ isobutylbenzene+1,2,3,4 tetrahydronaphthalene[END_REF], more work is necessary. Micro-gravity experiments, to avoid gravity-induced convection, are one possible way to provide further data on thermodiffusion in multicomponent mixtures [START_REF] Georis | Proceedings of the European Petroleum Conference[END_REF]Van Vaerenbergh et al., 2009;[START_REF] Touzet | Thermodiffusion: from microgravity experiments to the initial state of petroleum reservoirs[END_REF][START_REF] Bou-Ali | Benchmark values for the Soret, thermodiffusion and molecular diffusion coefficients of the ternary tetralin+isobutylbenzene+n-dodecane with 0.8-0.1-0.1 mass fraction[END_REF]. The Soret Coefficients in Crude Oil (SCCO) project aims at producing values of Soret coefficients of mixture of petroleum interest and in reservoirs conditions. In a first phase carried out in 2007 microgravity experiments were performed on board the Russian satellite FOTON-M3. One binary, two ternaries and one quaternary mixtures were studied (Van Vaerenbergh et al., 2009;[START_REF] Srinivasan | Measurements on thermodiffusion in ternary hydrocarbon mixtures at high pressure[END_REF][START_REF] Touzet | Thermodiffusion: from microgravity experiments to the initial state of petroleum reservoirs[END_REF]. The measurements were compared with molecular dynamics simulations and with theoretical calculations based on the Thermodynamics of Irreversible Processes. However, the conclusions were incomplete because of difficulties encountered during post flight analysis at the laboratories [START_REF] Touzet | Thermodiffusion: from microgravity experiments to the initial state of petroleum reservoirs[END_REF]. Now, on the occasion of the China Sea well explorations, a second phase of the SCCO space experiment has been scheduled. The thermodiffusion behaviour of the binary mixture decane-pentane, the ternary mixture decaneheptane-pentane and the quaternary mixture decane-heptane-pentane-methane, at two pressures and at 50°C, will be studied on-board the Shijian-10 (SJ-10) Chinese satellite during 2016 (Galliero et al., 2015). To assure the success of this new mission, both validating ground measurements and numerical simulations have been planned. In this paper we present results on the iso-massic binary mixture decane-pentane based on the measurement of nonequilibrium (NE) fluctuations.

In general, from the analysis of the dynamics of concentration NE fluctuations by lightscattering it is possible to measure the fluid transport properties coefficients, including the mass diffusion and Soret coefficients, as demonstrated for binary mixtures [START_REF] Croccolo | A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient[END_REF][START_REF] Giraudet | High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations[END_REF]. The technique has been adapted to high pressure [START_REF] Giraudet | High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations[END_REF]. In this work we extend the technique to the analysis of thermal fluctuations thus including the possibility of measuring the thermal diffusivity coefficient of the mixture. Conversely, due to the limited amplitude of the optical signal obtained for this system, we were not able here to measure the Soret coefficient.

The remainder of the paper is organized as follows: Section 2 reports the methodology, in Section 3 we provide results and discussion, and in Section 4 conclusions are drawn.

Methodology

Theoretical background

In a homogeneous multicomponent mixture a temperature gradient induces heat transfer as well as segregation of the components along the temperature gradient by means of the Soret effect (de [START_REF] De Groot | Nonequilibrium Thermodynamics[END_REF]. The segregation induces then Fickean diffusion and the combination of the two phenomena results in a steady concentration gradient which is convection-free only in microgravity conditions or in particular cases on ground. A thermodiffusion experiment on ground is typically performed by applying a stabilizing thermal gradient to a multicomponent fluid mixture, thus obtaining a superposition of the mentioned phenomena. Even if there is no total mass flux in the steady state, thermal and concentration NE fluctuations are always present. NE fluctuations are strictly related to the transport properties of the fluid. That is why from NE fluctuations analysis one can determine in principle all transport coefficients, like viscosity, thermal diffusivity and solutal diffusion and thermodiffusion coefficients. A detailed description of the theory of NE fluctuations can be found in the book by Ortiz de Zárate and Sengers (Ortiz de [START_REF] Zárate | Hydrodynamic Fluctuations in Fluids and Fluid Mixtures[END_REF].

Here we briefly recall the essential equations that will be used in the following.

In a binary mixture, the temporal correlation function of NE concentration fluctuations induced by the Soret effect is expected to be a single exponential decay for all wave vectors, with time constants ) (q S varying as a function of the wave vector q. For wave vectors much larger than a characteristic value * s q , the decay time is the solutal diffusive one:

) /( 1 ) ( 2 Dq q S , (Eq. 1)
where D is the mass diffusion coefficient. NE thermal fluctuations are faster and overlap to the solutal ones. For wave vectors larger than a thermal characteristic wave vector * T q , the decay time is the thermal diffusive one:

) /( 1 ) ( q q T , (Eq. 2)
where is the thermal diffusivity coefficient.

Experimental set-up

Our thermodiffusion cell (Fig. 1 of [START_REF] Giraudet | High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations[END_REF] Experiments have been performed with the iso-massic binary mixture of decane (Sigma-Aldrich, 99%) and pentane (Sigma-Aldrich, 99%). Components were used without further purification. The mixture is prepared in a bottle by weighting on a balance (Sartorius, TE313S, resolution 10 -2 g/200g) first the decane and then the pentane. The bottle is carefully closed by cover with Teflon sealing. Error in mass fraction is estimated less than 0.0001.

The filling system consists of: a rotary vacuum pump able to evacuate most of the air from the cell before filling operations down to a residual pressure of about 10Pa; a fluid vessel at atmospheric pressure; a manual volumetric pump and a number of valves to facilitate the procedure. Briefly, after a low vacuum is made inside the cell, the mixture to be studied is transferred to the cell by acting on the volumetric pump. Visual check allows avoiding bubbles during the injection procedure. After that, the cell is abundantly fluxed with the fluid mixture. At the end of the procedure a valve is closed and the volumetric pump is operated to modify the liquid pressure within the cell. A manometer (Keller, PAA-33X, pressure range: 0.1÷100MPa, precision ±0.04MPa) is connected between the volumetric pump and the cell to measure the pressure of the fluid mixture. A second identical manometer is connected to the outlet of the cell. The manometer signals are transferred using an acquisition card (National Instruments, NI 9215) interfaced to a computer. We perform our experiments by imposing a difference of temperature T on the horizontally positioned thin cell, previously filled with the homogenous fluid mixture.

In order to investigate NE fluctuations, it is common to use a scattering in the near field technique as the Shadowgraph [START_REF] Wu | Thermally induced fluctuations below the onset of the Rayleigh-Bénard convection[END_REF], for which the physical optics treatment was given by [START_REF] Trainoff | Physical optics treatment of the shadowgraph[END_REF] and [START_REF] Croccolo | Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren[END_REF]. The shadowgraph optical setup involves a low coherence light source (Super Lumen, SLD-MS-261-MP2-SM, = 675 13nm) that illuminates the bottom of the cell through a single-mode fiber. The diverging beam exiting from the fiber end is collimated by an achromatic doublet lens (f = 150mm, =50.8mm) and then passes through a linear film polarizer. In combination with a second linear polarizer after the cell the latter allows us to adapt the average light intensity.

The detection plane is located at about z = 95mm from the sample plane. As a sensor, we use a charge coupled device (AVT, PIKE-F421B) with 2048 2048 square pixels each of size 7.4 7.4µm 2 and a dynamic range of 14-bit. Images were cropped within a 768x768pix² in order to reach the maximum acquisition frame rate of the camera of about 30Hz.

Dynamic near-field imaging

Images acquired by means of a near-field scattering setup consist of an intensity map , I x t generated by the interference on the CCD plane between the portion of the incident beam that has passed undisturbed through the sample and the beams scattered by refractive index fluctuations occurring within the sample [START_REF] Trainoff | Physical optics treatment of the shadowgraph[END_REF][START_REF] Croccolo | Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren[END_REF]. Statistical analysis involving fast Fourier transforms provides accurate measurements of the intensity , s I q t of light scattered at each wave vector q grabbed by the optical setup and for all the times t of the acquisition sequence. Different setups show different responses to the acquired signal as a function of the wave number q, which is described by the so-called transfer function T q . Details of the quantitative dynamic analysis can be found elsewhere (Croccolo et al., 2006a;Croccolo et al., 2006b;[START_REF] Croccolo | Non-diffusive decay of gradient driven fluctuations in a free-diffusion process[END_REF][START_REF] Cerchiari | Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit[END_REF]. Here we just recall that the quantity directly obtained from the experiments is the so-called structure function 2 , ,

t q I t q C m m
, that is obtained by averaging (over all available times t in each image dataset and over the wave vector q azimuthal angle) the individual spatial Fourier transforms of the shadowgraph image differences, like the one shown in the example of Fig.

q B t q ISF q T q S t q C m , 1 2 , , (Eq.3)
with 1 0 , q ISF . In Eq.3, q S is the static power spectrum of the sample, q T is the optical transfer function and q B the background noise of the measurement. It is implicitly assumed in Eq.3 that the linear response of the CCD detector and any other electronic or electromagnetic proportionality parameters are aggregated inside T q and/or B q .

Results and Discussion

Thermodynamic conditions

To determine the thermodynamic conditions of the study, we have calculated, with TOTAL S.A. company BEST software, the biphasic envelop and critical coordinates of the iso-massic binary mixture of decane and pentane. For a given pressure P and a given temperature T, the software calculates the possible molar volumes v from the PPR78 equation of state [START_REF] Peng | A new two-constant equation of state[END_REF]. In Fig. 2 we report the calculated biphasic envelop. this temperature. Initially, a temperature difference of 20°C was applied to the system. To increase the optical signal, which remains low as revealed by Fig. 1b-c, we applied a temperature difference of 30°C. In all the investigated conditions the mixture was in its liquid state, even at low pressure and for temperature differences of T = 20 and 30°C. The red point in Fig. 2 indicates the thermodynamic conditions of the thermodiffusion experiment shown in Fig. 1, 3 and 4 (Tmean = 50°C, P = 20 MPa).

Structure function

At each investigated T and pressure P, 10 different image acquisition runs have been performed with a delay time dtmin = 35ms between two consecutive images. Each set, containing 2000 has then been processed on a dedicated PC by means of a custommade CUDA/C++ software [START_REF] Cerchiari | Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit[END_REF], in order to perform a fast parallel processing of the images to obtain the structure functions

t q C m ,
, for all the wave numbers and for all the correlation times accessible within the image datasets. In each experiment the temperature gradient is applied via two distinct temperature controllers, so that a linear temperature gradient sets up in some tens of seconds. The image acquisition is started about five hours later, to be sure that the concentration gradient due to the Soret effect is fully developed within the cell.

In Fig. 3 we present the mean structure function (a) as a function of the wave vector q for different correlation times t and (b) as a function of the correlation time t for different wave vectors q (Tmean = 50°C, P = 20MPa, T = 30°C).

Fig. 3a shows that for wave numbers q > 400cm -1 , the signal is completely lost in the background noise. For intermediate wave numbers, Fig. 3b shows that the time dependence of the structure function cannot be totally assumed mono-exponential, as it is visible for wave numbers q = 134cm -1 and 201cm -1 . To account for the solutal relaxation mode plus the thermal relaxation mode, we therefore decided to perform a quantitative analysis of the experimental structure functions by modeling the ISF as a double exponential decay, namely:

1 2 , exp 1 exp , t t ISF q t a a q q (Eq. 4)
where 1 and 2 are two relaxation times. Hence, we performed fittings of the experimental t q C m , as a function of t (see Fig. 3b) by substituting Eq.4 into Eq.3 and adopting as fitting parameters: the product q T q S , the background B q , the relative amplitude a, and the two decay times, 1 and 2. For the fitting procedure we used a Levenberg-Marquardt Non-Linear Least Square fitting algorithm. Eq.1 and the red solid line represents the theoretical relaxation times 2 / 1 q of Eq.2.

In Fig. 4 we show the two decay times obtained from modeling the ISF by Eq.4, as a function of the wave number. The horizontal dashed blue line corresponds to dtmin = 35ms, which is the physical limit of our experimental recording equipment.

Intuitively, we assumed that the fastest mode was associated with a thermal mode and the slowest to a solutal mode.

In the range of wave numbers 1 1 200 100 cm q cm (vertical dotted lines are plotted in Fig. 4 to guide the reader) the slowest mode was fitted with Eq.1 using D as free parameter and the fastest was fitted with Eq.2 using as free parameter. The results of the adjustments are reported by continuous lines in Fig. 4. For example, referring to the conditions of Fig. 4 (P = 20MPa, Tmean = 50°C) the two values obtained by fitting are D = (38 4)x10 -6 cm 2 /s and = (870 40)x10 -6 cm 2 /s. Uncertainties are the average of the deviations respect to the mean value of the 10 measurements.

Mass diffusion and thermal diffusivity coefficients

In Fig. 5 we report the values of mass diffusion and thermal diffusivity coefficients as a function of the pressure obtained for the iso-massic binary mixture of decane and pentane, at Tmean = 25°C and for a temperature difference T = 20°C. We found only one reference value of the mass diffusion coefficients at atmospheric pressure (Alonso De Mezquia et al., 2012) that we reported in Fig. 5a as a red point. The thermal In Fig. 5a we can notice a slight linear decrease in the mass diffusion coefficient with pressure that is consistent with an increase of the viscosity with pressure (mass diffusion coefficient being proportional to the inverse of the viscosity), as it has been shown in Alonso De Mezquia et al., 2012. Also in Fig. 5b we can see a linear increase in the thermal diffusivity coefficients with pressure that is consistent with an increase of density with pressure.

In Figure 6 we report the values of mass diffusion and thermal diffusivity coefficients as a function of the mean temperature obtained for the iso-massic binary mixture of decane and at P = 20MPa and for a temperature difference T = 30°C. In Fig. 6a we can see that the mass diffusion coefficient increases with the mean temperature, which is consistent with a decrease of the viscosity of the system with the mean temperature.

In Fig. 6b we can see that the thermal diffusivity coefficient decreases with the mean temperature. Again an overestimate of the reference values is

In Fig. 7 we report the values of diffusion and thermal diffusivity coefficients as a function of the pressure obtained for the iso-massic binary mixture of decane and pentane, at The resulting values at 50°C can be directly compared to measurements made in microgravity in the frame of the SCCO-SJ10 project.

  is specifically designed for applying a vertical temperature gradient with excellent thermal homogeneity and stability to a horizontal slab of a multicomponent fluid under high pressure while providing vertical optical access to a central area of the cell. The cell core consists of a stainless steel annulus of internal/external diameter 30/75mm with high pressure inlet and outlet at its opposite sides. This part accommodates Teflon®-coated Viton® O-rings for sealing, and square sapphire plates kept at a distance L = 5mm by the annulus itself, thus defining the sample thickness. In order to minimize the contact between the liquid sample and the conductive metal a Teflon annulus (internal/external diameter 19.8/30mm) with two thin holes (diameter 1mm) for inlet/outlet of the fluid has been inserted in the inner part of the stainless annulus zone. The external sides of the sapphire windows are in thermal contact with two aluminium plates with a central circular aperture (d=13mm), where two thermistors (Wavelenght Electronics, TCS651) are installed to monitor the sapphire temperatures. External to the aluminium plates, two Peltier elements (Kryotherm, TB-109-1.4-1.5 CH) with central circular aperture (d=13mm) provide/remove the heat necessary to maintain the set-point temperature as driven by two temperature controllers (Wavelenght Electronics, LFI-3751) maintaining the temperature of the internal side of each Peltier device with a stability better than 1mK RMS over 1 day. Finally, external to the Peltier elements, two aluminium plates are flushed with water coming from a thermostatic bath (Huber, ministat 125) to remove the excess heat of the Peltiers.

Figure 1 :

 1 Figure 1: Results of a near field scattering experiment (shadowgraph layout) on the iso-

  1. This experimental structure function is theoretically related to the temporal correlation function of NE composition fluctuations, also called intermediate scattering function (ISF), by:

Figure 2 :

 2 Figure 2: Phase diagram of the isomassic binary mixture decane-pentane: the continuous

  Figure 3: Experimental structure function t q C m ,

Figure 4 :

 4 Figure 4: Experimental decay times of NE fluctuations as obtained by fitting through Eqs.3

Figure 5 :

 5 Figure 5: Mass diffusion D and thermal diffusivity coefficients as a function of the pressure

  compared with values found in NIST data base(NIST website) and reported by a red continuous line in Fig.5b. Our values slightly overestimate reference values. However, over the entire pressure range studied, the relative deviation of the thermal diffusivity coefficients values does not exceed 5%. These results validate our hypothesis for the interpretation of the modes of the measured intermediate scattering function, namely that the fastest mode is the thermal relaxation mode of NE fluctuations and the slowest a mass relaxation mode.

Figure 6 :

 6 Figure 6: Mass diffusion D and thermal diffusivity coefficients as a function of the mean

  Tmean = 50°C and for a temperature difference T = 30°C. The same trends as for Fig.5are observed.

Figure 7 :

 7 Figure 7: Mass diffusion D and thermal diffusivity coefficients as a function of the pressure

Acknowledgements

This work has been supported by the European Space Agency through the SCCO project. Support from the French space agency CNES is also acknowledged. We thank TOTAL S.A.

for allowing the use of the BEST software and Research Groups (No. IT1009-16) and TERDISOMEZ (No. FIS2014-58950-C2-1-P) of MINECO.

Data

Ref