Dany Kao

Alain Chaintreau

Jean-Pierre Lepoittevin

Elena Giménez- Arnau

Mechanistic studies on the reactivity of sensitizing allylic hydroperoxides: investigation on the covalent modification of amino acids by carbon-radical intermediates

Many fragrance terpenes autoxidize yielding allylic hydroperoxides that are strong skin allergens. These chemicals are supposed to bind through radical reactions to proteins in the skin to start the immunotoxic process characterizing skin sensitization, and further allergic contact dermatitis. In order to get more insight into this reactivity, we investigated the chemical behavior of the allylic hydroperoxides responsible for the allergenicity of autoxidized limonene and linalool. We studied by liquid chromatography-mass spectrometry the reactivity in Fe(II)/Fe(III) systems, able to degrade peroxides in vivo, toward amino acids prone to radical reactions, together with glutathione. We validated that carbon radicals issued from these compounds alter directly the lateral chain of some of the amino acids tested forming adducts via radical processes. Though, in parallel, due to the high oxidative strength of the media, we show that redox processes can also be induced and engender chemical modifications on the amino acids themselves. Amino acids chemically modified by the oxidant stress can then react with radicals issued from the hydroperoxides through what we call a "non-direct" reactivity process. Understanding protein binding processes to allergenic allylic hydroperoxides needs thus to consider both, covalent binding of carbon radicals to the amino acids, and additional oxido-reduction processes contributing to their sensitizing potential.

Introduction

Allergic contact dermatitis is an important occupational and environmental health issue. It is a delayed-type hypersensitivity reaction induced by skin contacts with xenobiotic substances, and is the most frequent expression of immunotoxicity in humans. [START_REF] Kimber | Allergic contact dermatitis[END_REF][START_REF] Rustemeyer | Mechanisms of irritant and allergic contact dermatitis[END_REF] Chemical allergens are unable themselves to stimulate an adaptive immune response. Immunogenicity is attained by formation of stable protein conjugates that will be recognized and processed for further presentation to the immune system. Most contact allergens contain the chemical function necessary to react with skin proteins and this way allow the formation of the immunogenic-antigenic complex. [START_REF] Lepoittevin | Molecular aspects in allergic and irritant contact dermatitis[END_REF] Though, there are also other allergens that are non-sensitizers originally, non-protein reactive, that become reactive species through metabolic activation in the skin, known as prohaptens, or under simple oxidation, for prehaptens. [START_REF] Lepoittevin | Metabolism versus chemical transformation or proversus prehaptens?[END_REF] These chemicals account for at least one third of known allergens today.

Terpenes are widespread fragrance compounds of natural origin, used in the production of fine perfumes, fragranced cosmetics, household and industrial products. Some of them behave as prehaptens, as they autoxidize easily to form clear allergenic allylic hydroperoxides. This is the case for R-(+)limonene 1 and for linalool 2, forming 3 and 4 respectively (Scheme 1). [START_REF] Karlberg | Hydroperoxides in oxidized d-limonene identified as potent contact allergens[END_REF][START_REF] Skold | Contact allergens formed on air exposure of linalool. Identification and quantification of primary and secondary oxidation products and the effect on skin sensitization[END_REF] Scheme 1 Chemical structures of R-(+)-limonene 1, linalool 2, 2hydroperoxylimonene 3 and 7-hydroperoxy-3,7-dimethylocta-1,5-dien-3-ol 4.

We know that, to be immunogenic, these hydroperoxides must react with proteins in the skin most probably via mechanisms involving radical intermediates. [START_REF] Karlberg | Allergic contact dermatitis-Formation, structural requirements, and reactivity of skin sensitizers[END_REF] Cleavage of the hydroperoxide O-O/O-H bonds, having bond dissociation energies that are relatively weak (175 and 368 kJ mol -1 ), [START_REF] Luo | BDEs of O-X bonds[END_REF] affords alkoxyl RO• and peroxyl ROO• radicals, which rapidly can lead to the formation of carbon-centered radicals R• via intramolecular cyclization, fragmentation or hydrogen abstraction. [START_REF] Giménez-Arnau | Identification of radical species derived from allergenic 15hydroperoxyabietic acid and insights into the behavior of cyclic tertiary allylic hydroperoxides in Fe(II)/Fe(III) systems[END_REF] Carbon-radical reactive intermediates derived from these xenobiotics could thus have an important role in damaging biomolecules. Supporting this hypothesis, clinical studies on allergenic hydroperoxides of different chemical structures show that allergic responses are specific. This indicates that specific antigens formed from particular radicals derived from each hydroperoxide must be responsible for the allergenic activity. [START_REF] Brared-Christensson | Hydroperoxides form specific antigens in contact allergy[END_REF] We have reported previously the identification and possible involvement in allergic contact dermatitis of carbon-centered radicals R• derived from allylic hydroperoxides using chemical traps. [START_REF] Giménez-Arnau | Identification of radical species derived from allergenic 15hydroperoxyabietic acid and insights into the behavior of cyclic tertiary allylic hydroperoxides in Fe(II)/Fe(III) systems[END_REF][START_REF] Bezard | Identification of carbon-centred radicals derived from linalyl hydroperoxide, a strong skin sensitizer: a possible route for protein modifications[END_REF][START_REF] Giménez-Arnau | Identification of alkyl radicals derived from an allergenic cyclic tertiary allylic hydroperoxide by combined use of radical trapping and ESR studies[END_REF] Recently, we examined the formation of carbon R• intermediates derived from 3 and 4 by using spin-trapping-EPR spectroscopy. [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF][START_REF] Johansson | Carbon-and oxygen-centered radicals are equally important haptens of allylic hydroperoxides in allergic contact dermatitis[END_REF] Radical initiation by using Fe(II)/Fe(III) confirmed the formation of oxygenated RO•/ROO• and carbon-

1 OH 2 3 OOH OH 4 OOH O 2 O 2
centered R• free radicals derived from these hydroperoxides. To first approach the reactivity of these species with amino acids, we demonstrated, using liquid chromatography combined to mass spectrometry (LC/MS), the formation of adducts via radical mechanisms between R• derived from the hydroperoxides and N-acetyl-histidine methyl ester. [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] To complement these studies, and based on knowledge we have acquired on radical formation from the spin-trapping-EPR spectroscopy analyses, we now report potential additional terpene-amino acid adducts obtained by reaction of 3 and 4 with several amino acids prone to radical reactions, together with reactivity toward glutathione (GSH). A Fe(II) or Fe(III) source was used as initiator of the radical reactions because of the known role in the degradation of peroxides in vivo. [START_REF] Szpilman | Iron(II)-induced degradation of antimalarial β-sulfonyl endoperoxides. Evidence for the generation of potentially cytotoxic carbocations[END_REF] Reactivity was followed by liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS/MS).

Studies reported here give additional information on basic chemical mechanisms that could explain the reactivity of allylic hydroperoxides toward proteins and thus their sensitizing potential. The long-term effect of this research shall be further exact elucidation of the different potentially immunogenic protein chemical modifications.

Experimental section

Caution: Skin contact with allylic hydroperoxides must be avoided because they are skin-sensitizing substances.

Chemicals

Compounds 3 and 4 were synthesized using procedures we have reported previously. [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] N-Acetyl-cysteine methyl ester (N-Ac-Cys-OMe), N-acetyl-tyrosine ethyl ester (N-Ac-Tyr-OEt), N-acetyl-tryptophan ethyl ester (N-Ac-Trp-OEt), and GSH were purchased from Sigma-Aldrich (France) and N-acetyl-lysine methyl ester (N-Ac-Lys-OMe) from Bachem (Germany). The amine and carboxyl groups of the amino acids were protected to mimic the structure as part of a protein sequence, and to avoid the reactivity of the amine terminus with hydroperoxide decomposition products having carbonyl groups (Schiff base formation). Each amino acid specific side-chain was thus available for reaction. All other reagents and solvents were obtained from commercial sources and used as received. Spectrophotometric grade acetonitrile (99.8 %) was used, and aqueous solutions were prepared with deionized water. Reactions were conducted in flame-dried glassware, under inert atmosphere of argon, and with previously deaerated solvents.

Instrumentation

LC-ESI-MS/MS analyses were performed using an ion trap mass Bruker HCT Ultra spectrometer or an Agilent QToF spectrometer. Both instruments were connected to an Agilent 1200SL-RRLC HPLC system. The HPLC system was equipped with a binary pump, an automatic sample injector and a diode array absorbance detector scanning 190 to 700 nm. The samples were subjected to reverse phase chromatography on C18 columns (Thermo Hypersil Gold, 1 × 100 mm, 1.9 µm particle size; 1 × 30 mm, 1.9 µm particle size; Supelco Discovery, 2 × 250 mm, 5 µm particle size) at a flow rate of 0.2 mL/min. They were eluted from the column using a mobile phase A (0.01% formic acid in H 2 O) and a mobile phase B (acetonitrile) with a gradient. The gradient started at 2% B and was increased to 90% B after 20 min, was at 90% B during 10 min, and was decreased again to 2% B for the last 10 min. After passing through the diode array absorbance detector, the eluent was directed to the connected ion trap mass spectrometer with a standard electrospray source. The ionization method used was ESI in the positive ion mode (heated capillary temperature 300°C, gas flow 8 L/min, nebulizer gas 40 psi). Full scan mass spectra were acquired in the profile mode scanning m/z 50 to 1000. For the ESI-MS/MS studies, the mass spectrometer was equipped with the ESI source used for ESI-MS studies described above and with the same source parameter settings. The ionization mode was ESI in the positive ion mode. The isolation width was 4 m/z. Data were processed using Agilent MassHunter Qualitative Analysis software. Only molecular ions detected by LC-ESI-MS having an m/z value in agreement with potential adducts were considered as molecular species provided that they were relatively abundant. Even if unlikely, the eventuality of these ions being fragments of other molecular species cannot be excluded. [START_REF] Kimber | Allergic contact dermatitis[END_REF] H and [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C NMR were recorded on a Bruker Avance 300 spectrometer ( 1 H, 300 MHz; [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C, 75 MHz). Two-dimensional 1 H- [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C NMR experiments HSQC (heteronuclear single-quantum correlation) and HMBC (heteronuclear multiple-bond correlation) were recorded on a Bruker Avance 400 spectrometer ( 1 H, 400 MHz; [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C, 100 MHz). Chemical shifts (δ) are reported in ppm and are referenced to TMS via the solvent signal (CDCl 3 : δ 1 H = 7.26, δ 13 C = 77.0).

Reactivity studies: general procedure

Hydroperoxide 3 (300 mg, 1.78 mmol) or 4 (140 mg, 0.76 mmol) were dissolved in deareated 1:1 (v/v) H 2 O/acetonitrile (100 mL for 3, 50 mL for 4). The amino acids or GSH (2 equiv) were added, together with a catalytic amount (0.1 equiv) of FeCl 3 (Fe(III) source) or FeSO 4 heptahydrate (Fe(II) source). The reaction mixtures were continuously stirred at room temperature, and kept under argon atmosphere to minimize competing reactions with oxygen. Reactions were monitored by TLC (0.25 mm silica gel plates; 60F 254 ). After migration, TLC plates were inspected under UV light (254 nm), then sprayed with a solution containing phosphomolybdic acid (5 g), cerium (IV) sulfate (2 g) and sulphuric acid (12 mL) in H 2 O (188 mL), or a solution containing p-anisaldehyde (0.5 mL), oanisaldehyde (0.5 mL), sulphuric acid (5 mL) and ethanol (8 mL) in acetic acid (100 mL), followed by heating. Reactions were stopped after 7 days if the starting hydroperoxides were still present in the reaction mixtures and the reactions did not evolve after that time. The mixtures were filtered on Celite (Celite 545) in order to remove iron salts. The solvent was removed under reduced pressure. The crude products were analyzed by LC-ESI-MS associated with ESI-MS/MS. Only in the case of the reaction with N-Ac-Cys-OMe the crude product could be fractionated by column chromatography on silica gel (Geduran® 60, 40-63 mm), in order to try to elucidate its nature by NMR (Supplementary Information data).

Results and discussion

Reactivity with N-Ac-Cys-OMe

Cysteine is one of the most labile residues involved in radical reactions induced by peroxides. Gardner et al. proposed a radical mechanism for the reaction, catalyzed by FeCl 3 , of linoleic acid hydroperoxide with N-Ac-Cys. Reaction products resulted from a thio-bond formation between the thiyl radical derived from the side-chain of cysteine and a carbon-centered radical derived from the hydroperoxide. [START_REF] Gardner | Addition of Nacetylcysteine to linoleic acid hydroperoxide[END_REF][START_REF] Gardner | The epoxyallylic radical from homolysis and rearrangement of methyl linoleate hydroperoxide combines with the thiyl radical of N-acetylcysteine[END_REF] As in our studies, reactions were carried out in argon atmosphere to minimize the competing reaction with oxygen and assure higher formation of adducts. [START_REF] Gardner | The epoxyallylic radical from homolysis and rearrangement of methyl linoleate hydroperoxide combines with the thiyl radical of N-acetylcysteine[END_REF][START_REF] Gardner | Degradation of linoleic acid hydroperoxides by a cysteine . FeCl3 catalyst as a model for similar biochemical reactions. I. Study of oxygen requirement, catalyst and effect of pH[END_REF] This was also described for the Fe(II)/Fe(III) mediated chemistry of artemisinin and synthetic 1,2,4-trioxanes with GSH. [START_REF] Singh | Chemistry of 1,2,4-trioxanes relevant to their mechanism of action. Part 1: Reaction with Fe(II) salts[END_REF] Allylic hydroperoxide 3. Compound 3 was totally consumed within one hour when incubated with N-Ac-Cys-OMe. When the reaction was initiated with FeCl 3 , LC-MS of the crude product showed one major peak with an associated m/z of 353 corresponding to the cysteine disulfide dimer 5 (Fig. 1), and two other peaks with m/z 328 and 344. MS fragmentation of 328 showed a fragment ion at m/z 178 due to the loss of N-Ac-Cys-OMe. Mechanistically, cysteine is known to reduce Fe(III), and hydroperoxides to oxidize Fe(II). Under reduction of Fe(III) thiyl radicals are formed, and Fe(II) can then generate RO• radicals through a Fenton-like reaction. As we have shown previously with a monocyclic hydroperoxide model, these RO• are able to perform allylic hydrogen abstraction. [START_REF] Giménez-Arnau | Identification of radical species derived from allergenic 15hydroperoxyabietic acid and insights into the behavior of cyclic tertiary allylic hydroperoxides in Fe(II)/Fe(III) systems[END_REF] In the case herein, most labile protons are those in position α to the double bonds, as the carbon-centered radical so formed would have been stabilized by resonance. Hydrogen abstraction being thus possible from positions 4 and 5, structures 6a and 6b can be suggested (Fig. 1). The value of the [M+H] + molecular ion at m/z 344 corresponds to a mass increment of 16 from m/z 328, and could thus match with hydroperoxide analogues 7a/7b.

Exceptionally in this single case, we could perform some NMR analysis. For all other reactions described in this manuscript, isolation of products in the very complex mixtures was no longer possible and NMR analysis could not be performed. Two fractions were isolated from the crude product by column chromatography on silica gel (acetone/pentane 1:9, acetone/pentane 2:8). One corresponded to the cysteine disulfide dimer 5. HSQC experiments showed two protons at 3.19 ppm correlated to a carbon atom at 40.7 ppm, δ characteristic of the -CH 2 in position α to the disulfide bond (Supplementary Information data). NMR analysis of the second fraction suggested the formation of two diasteromers. 1 H- [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C NMR HSQC and HMBC data revealed that the vinyl group and the isoprenyl group of 3 had been preserved during the reaction. The experiments also suggested the replacement of the initial hydroperoxide methylallyl group of 3 by a secondary alcohol methylallyl function, confirming the preservation of the menthene ring. Finally, there was a cysteine unit linked as the characteristic δ of the -CH 2 in position α to the thiol group of the side-chain at 27.2 ppm shifted to 34.9 ppm with protons at 2.96/3.10 ppm (Supplementary Information data). The NMR information was in agreement with adducts 6a/6b (Fig. 1), for which two diasteromers are possible. The ipso hydrogen atom to the hydroxyl group and the methyl groups being preserved, hydrogen abstraction could only be from positions 4 and 5 affording 6a and 6b respectively. However, NMR data did not help to discriminate between the two regioisomers 6a and 6b, even if NMR 1 H and [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF] C δ of the isoprenyl group should be slightly different depending on the sulfur atom fixing position. As we have described previously, 9 a suggestion for the formation of 6a, applicable also for 6b, is given in Scheme 2. 20 In the reaction initiated with FeSO 4 , the LC-MS profile of the crude product was somewhat different (Fig. 2a). Disulfide dimer 5 was not the major species, and two significant peaks with [M+H] + molecular ion at m/z 328 appeared at t R 2.5 and 2.7 min. ESI-MS/MS of the peak at t R 2.5 min was identical to the one obtained in the reaction with FeCl 3 and was attributed to 6a/6b. However, m/z 328 can also fit with epoxide 8 (Fig. 1), explaining this way the second peak at 2.7 min. ESI-MS/MS of the signal at t R 2.7 min showed fragments at m/z 178 and 144 typical from the loss of N-Ac-Cys-OMe. [START_REF] Perfetti | Neurotoxic thioether adducts of 3,4-methylenedioxymethamphetamine identified in human urine after ectasy ingestion[END_REF] Mechanistically, the hydroperoxide is now able to oxidize Fe(II) to Fe(III) generating RO• radicals. These, due to the presence of the allylic double bond, have been shown to undergo under these experimental conditions a fast cyclization to give α-oxiranylcarbinyl radicals that can be trapped by the lateral chain of N-Ac-Cys-OMe and afford 8. [START_REF] Giménez-Arnau | Identification of radical species derived from allergenic 15hydroperoxyabietic acid and insights into the behavior of cyclic tertiary allylic hydroperoxides in Fe(II)/Fe(III) systems[END_REF][START_REF] Grossi | Oxiranylcarbinyl radicals from allyloxyl radical cyclization: characterization and kinetic information via ESR spectroscopy[END_REF] Indirect evidence of the formation of 8 was given by a tiny peak at t R 1.8 min with a m/z associated value of 346. The mass increment of 18 with regard to m/z 328 corresponded to the addition of H 2 O. ESI-MS/MS fragmentation was in agreement with compound 9 (Fig. 2b). It may then be suggested that nucleophilic addition of H 2 O, present in the reaction solvent, on the electrophilic epoxide 8 afforded 9. Adducts 7a/7b were identified at t R 2.4 min. Another molecular ion (m/z 355) producing a m/z 178 fragment (loss of N-Ac-Cys-OMe) was identified but the structure could not be assigned.

Allylic hydroperoxide 4.

Compound 4 needed few hours to react completely with N-Ac-Cys-OMe. Regardless of the experimental conditions used, prevailing oxidation of cysteine to form 5 was observed, together with a LC peak with m/z 330. On the other hand, only with Fe(II) compounds with m/z 346 and m/z 364 were detected. ESI-MS/MS of all the signals released the characteristic amino acid fragment at m/z 144 (Fig. 3). Based on the mechanisms discussed for the reactivity of hydroperoxide 3, structures 10 and 11 matched with m/z 346, and 12 with m/z 364. Unlike 3, allylic hydrogen abstraction is here possible at a single position, forming compound 10. The fact that 12 was observed only with Fe(II) was again in agreement with the favored formation of α-oxiranylcarbinyl radicals in these experimental conditions, at the origin of compound 11. For the first time β-scission of initially obtained RO• radicals could be suggested (Scheme 3), as m/z 330 matched well with 13 and ESI-MS/MS analysis gave a consistent fragmentation (Fig. 3). Observations on the results. Reactivity studies of 3 with N-Ac-Cys-OMe have been already reported in the literature. [START_REF] Johansson | Mechanistic proposal for the formation of specific immunogenic complexes via a radical pathway: a key step in allergic contact dermatitis to olefinic hydroperoxides[END_REF] Our studies bring some more new information on this reactivity, complemented with that of hydroperoxide 4. Previously, the reactivity of 3 with N-Ac-Cys-OMe in the presence of 5,10,15,20-tetraphenyl-21H,23H-porphyrin iron (III) chloride was studied by LC-MS. Adducts different from the ones we report here were described. [START_REF] Johansson | Mechanistic proposal for the formation of specific immunogenic complexes via a radical pathway: a key step in allergic contact dermatitis to olefinic hydroperoxides[END_REF] The authors observed also LC-MS peaks with m/z 328 and 344. They showed that 3 evolves easily to the formation of carvone in the presence of iron, [START_REF] Johansson | Carbon-and oxygen-centered radicals are equally important haptens of allylic hydroperoxides in allergic contact dermatitis[END_REF] and proved thus accurately the formation of adducts by addition of the thiol group of cysteine either to the endocyclic bond of carvone or to the double bond of its isoprenyl group through a 2-electron reaction pathway, adducts having m/z 328. In our studies, adducts with m/z 328 were in agreement with 6a/6b (Fig. 1), where the isoprenyl group had been preserved and the hydroperoxide methylallyl group replaced by a secondary alcohol methylallyl function (Supplementary Information data). Data agreed with the formation of a RO• radical further performing allylic hydrogen abstraction. We showed this kind of reactivity in earlier studies using a monocyclic 15hydroperoxyabietic acide-like compound as model of allergenic hydroperoxide. [START_REF] Giménez-Arnau | Identification of radical species derived from allergenic 15hydroperoxyabietic acid and insights into the behavior of cyclic tertiary allylic hydroperoxides in Fe(II)/Fe(III) systems[END_REF] We also suggest the formation of 8, converted into observed compound 9 (m/z 346) after opening of the epoxide function by attack of H 2 O. The fact that we characterized these adducts does not exclude the addition of cysteine on carvone. The experimental conditions being different, all kind of adducts should be pondered. For m/z 344, structures derived also from carvone were proposed, from addition of the thiol group to the endocyclic or to the double bond of the isoprenyl group with oxidation/epoxidation of either one double bond or the other (m/z 344=N-Ac-Cys-OMe+carvone+O). It was considered that the increment of m/z 16 (+O) could not fit with an OOH group as all starting material was consumed. However, it is known that the mechanism for the O-O bond cleavage of hydroperoxides by Fe(III) porphyrin complexes can induce the presence of RO• and ROO• radicals simultaneously in the reaction media. [START_REF] Labeque | Homolytic and heterolytic scission of organic hydroperoxides by (meso-tetraphenylporphinato) iron(III) and its relation to olefin epoxidation[END_REF][START_REF] Traylor | Reactions of hydroperoxides with iron(III) porphyrins: heterolytic cleavage followed by hydroperoxide oxidation[END_REF] Even if there is no a clear agreement on the mechanism, Traylor et al. proposed a heterolytic O-O cleavage, followed by a fast side reaction between a so formed highvalent Fe(IV) oxo porphyrin cation radical intermediate and the hydroperoxide, resulting in the formation of both RO• and ROO• radicals. [START_REF] Traylor | High-yield epoxidations with hydrogen peroxide and tert-butyl hydroperoxide catalyzed by iron(III) porphyrins: heterolytic cleavage of hydroperoxides[END_REF] Our previous EPR studies on the formation of radicals from 3 in iron systems confirmed indeed the coexistence of both kind of radicals in the solutions. [START_REF] Kao | Synthesis of allylic hydroperoxides and EPR spin-trapping studies on the formation of radicals in iron systems as potential initiators of the sensitizing pathway[END_REF][START_REF] Johansson | Carbon-and oxygen-centered radicals are equally important haptens of allylic hydroperoxides in allergic contact dermatitis[END_REF] Through a similar mechanism to that depicted in Scheme 2 for RO• radicals, the so formed ROO• could form carbon radical species via abstraction of allylic hydrogen. In the present studies, this was confirmed by the potential obtention of 7a/7b with m/z 344. Looking all in all at these results, it seems clear that distinct adducts can be formed due to the complex redox mechanisms involved in the reactions. It is thus possible that in our experiments small amounts of adducts described elsewhere had also been formed but could not be identified. The same kind of chemistry outlined for 3 was applicable to 4. The formation of adducts through reaction of the thiol group resulted from allylic hydrogen abstraction, possible at one single position (adduct 10), and from the formation of αoxiranylcarbinyl radicals with further opening of the epoxide cycle (adducts 11, 12). Interestingly in the case of 4, the acyclic chemical structure could allow β-scisssion of the RO• radicals (adduct 13), this process being favoured with Fe(III).

Reactivity with N-Ac-Trp-OEt

Tryptophan is a redox-active amino acid playing a decisive role in a number of biological multistep electron transfer processes. Several studies have thus focused on the characterization of tryptophan radicals in proteins. [START_REF] Stubbe | Protein radicals in enzyme catalysis[END_REF][START_REF] Stoll | Hydrogen bonding of tryptophan radicals revealed by EPR at 700 GHz[END_REF][START_REF] Shafaat | Spectroscopic comparison of photogenerated tryptophan radicals in azurin: effects of local environment and structure[END_REF][START_REF] Eiserich | Nitric oxide rapidly scavenges tyrosine and tryptophan radicals[END_REF] Allylic hydroperoxide 3. Reactivity was far slower, as 3 was not completely consumed after a week. The crude product LC-MS profile was identical with Fe(II) or Fe(III) (Fig. 4). Several oxidation/degradation products of N-Ac-Trp-OEt were identified. The indole functional group was susceptible to oxidation giving mono and dihydroxylated derivatives 14 and 15. Tryptophan oxidation by hydroxyl radicals in Fe(II)/Fe(III) redox systems is indeed known. [START_REF] Maskos | The hydroxylation of tryptophan[END_REF][START_REF] Finley | Identification of tryptophan oxidation products in bovine α-crystallin[END_REF][START_REF] Simat | Oxidation of free tryptophan and tryptophan residues in peptides and proteins[END_REF] 2-,4-,5-,6-, and 7-hydroxyltryptophan isomers have been reported. Monohydroxylated derivative 14 can thus correspond to many different position isomers. This could explain why several LC peaks had m/z values of 291. The same argument is realistic for dihydroxylated derivatives 15. Like in our studies, dihydroxylation of tryptophan has been reported in the literature by the observation of an increment of m/z 32 to the amino acid mass. [START_REF] Peng | Tyrosine modification is not required for myeloperoxidase-induced loss of apolipoprotein A-I functional activities[END_REF] Oxidative degradation of N-Ac-Trp-OEt afforded also N-Ac-N'-formylkynurenine-OEt 16 and N-Ackynurenine-OEt 17. This was not surprising as the kynurenine pathway accounts for the principal oxidative ring opening and subsequent degradation of tryptophan in mammalian cells. [START_REF] Schwarcz | The kynurenine pathway of tryptophan degradation as a drug target[END_REF] A peak with m/z 441 was observed, and ESI-MS/MS analysis showed a fragment with m/z 275 typical of N-Ac-Trp-OEt loss, this being characteristic of an 18-like adduct. Also, a peak with m/z 445 was detected and ESI-MS/MS showed the loss of a fragment with m/z 279 specific to N-Ackynurenine-OEt 17. This was in agreement with a 19-like structure. Mechanistically, a carbon radical R• issued from 3 could react with a carbon radical located on the aromatic lateral chain of N-Ac-Trp-OEt or N-Ac-kynurenine-OEt. Several positions are available for radical formation in the case of tryptophan as shown by the mentioned studies on its oxidation and hydroxylation. [START_REF] Maskos | The hydroxylation of tryptophan[END_REF][START_REF] Finley | Identification of tryptophan oxidation products in bovine α-crystallin[END_REF][START_REF] Simat | Oxidation of free tryptophan and tryptophan residues in peptides and proteins[END_REF] Thus, the binding of R• could happen in different lateral chain positions of N-Ac-Trp-OEt preventing the exact elucidation of the chemical structure of 18. Regarding N-Ac-kynurenine-OEt, the amino group would favour the addition of R• in the α position. Yet, LC-ESI-MS/MS data did not allow drawing a conclusion concerning the exact chemical structure of 19. Allylic hydroperoxide 4. As for 3, 4 remained still in the reaction mixture after a week. Oxidation products 14-17 were identified. Only in the presence of Fe(II), m/z values of 443 and 459 were observed, corresponding to adducts. MS/MS of m/z 443 matched with structures 20-21 (Fig. 5). A carbon R• issued from RO• hydrogen abstraction could react with a carbon radical located on the aromatic lateral chain of N-Ac-Trp-OEt and afford 20. Also, the allylic RO• radical could an intramolecular cyclization and the α-oxiranylcarbinyl radical so formed react to give 21. There was a single loss of H 2 O but structure 20 was still favored, as epoxyalcohols and epoxides follow a different fragmentation pattern. [START_REF] Nilsson | LC-MS/MS analysis of epoxyalcohols and epoxides of arachidonic acid and their oxygenation by recombinant CYP4F8 and CYP4F22[END_REF] Typical MS fragments of tryptophan (m/z 130 and 157) were observed. [START_REF] Domingues | Identification of oxidation products and free radicals of tryptophan by mass spectrometry[END_REF] The value m/z 459 corresponded to a mass increase of 16 from m/z 443. MS/MS analysis gave a fragment derived from tryptophan with m/z 146, thus a 16 mass increase from the typical m/z 130 tryptophan fragment (Fig. 5). Knowing that N-Ac-Trp-OEt was oxidized in the reaction media to form 14-like mono-hydroxylated derivatives, we considered that these could further react with a carbon R• derived from the hydroperoxide. Even if this could occur with an oxiranylcarbinyl radical or with a radical derived from hydrogen abstraction, affording adducts 22 and 23 respectively, the loss this time of 2 molecules of H 2 O was in favor of the formation of 22.

Observations on the results. Several reaction mechanisms seem to be involved. Adducts can be formed from radical processes between tryptophan itself and carbon radicals derived from the hydroperoxides, in what we call a "direct" reaction amino acid-hydroperoxide (adducts 18, 20 and 21). In parallel, oxido-reduction processes were induced by 3 and 4, producing chemical modifications on the amino acid. Modified tryptophan could then react with the allergen, through a "non-direct" reactivity process. The amino acid did not react directly, but an intermediate formed as a consequence of oxidant stress. Oxidation/degradation products of N-Ac-Trp-OEt were identified such as 14-17. Due to the oxidative strength of the reaction media containing hydroperoxides, this was not surprising as the kynurenine pathway and hydroxylation processes are known oxidative degradations of tryptophan. Up to our knowledge, this is the first time these reactive intermediates were observed in the presence of allergenic allylic hydroperoxides. Moreover, they were able to react, most probably through radical mechanisms, with the hydroperoxides. This was the case for 19, resulting from the reaction between N-Ac-kynurenine-OEt 17 and 3, and for adducts 22-23, resulting from the reaction of monohydroxylated 14-like derivatives with carbon radicals derived from 4.

Reactivity with N-Ac-Lys-OMe

It has been reported in the literature the formation of an amidelike adduct between 13-hydroperoxyoctadecadienoic acid and N-benzoyl-glycyl-lysine, used as model for lysine residues in proteins. Also, lysine oxidation has been extensively reported giving rise, among others, to hydroxylated derivatives or fragments possessing highly reactive carbonyl groups. [START_REF] Morin | 3-Hydroxylysine, a potential marker for studying radical induced protein oxidation[END_REF][START_REF] Stadtman | Free radical-mediated oxidation of free amino acids and amino acid residues in proteins[END_REF][START_REF] Hawkins | Generation and propagation of radical reactions on proteins[END_REF][START_REF] Kato | Formation of Nε-(hexanonyl)lysine in protein exposed to lipid hydroperoxide[END_REF] Allylic hydroperoxide 3. The reaction was slow. After a week, 3 was not completely consumed. The LC-MS profile of the crude product was identical with Fe(II) or Fe(III) initiation. Oxidation of N-Ac-Lys-OMe was not observed. Only one possible adduct was detected with m/z 353 (Fig. 6). The presence of the lysine residue was attested by MS/MS, giving a fragment typical for the loss of N-Ac-Lys-OMe (m/z 203), together with fragments m/z 171 and 129, principal ions derived from fragmentation of the amino acid itself. [START_REF] Yalcin | Ion chemistry of protonated lysine derivatives[END_REF][START_REF] Fenaille | Study of peptides containing modified lysine residues by tandem mass spectrometry: precursor ion scanning of hexanal-modified peptide[END_REF] Curiously, the production of amides by Cu(II) catalyzed reaction between 13hydroperoxyoctadecadienoic acid and primary amines has been reported. [START_REF] Onorato | Pyridoxamine, an inhibitor of advanced glycation reactions, also inhibits advanced lipoxidation reactions[END_REF] It was proposed that a carbonyl intermediate formed from metal catalyzed reduction of the hydroperoxide was involved in the reaction. The reaction continued by the formation of a carbinolamine adduct by addition of the amine on the carbonyl intermediate, followed by a metal-catalyzed oxidative cleavage of the carbon-carbon bond adjacent to the carbonyl group. Based on a similar mechanism, it would be possible to suggest the formation of adduct 24 via the formation of carvone from metal catalyzed reduction of 3 (Scheme 4). Another possible structure could be ketone 25, obtained through a 1,4-Michael addition reaction of the amino group of lysine on carvone. MS/MS of m/z 353 gave characteristic fragments of the amino acid, these being the same for 24 and 25. Though, the presence of a distinguishing fragment at m/z 229 would be more in favor of the formation of 24. Indeed, fragment with m/z 229, containing the ε-NH 2 group of lysine modified by the addition of a carbonyl group, would not be formed from adduct 25. Observations on the results. As mentioned above, the evolution of 3 to the formation of carvone in the presence of iron is known. [START_REF] Johansson | Carbon-and oxygen-centered radicals are equally important haptens of allylic hydroperoxides in allergic contact dermatitis[END_REF][START_REF] Johansson | Mechanistic proposal for the formation of specific immunogenic complexes via a radical pathway: a key step in allergic contact dermatitis to olefinic hydroperoxides[END_REF] The previously reported participation of carvone in the reaction 3/cysteine was in our case highlighted when studying the reactivity with N-Ac-Lys-OMe. The formation of 24-25 could be mechanistically explained by the reaction of the amino group of lysine with carvone, itself obtained by decomposition of the hydroperoxide, either by 1,4-Michael addition, either by the formation of a carbinolamine adduct, followed by a metal-catalyzed oxidative cleavage of the carbon-carbon bond adjacent to the carbonyl group. These results are in agreement with the fact that carvone is a determinant reactive intermediate for hydroperoxide 3. On another hand, β-scission of RO• radicals formed from linalool hydroperoxide 4, already seen in the reactivity with cysteine, was supported in here by results obtained from the reactivity with N-Ac-Lys-OMe. The free amino group of lysine could react through a 2-electron reaction pathway with the α,βunsaturated ketone so formed, either at the carbonyl level giving 26, either through a 1,4-Michael addition forming 27.

Reactivity with N-Ac-Tyr-OEt

Tyrosine chemical modification by biologically relevant oxidants typically depends on the formation of tyrosyl radicals located in carbon-centered positions on the benzene ring. EPR evidence of electron-transfer mechanisms in the peroxynitritemediated oxidation of tyrosine has been reported. [START_REF] Grossi | Evidence of an electron-transfer mechanism in the peroxynitrite-mediated oxidation of 4-alkylphenols and tyrosine[END_REF] Moreover, for proteins associated with hydrophobic environments, it has been reported that lipid peroxyl radicals can mediate tyrosine oxidation processes. [START_REF] Bartesaghi | Lipid peroxyl radicals mediate tyrosine dimerization and nitration in membranes[END_REF] Allylic hydroperoxide 3. LC chromatograms showed, regardless of Fe(II)/Fe(III), a major peak corresponding to N-Ac-Tyr-OEt (m/z 252), together with two weak distinct peaks with m/z value of 501 (Supplementary Information data). These could correspond to dityrosine 28 and to the Pummerer-like ketone 29, both known oxidation products of tyrosine (Scheme 6). [START_REF] Grossi | Evidence of an electron-transfer mechanism in the peroxynitrite-mediated oxidation of 4-alkylphenols and tyrosine[END_REF][START_REF] Giulivi | Tyrosine oxidation products: analysis and biological relevance[END_REF] In presence of Fe(III) a possible adduct with m/z 418 was observed but in a very tiny amount, not excluding thus that it could be formed with Fe(II) in an undetectable amount. As expected, MS/MS of m/z 418 afforded the characteristic N-Ac-Tyr-OEt fragment (m/z 252), suggesting a 30-like adduct (Supplementary Information data). Unfortunately, no further data could be obtained in order to give more detailed information on the chemical structure.

Allylic hydroperoxide 4.

In all experiments, only amino acid oxidation products 28 and 29 were detected.

Observations on the results. RO•/ROO• and carbon-centered free radicals derived from 3 and 4 could mediate, as for lipid peroxyl radicals, [START_REF] Bartesaghi | Lipid peroxyl radicals mediate tyrosine dimerization and nitration in membranes[END_REF] the formation of phenoxy tyrosine radicals. Further radical isomerization involves the formation of monomers that can, by diradical reaction, combine between themselves affording 28 and 29 (Scheme 6). The chemical modification of tyrosine due to the relevant oxidant properties of allylic hydroperoxides was thus confirmed by the formation of large amounts of tyrosine-tyrosine dimers 28-29.

Reactivity with GSH

GSH plays a major role protecting cells against oxidative stress and free radical damage, directly neutralizing free radicals and reactive oxygen species. [START_REF] Kidd | Glutathione: systemic protectant against oxidative and free radical damage[END_REF][START_REF] Valko | Free radicals and antioxidants in normal physiological functions and human disease[END_REF] Its biological activity is due to the potent electron-donating capacity of the thiol group, able to scavenge highly reactive radicals that damage cells through oxidative stress. Hence, because the oxidant nature of 3 and 4, we studied the reactivity toward GSH. Allylic hydroperoxide 3. 3 was fully consumed after one hour of reaction. Oxidized form GSSG was not observed. LC-MS of the crude product exhibited molecular ions at m/z 458 and 476. Similar to the reactivity with cysteine, m/z 458 was initially attributed to compound 31 but could also match with compound 32 (Fig. 7a). The ability of GSH to reduce iron efficiently is well known. [START_REF] Tien | Thiol-dependent lipid peroxidation[END_REF] Thus, a similar mechanism to the one described in Scheme 2 can be suggested for the formation of 31-like adducts, being the major drawback the impossibility to know exactly the position of GSH binding. On another hand, cyclization of allyloxyl RO• radicals afford α-oxiranylcarbinyl radicals that can be trapped by GSH to form 32. 31-32 structures cannot be assigned unambiguously. Indirect evidence of 32 was given by the presence of the molecular ion at m/z 476. ESI-MS/MS indicating the loss of two molecules of H 2 O together with GSH was in agreement with 33 (Fig. 7a). The mass increment of 18 with regard to m/z 458 would correspond to the addition of H 2 O on epoxide 32. Allylic hydroperoxide 4. 4 needed few hours to completely react in all experimental conditions. GSSG was not observed. The most attracting signals are shown in Fig. 7b-7c. Fragmentation of m/z 462 showed the typical peak [GSH+H] + at m/z 308, together with peaks of characteristic fragmentation of GSH conjugates. [START_REF] Murphy | Fragmentation characteristic of glutathione conjugates activated by high-energy collisions[END_REF][START_REF] Camera | Simultaneous determination of reduced and oxidized glutathione in peripheral blood mononuclear cells by liquid chromatographyelectrospray mass spectrometry[END_REF] m/z 462 corresponded well with 34. As for the reaction with cysteine, β-scission of RO• radicals to form an α,β-unsaturated ketone could be possible. While in that case there was radical addition of the amino acid on the carbon radical formed during the β-scission process and after allylic hydrogen abstraction, this time m/z 462 was in favour of a 1,4-Michael addition of the -SH group of GSH on the α,βunsaturated ketone. By analogy with the observed reactivity for 3, structures 35 and 36 could match with m/z 476, and 37 with m/z 494. Unlike 3, allylic hydrogen abstraction was only possible at one position forming 35. Again, indirect evidence of the possible formation of epoxide 36 was the existence of the signal with a mass increment of 18, at m/z 494, corresponding to 37 and resulting from the epoxide opening by H 2 O.

Observations on the results. Reactivity of 3 with GSH was in agreement with results found for the reactivity with cysteine. This can be resumed to the formation of RO•, and further allylic hydrogen abstraction or intramolecular cyclization to form carbon radicals reacting with the -SH group of GSH. As for cysteine, some authors studied previously the reactivity of 3 toward GSH. [START_REF] Johansson | Mechanistic proposal for the formation of specific immunogenic complexes via a radical pathway: a key step in allergic contact dermatitis to olefinic hydroperoxides[END_REF] They gave arguments similar to those rationalized for the reactivity observed with cysteine. Adducts carvone-GSH (m/z 458) and carvone+GSH+O (m/z 474) were described. Thus, once more, the obtention of distinct adducts depending on the experimental conditions tested may be considered. The same kind of chemistry outlined for 3 was applicable to the reactivity of 4 with GSH. The formation of adducts through the reaction of the thiol group resulted from allylic hydrogen abstraction, only possible at one position in the case of 4, and from the formation of α-oxiranylcarbinyl radicals with further opening of the epoxide cycle. The acyclic chemical structure of 4 allowed β-scisssion of the formed RO• radical, and thus the formation of an electrophilic reactive intermediate that could form 34 through a 1,4-Michael addition.

Conclusions

To complement previous studies on the identification of reactive radical intermediates issued from allergenic allylic hydroperoxides, we studied the potential reactivity of 2hydroperoxylimonene 3 and 7-hydroperoxy-3,7-dimethylocta-1,5-dien-3-ol 4, derived from autoxidation of limonene and linalool, towards amino acids prone to radical reactions in order to give new insights on their supposed ability to form immunogenic structures by reacting with skin proteins through radical mechanisms. Studies reported here give innovative understanding on basic radical mechanisms that could explain the reactivity of allylic hydroperoxides towards proteins and thus their sensitizing potential. Radical initiation by using Fe(II)/Fe(III) redox cycles confirmed that carbon-centered radical intermediates derived from 3 and 4 can chemically modify amino acids by forming stable covalent bonds. It is known that reductive cleavage of peroxides and hydroperoxides occurs with reduced metals such as Fe(II), but also with cytochrome enzymes and related Fe(III)-heme-containig models. Indeed, reaction time and product outcome did not vary significantly depending on the starting ion used, Fe(II) or Fe(III). We have shown that the high oxidative strength of the media containing hydroperoxides induces the production of a number of reactive radical species involved in a permanent game of redox reactions. These intermediates are able to react with amino acids, either through a "direct" pathway with the lateral chain, either through a "non-direct" pathway with previous redox modification of the amino acid. The results of the reactivity with tryptophan are the perfect example underlining that the understanding of the hapten-protein binding process to allylic hydroperoxides needs to consider both, the direct binding to the amino acids via radical mechanisms, as well as the involvement of oxido-reduction processes able to produce chemical modifications on the amino acid itself. Amino acids chemically modified by the oxidant stress can then react with carbon-centered radicals issued from the hydroperoxides. Thus, a certain number of radical intermediates can issue from these compounds and be at the origin of different potentially immunogenic protein chemical modifications. These qualitative studies, even if elucidation of the exact chemical structure of the adducts is difficult, open new insights into the comprehension of mechanisms inducing chemical modification of biomolecules by carbon-centered radical species issued from xenobiotics.

Fig. 1

 1 Fig. 1 Products suggested for the reaction of 3 with N-Ac-Cys-OMe.

3 HFig. 2

 32 Scheme 2 Possible mechanistic pathway for the formation of 6a.

Scheme 3

 3 Scheme 3 Mechanistic pathway suggested for the formation of 13.

Fig. 3

 3 Fig. 3 Adducts 10-13 observed by LC-ESI-MS/MS from the reaction 4/N-Ac-Cys-OMe (tR are indicated when using Fe(II) and Fe(III)) and ESI-MS/MS analysis of m/z 330.

Fig. 4

 4 Fig. 4 Reaction 3/N-Ac-Trp-OEt/FeCl3: LC chromatogram of the crude product, peaks with m/z associated values of interest, and chemical structures of amino acid oxidation/degradation products 14-17 and adducts 18-19.

Fig. 5 Fig. 6

 56 Fig. 5 Reactivity of 4 with N-Ac-Trp-OEt. MS/MS analysis of possible adducts 20-23.

Scheme 4 Scheme 5

 45 Scheme 4 Mechanism proposed for the formation of 24 and 25.

Scheme 6

 6 Scheme 6 Proposed reaction mechanism by which hydroperoxide derived radicals can participate in tyrosine oxidation.

Fig. 7

 7 Fig.7 Reactivity with GSH. (a) Potential adducts from reaction of 3. (b) Potential adducts from reaction of 4. (c) ESI-MS/MS of m/z 462 and 476.

m/z 291

Acknowledgements

We gratefully acknowledge Firmenich SA (Geneva, Switzerland) for financial support to D. K. We also thank Patrick Wehrung (Pharmaceutical Department, University of Strasbourg, France) for his valuable technical support on the LC-ESI-MS/MS studies.


A Terfous

S Chiban

A Ghenaim

Modeling sediment deposition from marine outfall jets

Keywords: Turbulent flow, Suspended sediment, Mathematical models, Marine outfall jets, Deposition

This paper presents a two-dimensional model to study the sediment deposition from marine outfall jets. The introduced unidirectional coupling (fluid-sediment) is an appropriate choice in the case of low-concentrated particle-laden jets such as municipal wastewater discharge, where the concentration of particles is small enough and does not affect the hydrodynamic development of the jet in the nearfield. The sedimentation model takes advantage of the preferential concentration phenomenon. The deposition criterion states that the deposition of sediments begins when the vertical component of the entrainment velocity becomes smaller than the settling velocity. Once the deposition process begins, it is controlled by the settling velocity, entrainment velocity, volume flux, and sediment concentration. The deposition along the jet trajectory is expressed by an ordinary differential equation coupled with the liquid phase equations. Experiments of Lane-Serff and Moran (2005), Cuthbertson and Davies (2008) and Lee (2010), chosen from bibliography, are used to validate the model. These experiments cover the cases of horizontal and inclined buoyant jets in stationary ambient, horizontal buoyant jets in co-flow current and non-buoyant horizontal jets in stationary ambient. Good agreement between the experiments and the obtained simulations is revealed.

Introduction

Wastewater is an important source of anthropogenic pollution in coastal waters and the suspended solids present a significant part of this pollution [START_REF] Wasserman | Mercury concentrations in sediment profiles of a degraded tropical coastal environment[END_REF][START_REF] Ismail | Trace metals in sediments and molluscs from an estuary receiving pig farms effluent[END_REF][START_REF] Perin | Heavy metal pollution in central venice lagoon bottom sediments : Evaluation of the metal bioavailability by geochemical speciation procedure[END_REF]. For guidance, the variation interval of the concentration of Total Suspended Solids (TSS) in the raw municipal wastewater (The values indicated are the values after the preliminary treatment "screening, grit removal, flotation") is from 150 to 500 mg/l in France [START_REF] Degrémont | Memento Technique de l'Eau[END_REF]. However, the European Directive 91/271/EEC, determines the requirements for discharges from the secondary treatment as 35 mg/l of TSS or a minimum percentage of reduction of 90% in relation to the TSS load of the influent. The study of suspended solids deposition from low concentrated particles-laden jets as municipal wastewater discharge has been performed for only few scenarios in nonstratified ambient. Neves and Fernando [START_REF] Neves | Sedimentation of particles from jets discharged by ocean outfalls: A theoretical and laboratory study[END_REF] performed an experimental study with dimensional analysis on the deposition of particles from vertical round jets in stationary ambient. Ernst et al. [START_REF] Ernst | Sedimentation from turbulent jets and plumes[END_REF] developed a theoretical model for deposition from vertical jets and plumes. McLarnon [START_REF] Mclarnon | Sedimentation from a finite volume buoyant jet[END_REF] performed a detailed experimental study to investigate the sedimentation from horizontal buoyant jets in stationary ambient. Bleninger and Carmer [START_REF] Bleninger | Sedimentation in Particle-Laden-Jets: Experimental and numerical study on sedimentation of suspended material from non-buoyant horizontal jets in unbounded ambient[END_REF] performed an experimental study followed by an analytical solution for the deposition from horizontal nonbuoyant round jets in stationary ambient. Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] performed an experimental study and developed an integral model for deposition from horizontal and inclined buoyant round jets in stationary ambient. Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] performed an experimental study with scaling arguments on the deposition from horizontal buoyant round jets in stationary and coflowing ambient. Li [START_REF] Li | Theoretical modeling and experimental studies of particle-laden plumes from wastewater discharges[END_REF] studied experimentally the deposition from horizontal buoyant jets in stationary ambient and adopted a Lagrangian approach to model the phenomenon. Cuthbertson et al. [START_REF] Cuthbertson | Deposition from particle-laden, plane, turbulent, buoyant jets[END_REF] performed an experimental study on deposition from plane buoyant jets in stationary ambient followed by a Computational Fluid Dynamics (CFD) modelling. Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] performed an experimental study followed by particle-tracking model in addition to CFD modelling in order to study the deposition from horizontal nonbuoyant round jets in stationary ambient. The common point between these research works is considering the concentration of solid particles small enough in the discharge so that the presence of these particles has no significant influence on the jet trajectories over a wide range of forcing conditions. This concentration criterion is defined by Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] as a volumetric source concentration of (~0.1%); while Lane-serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] indicated that a concentration of 10 gr/l of solid particles has negligible impact on the flow. Other common considerations for deposition in the nearfield are considering the solid particles noncohesive, and monodisperse having the same size and shape and thus having one terminal fall velocity w s which is the velocity value for the ambient fluid density [START_REF] Bleninger | Sedimentation in Particle-Laden-Jets: Experimental and numerical study on sedimentation of suspended material from non-buoyant horizontal jets in unbounded ambient[END_REF][START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF][START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF][START_REF] Cuthbertson | Deposition from particle-laden, plane, turbulent, buoyant jets[END_REF]. However, Cuthbertson et al. [START_REF] Cuthbertson | Deposition from particle-laden, plane, turbulent, buoyant jets[END_REF] studied numerically the dependence of w s upon local fluid density and compared a w s value that varied with the local fluid density with a constant w s value for the ambient fluid density and found that the two cases give indistinguishable deposition profiles due to the rapid dilution of the buoyant jet following release. Finally, all the above experiments and simulations consider that the upper surface of the receiving ambient is free and the seabed is considered as flat and horizontal solid boundary. The objective of this work is to present a simple model that accurately predicts the deposition from low-concentrated particle-laden turbulent jets in different scenarios. Our proposed model is a Lagrangian model that takes advantage of the preferential concentration phonemene. The unidirectional coupling (fluid-sediment) is used in the modeling because the concentration of solid particles in the municipal wastewater discharge is small enough and does not affect the hydrodynamic developement of the jet. The obtained model is validated using the results of experiments done by Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF].

The hydrodynamic model for the nearfield zone

The high momentum turbulent jet creates a zone of low pressure that aspirates the ambient water. In the case of buoyant jets, the momentum flux, in addition to the buoyancy flux, draw the effluent trajectory. When the jet reaches the free surface or the neutral level, it spreads horizontally creating the surface gravity current. In the case of non-buoyant jets "neutral jet" there is no presence of the buoyancy forces. In this work, we treat jets in stationary ambient and in presence of coflow current. The velocity vector V is located in the x-z plane and it is horizontal or inclined with an angle ϕ on the x-axis, so it has two components u and w. Considering the coflow current and regarding the absence of other external forces, the jet axis remains in the x-z plane as shown in Figure 1.

Figure 1. Lagrangian model for buoyant jet in two-dimensional space. Using a fixed time step, we note that the first slices are longer than the last slices because the jet velocity decreases with time.

Integral methods are used to convert the governing partial differential equations (hydrodynamic model presented by the continuity equation and the momentum conservation equation) to a series of ordinary differential equations. These methods were found to produce very good approximations to fluid behaviors as long as the boundary effects do not enter the problem. Integral methods require that appropriate distribution profiles be assumed for velocity, temperature, and concentration. The origins of integral methods are the works of Hirst [START_REF] Hirst | Analysis of buoyant jets within the zone of flow establishment[END_REF], and Schatzmann [START_REF] Schatzmann | The integral equations for round buoyant jets in stratified flows[END_REF]. The continuity equation and Navier-Stokes equation are reduced to the following forms [START_REF] Davis | Fundamentals of Environmental Discharge Modeling[END_REF]:

Conservation of mass dm E dt = ( 1
)
where m is the mass and t is the time. Equation [START_REF] Wasserman | Mercury concentrations in sediment profiles of a degraded tropical coastal environment[END_REF] indicates that the change in the flow rate within the jet equals to the fluid entrained E. The entrainment E can be divided to the aspiration entrainment and forced entrainment. In the stationary ambient, or in a very weak current, the aspiration entrainment (Figure 1) presents the dominant entrainment while the forced entrainment is neglected.

Conservation of scalar product

dmC dt = C a dm dt ( 2
)
Where C is the concentration of scalar product in time t. C a is the product concentration in the ambient fluid.

Conservation of momentum along the trajectory

dmV dt = u a dm dt + mg ρ a -ρ ρ a ( 3
)
where V is the jet centerline velocity, u a is the current velocity, ρ is the density in the jet, and ρ a is the ambient density.

In the nearfield modeling, we present a two-dimensional version of the Lagrangian integral model presented by Lee and Cheung [START_REF] Lee | Generalized Lagrangian model for buoyant jets in current[END_REF]. The cross-sectional slice of the jet is considered with the Lagrangian formulation as having a coordinate system that moves with the jet. Integration is with time and the calculation takes place at discrete time steps. The slice that is followed is usually in the shape of a section in a bent cone as shown in Figure 1. Properties within the slice are assumed to be uniform (top-hat profiles) but they vary along the trajectory with time. The size and shape of the slice vary as a result of the plume bending, entrainment, and plume growth. The calculation stops when the jet reaches the free surface (in the case of a buoyant jet) or a prescribed distance (in the case of a horizontal nonbuoyant jet). In the literature, we find different formulas for calculating the entrainment [START_REF] Lee | Generalized Lagrangian model for buoyant jets in current[END_REF][START_REF] Baumgartner | Dilution models for effluent discharges[END_REF][START_REF] Jirka | Integral model for turbulent buoyant jets in unbounded stratified flows, Part I: Single round jet[END_REF]. However, in this work only the aspiration entrainment is considered. This entrainment flux (mass/time) into a slice (k) is the entrainment velocity multiplied by the ambient density and the slice surface

𝐸 ! ! = 𝑉 ! ! . 𝜌 ! . 2 . 𝜋 . 𝑏 ! . ℎ ! (4)
The ambient water entrainment velocity Ve is proportional to the centreline velocity via the entrainment coefficient α. Following [START_REF] Lee | Turbulent jets and plumes. A Lagrangian approach[END_REF], α = 0.057.√2 which is the classical value reported for top-hat profiles in round jets.

r b Ve V V α = = = (5)
Ve is the entrainment velocity, V is the centerline velocity, b is the jet half-width, α is the entrainment coefficient and h is the slice length.

In each time step k, we calculate the slice mean density ρ, mass m, velocity V, inclination ϕ, flow Q, half width b and length h. The slice properties calculation is based on the previous slice properties and the loop stops when zb2(k) < zsea, where zb2(k) is the upper boundary of the jet and zsea is the free surface height above the discharge point. In the case of nonbuoyant horizontal jets, the loop stops when x(k) < xa, where xa is the prescribed distance from the point source. The model is explained in the following equations [START_REF] Lee | Turbulent jets and plumes. A Lagrangian approach[END_REF]. The authors put here briefly the liquid phase equations to avoid repetition. However, the following equations can be revealed from a simple forward discretization of Equations ( 1), (2), and (3) using a constant time step:

The mass in the new slice

1 . k k k m m E t α + = + Δ (6)
The mass difference between the two slices k and k+1

. k k m E t α Δ = Δ (7)
The density in the new slice

1 1 . . k k k a k k m m m ρ ρ ρ + + + Δ = (8)
The horizontal velocity

1 1 . k k k a k k m u m u u m + + + Δ = (9)
The vertical velocity

𝑤 !!! = ! ! .! ! ! !!! + ! ! ! ! !!! ! ! 𝑔 Δ𝑡 (10)
The centerline velocity

2 2 1 1 1 k k k V u w + + + = + (11)
The length of the new slice

1 1 . k k h V t + + = Δ (12)
The half-width of the new slice

1 1 1 1 . . k k k k m b h ρ π + + + + = (13)
The inclination of the jet axis in the new slice,

1 1 1 arctan k k k w u φ + + + = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (14)
The distance from the source to the new slice along the jet axis

𝑆 !!! = ℎ ! !!! !!! (15)
The coordinates of the center of the upper surface in the new slice

1 . k k k x x u t + = + Δ (16) 1 . k k k z z w t + = + Δ (17)
The coordinates of the boundaries of the upper surface in the new slice (inferior point 1 and high point 2):

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 sin 1 cos 2 sin 2 cos k k k k k k k k k k k k k k k k xb x b zb z b xb x b zb z b φ φ φ φ + + + + + + + + + + + + + + + + = + = - = - = + (18)
The ambient fluid entrainment into the new slice

1 1 1 1 1 . . .2. . . k k k a k k E V b h α α ρ π + + + + + = (19)
The first slice (Slice 0) characteristics can be deduced from the initial conditions of the jet as follows

(u, w) 0 = (V 0 cos ,V 0 sin ) ( 20
)
The half width b 0 and the length h 0

(b,h) 0 = (0.5D, 0.5D) ( 21
)
Where D is the nozzle diameter and ϕ 0 is the initial inclination of the jet.

The initial time step, which is taken as a constant in the calculation

0 0 0.1 h t V Δ = ⋅ (22)
The coordinates of the first slice (x, z) 0 = (0, 0)

For horizontal nonbuoyant jets, this routine can be modified because the vertical velocity w is eliminated from all equations and the calculation stops after the prescribed distance xa. In this case, Equation ( 8) is eliminated because there is no density difference between the two fluids. Equation ( 10) is eliminated because there is neither initial vertical velocity nor buoyancy forces, and the same for Equations [START_REF] Hirst | Analysis of buoyant jets within the zone of flow establishment[END_REF], and [START_REF] Lee | Generalized Lagrangian model for buoyant jets in current[END_REF]. Basing on these eliminations, Equations ( 11), ( 13), [START_REF] Baumgartner | Dilution models for effluent discharges[END_REF], and (20) are modified.

The sediment deposition model for the nearfield zone

The preferential particles concentration in turbulent flow is the formation of concentration inhomogeneity that is related to the fact that the particles, which are more dense than the flow, have the tendency to accumulate in the weak vorticity zones because of the centrifugal force that trains them towards the periphery of the turbulent structures [START_REF] Maxey | Equation of motion for a small rigid sphere in a non-uniform flow[END_REF][START_REF] Eaton | Preferential concentration of particles by turbulence[END_REF][START_REF] Oesterlé | Ecoulements multiphasiques; des fondements aux méthodes d'ingénierie[END_REF][START_REF] Monchaux | Analyzing preferential concentration and clustering of inertial particles in turbulence[END_REF]. This phenomenon of preferential concentration or correlation between the instantaneous distribution of solid particles and the fluctuations of fluid velocity results in the existence of solid particles agglomerations that move with turbulence big structures.

In turbulent jets, the vorticity is highest in shear layers. In stationary ambient and in the presence of coflow, these shear layers are located at the boundaries of turbulent jets. The

0 φ 0 φ
Digimage tracking measurements of particle-laden buoyant jets discharging into initially stationary ambient and coflowing ambient body, made by Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] shows clearly the maximum vorticity located at the jet boundaries. However, in the presence of cross flow, the interaction of the jet momentum results in a complicated turbulent shear flow. Vortices of various kinds are being generated close to the source, in particular a pair of twinvortices in the bent-over phase of the buoyant jet. A simple pair of vortex eyes can be seen [START_REF] Lee | Turbulent jets and plumes. A Lagrangian approach[END_REF].

According to these observations, and to the fact that solid particles will accumulate in the low-vorticity areas, two different deposition patterns can be revealed for turbulent free jets in homogenous ambient. The first is for deposition from turbulent jets in stationary and coflow ambient and the second is for deposition from turbulent jets in cross flow. In the context of our study (deposition from low-concentrated particles-laden jets), the first pattern is the one studied so far in the available literature, experimentally and numerically. Depending on the experiments of Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF], and the experiments of Bush et al. [START_REF] Bush | Particle clouds in homogeneous and stratified environments[END_REF] on particle cloud that initially assumes the form of a turbulent thermal, this pattern results in localized deposition [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF][START_REF] Bush | Particle clouds in homogeneous and stratified environments[END_REF].

Considering the above researches, we assume that solid particles deposit from the inferior central part of the jet, as Figure 2 shows. The following hypotheses are made in order to build the sediment deposition model basing on the preferential concentration phenomenon:

1-We consider that the solid particles begin to deposit when their settling velocity is greater than the vertical component of the entrainment velocity . .cos

s k k k w V α φ > (24)
Thus, the vertical velocity of the solid particle depositing from the jet will be:

We would like to mention that a similar term is used by Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF]. But w out adopted in the model of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] is taken on the axis of the

w out = w s -α k V k cosφ k
entrainment velocity, perpendicularly on the jet axis (The criterion Equation ( 24) is written in this case: w s . cos φ k> > α k V k ); while in our model we considered the projection, on the z-axis, of the result of the two acting velocities. However, several tests were performed to investigate the effect of the choice of projection axis, in the cases of horizontal buoyant jets and slightly-inclined buoyant jets (17° and -15°), we found that in practice, the two choices give very close predictions of the longitudinal deposition, because the criterion is met in a distance too near to the nozzle, where the trajectory does not bent yet under the effect of buoyancy but it still rather horizontal and cosφ k ≅ 1 which makes no difference between the two formulas. However, further investigations on more inclined jets will help in determining which choice is the more convenient in the Lagrangian modeling.

2-The zone of deposition does not spread on all the width of the jet cross-section, but it has a smaller width depends on the ratio between the entrainment velocity and the settling velocity. The greater the settling velocity compared with the entrainment velocity, the bigger the zone of deposition and thus the higher deposition rate and vice versa. In other words, the portion of the cross-section area occupied by the deposition zone is proportional to the ratio of entrainment velocity to settling velocity. For example, in the high-momentum region, the zone of deposition occupies a small portion of the jet crosssection, but in the buoyancy-dominated region, the settling velocity is largely bigger than the entrainment velocity, so the deposition zone occupies almost all the jet cross-section.

The portion of the cross-section area occupied by the deposition zone can be described by the parameter (1 -αV cosφ / w s ). In this way, we do not need to assume a specific geometry of the deposition zone in the cross-section area (that can be ring or circle as Figure 2 shows, or an angular sector as the deposition zone geometry proposed by Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF]). However, Figure 3 shows the evolution of this parameter in a horizontal buoyant jet.

Figure 3. The velocity profile along the jet axis corresponding to experiments of Lee [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] for case 3 in Table .1, in addition to the evolution of the parameter (1 -αV cosφ / w s ) " the dashed line with the axis on the right ". The markers on (u) and (w) profiles are put every 400 step of calculation.

Considering the fundamental deposition model of Koh and Chang [START_REF] Koh | Mathematical model for barged ocean disposal of wastes[END_REF] for the settling of barge disposed wastes:

(

) 26
Where P is the solid flux in the jet; S is the distance along the jet axis, Cp is the solid concentration (Cp = P/Q) and β is a constant taken normally β = 0 [START_REF] Koh | Mathematical model for barged ocean disposal of wastes[END_REF][START_REF] Johnson | User's guide for models of dredged material disposal in open water[END_REF].

The model presented in this study is based on this fundamental model, where the terms are developed to incorporate more general cases. The model is written as follows (the number below the term indicate the number of the formerly-mentioned assumption used to built the term): [START_REF] Johnson | User's guide for models of dredged material disposal in open water[END_REF] Where cf is a constant that reflects the effect of buoyancy forces in inhibiting the deposition: cf = 1 in considerably buoyancy-dominated flow (g 0 ' = 0.384 m/s 2 , approximately, that can correspond to a discharge of an initial density of 1000 kg/m 3 in a milieu of average density of 1040 kg/m 3 ). cf = 1.5 in moderately buoyant-dominated flow (g 0 '= 0.185 m/s 2 , approximately, that can correspond to a discharge of an initial density of 1000 kg/m 3 in a milieu of average density of 1020 kg/m 3 ). cf = 2 for nonbuoyant jets. This parameter is always taken 1 (cf = 1) in the case of presence of coflow.

We will discretize the Equation ( 27) in a finite difference step forward framework, in order to couple it with the near field model, thus we can get the solid flux in each slice k, which enables us to reveal the deposition rate curve along the jet trajectory: Equation 27 is arranged by replacing C p by P/Q as follows: (28)

Better numerical accuracy can be achieved by rearranging Equation (28) using .

(29)

We discretize Equation (29) in a finite difference step forward framework as follows:

(30)

1 l n dP d P P dS dS = dP dS = -2w s C p b(1-β) dP dS = -2(w s -αV cosφ 1      )C P b(1- αV cosφ w s 2      )cf 1 P dP dS = -2(w s -αV cosφ ) ⋅ b Q ⋅ (1- αV cosφ w s ).cf d ln P dS = -2(w s -αV cosφ ) ⋅ b Q ⋅ (1- αV cosφ w s ).cf ln P k+1 -ln P k h k = -2(w s -αV k cosφ k ) ⋅ b k Q k ⋅ (1- αV k cosφ k w s ) ⋅ cf
The formula that is coupled with the fluid phase model and put in the calculation routine becomes:

(31)

Results and discussions

The cases that we study fall under four distinct categories: Horizontal buoyant jets in stationary ambient (I); Inclined buoyant jets in stationary ambient (II); Horizontal buoyant jets in coflowing ambient (III) and Horizontal nonbuoyant jets in stationary ambient (IV).

These categories are found in the available literature about deposition from buoyant and nonbuoyant jets, which enable us to calibrate and validate the model presented.

We choose to keep the same units of experimental data as stated in the original references for deposition rates in order to demonstrate the different ways and units used in presenting the deposition rate and for the simplicity in comparison when referring to the experiment in its original reference. Particle density function (PDF) in the experiments of Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF], and gr/m.s for the other experiments.

The proposed model is validated using the data in Table 1. The experiments of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] are used in order to study the deposition from buoyant and non-buoyant jets and validate the proposed model. We demonstrate the jet hydraulic structure; and compare deposition simulation with the experimental results. We would like to mention that the initial form of data taken from the works of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF], and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] are experimental points of longitudinal deposition curve, while the initial form of data taken from the work of Bleninger and Carmer [START_REF] Bleninger | Sedimentation in Particle-Laden-Jets: Experimental and numerical study on sedimentation of suspended material from non-buoyant horizontal jets in unbounded ambient[END_REF] is the number of particles deposited in each cell of a grid located on the ground, after a simple treatment of these raw data, we get the longitudinal deposition curve.

Table 1. Experimental data of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF], and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] used to calibrate and validate the proposed model.

Category Case

Data source

V 0 (m/s) D (mm) ρ 0 (kg/m 3 ) ρ a (kg/m 3 ) u a (m/s) ϕ 0 (°) z sea , or xa* (m) w s0 (m/s) I 1 [ 10
ln P k+1 = ln P k -2(w s -αV k cosφ k ) ⋅ b k Q k ⋅ (1- αV k cosφ k w s ) ⋅ cf ⋅ h k
Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] performed experiments on inclined and horizontal round buoyant jets. The experiments were conducted in a rectangular glass tank, with length 1.2 m, width 0.3 m and depth 0.4 m. The tank was filled to a depth of approximately 0.3 m with saline solution (ρ a ~ 1040 kg/m 3 ). A buoyant sediment-laden plume was created by introducing fresh water (or a weak saline solution) from an outlet of diameter D = 5 mm near the bottom of the tank. Two different sieved size fractions of sand were used (fine: 75 µm < d < 150 µm) and (coarse: 75 µm < d < 150 µm). The amount of sand in the fluid source was kept small (less than 10 gr/L) to minimize its impact on the flow.

The unit of the deposition rate in the experimental results is gr/m.sec. To obtain such unit in our model, we entered the initial solid particles concentration as indicated in the experiment (c p0 = 10 gr/L), we calculate the initial solid flux P 0 = c p0 *Q 0 (gr/sec), then the model can calculate the deposition from each slice (gr/sec) and dividing this value by the thickness of each slice (h k ) gives the unit (gr/m.sec).

Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] performed experiments on horizontal buoyant jets in stationary and coflowing ambient. The experiments were conducted in a recirculating water channel of length 10.0 m, width 1.0 m, and depth 1.2 m. The channel was filled to a prescribed depth H (0.55 m ≤ H ≤ 0.75 m) with homogeneous saline water of initial density (1020 -1040 kg/m 3 ). Steady uniform ambient flow conditions were established within the channel with depthaveraged velocity (0.017 -0.052 m/sec). A particle-laden buoyant jet with source density (1000 kg/m 3 ) was discharged horizontally into the coflowing ambient receiving water through a single round port of internal diameter D = 11.5 mm. Two types of noncohesive, spherical particles were used in the experiments (500 -600 µm, 1500 kg/m 3 ) and (630 -850 µm, 1150 kg/m 3 ). The particles were added to the source fluid to a volumetric concentration of about 0.1 %. Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] has performed experiments of horizontal sediment buoyant and non buoyant jets discharged in stationary ambient water. The bottom deposition rate of different jet flow rates, particle sizes and densities for jets were measured with bottom tray collection. The particle concentration across the jet cross sections of jets was measured by both the direct suction sampling technique and particle imaging technique. The settling velocities of particles were measured by the settling column experiments and compared with the settling formula using the size measurement from the Laser Diffraction Particle size Analyzer. The jet velocity field was checked by Laser Doppler Anemometry measurement. The experiments of horizontal jets in stationary ambient water were carried out in a 1 m long x 1 m width x 0.5 m high water tank. A constant water depth of roughly 0.45 m is maintained. The jet exit from a nozzle (6 mm diameter) with a flow ranged between 10 and 100 L/hour. In these experiments, freshwater is used as ambient fluid and ethanol-water mixture to produce the buoyancy jet. A wide range of particle size and density of spherical glass particles (d 50 = 115 -215, µm, ρ p = 2500 kg/m 3 ) and synthetic particles (d 50 = 621 and 716 µm, ρ p = 1140 and 1160 kg/m 3 ) are used to perform these experiments.

Table 2 shows the calculation details for all of the simulated experiments. We can see that the deposition criterion is satisfied after a trajectory less than one millimeter for all the experiments due to the abrupt loss of initial quantity of movement, once the discharge comes in contact with ambient water.

Table 2. The simulation details and results for the experiments of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF], and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] used to validate the proposed model.

The results obtained with the present model for horizontal buoyant jets in stationary ambient are shown in Figure 4. They are compared to data issued from experiments of Cuthberson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF]. A good agreement between the experimental data corresponding to case 1 in tables and the model is clear, where the majority of solid particles deposit in the nearfield (97 %). The deposition in the near field is the dominant mechanism in this case. Figure 5 shows the model results for inclined buoyant jets in stationary ambient. In this case, we note an acceptable agreement between the model and the experimental data obtained by Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] corresponding to case 2 in tables. This agreement can be explained by the longer trajectory of jet before reaching the free surface (as the jet is inclined down) so the deposition in the nearfield is a dominant mechanism in a considerable part of the jet before approaching the free surface and the development of the surface gravity current. The difference between calculated values and measured values is probably because of the initial jet inclination towards the bottom, then change of direction towards the surface which creates a stagnant zone in the inferior part of the jet enhances the deposition. Another reason for this this difference is the possible interaction between the jet and the bottom of the tank.

Figure 5. Model validation using data of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF] for case 2 corresponding to the category of inclined buoyant jets in stationary ambient.

Figure 6 shows the model results for buoyant jets in a weak coflow compared to experimental data of Cuthberson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF] corresponding to case 3 in Tables. We see a good agreement between the data and the model even if the deposition rate peak was higher in our model. This is probably because the model underestimates the effect of ambient current or because the settling velocity in the presence of ambient current was in reality a little slower than the value reported in the reference. However, we can see that the deposition from nearfield is the dominant mechanism with 96 % of solid particles deposited in the near-field. Globally we see that the model is in good agreement with experimental data of the five cases studied in this paper. In the case of horizontal buoyant jets in stationary ambient, the importance of buoyancy forces that decrease the deposition in the near-field and naturally give more importance to the second stage of deposition from surface gravity currents. In the case of inclined buoyant jets in stationary ambient, the initial vertical velocity is negative and it increases slowly due to the buoyancy forces. A little difference between calculated values and measured values is noted, probably because of the initial jet inclination towards the bottom, which creates a stagnant zone in the inferior part of the jet.

For horizontal buoyant jet in coflowing ambient, the horizontal velocity is very close to the vertical velocity because of the presence of u a contrarily to all the previous experiments where the vertical velocity was always dominant in the last section and u a = 0. We see a good agreement between the data points and the model even if the deposition rate peak was higher in our model. This is probably because the model underestimates the effect of ambient current or because the settling velocity in the presence of ambient current was in reality a little slower than the value reported in the reference. The mechanism of deposition in the nearfield is the dominant mechanism in the majority of the studied cases.

Conclusion

Unidirectional coupling between the fluid mouvement and the sediment transport is successfuly performed in order to study the deposition from low-concentrated particle-laden turbulent jets in marine oufalls. A developed bidimensional lagrangian integral model is used in this study.

The deposition from each slice depends on the difference between two acting velocities, the first velocity, the particle settling velocity and the second velocity is the jet entrainment velocity. The deposition begins when the first velocity is greater than the second.

Laboratory experiments of Lane-Serff and Moran [START_REF] Lane-Serff | Sedimentation from Buoyant jets[END_REF], Cuthbertson and Davies [START_REF] Cuthbertson | Deposition from particle-laden, round, turbulent, horizontal, buoyant jets in stationary and coflowing receiving fluids[END_REF], and Lee [START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] were selected from litterautre and used to validate the poposed model. The experiments consist of inclined and horizontal buoyant jets in stationary ambient, horizontal buoyant jet in coflowing ambient and nonbuoyant horizontal jet in stationary ambient. Globally, the model shows good agreement with experimental data especially when we have high deposition rates from the nearfield which makes the deposition mechanism studied here the dominant mechansim.

Experimental studies on more inclined jets seem indispensable in order to confirm the choice of deposition criterion. In addition to that, the integration of other mechanisms of deposition in the model like particles re-entrainment, deposition from surface gravity currents, the effect of confinement and the effect of surface waves in several scenarios are promising points at later steps of this work.

Figure 2 .

 2 Figure 2. Up-Indicative schema for the vorticity field in the cross-section of turbulent jets in stationary or co-flow ambient (Left), and in cross-flow (Right). Middle-The preferential concentration of solid particles in low vorticity areas, in the inferior parts the jet. Down: Localised deposition (Left) and Ring deposition (Right).

Figure 4 .

 4 Figure 4. Model validation using data of Cuthbertson and Davies [10] for case 1 corresponding to the category of horizontal buoyant jets in stationary ambient.

Figure 6 .

 6 Figure 6. Model validation using data of Cuthbertson and Davies [10] for case 3 corresponding to the category of horizontal buoyant jets in presence of co-flow.

Figure 7 .

 7 Figure 7. Model validation using data of Lee[START_REF] Lee | Mixing of horizontal sediment laden jets[END_REF] for case 4 corresponding to the category of horizontal non-buoyant jets in stationary ambient for particles with small diameter and high density (d 50 = 115, 215 µm, ρ p = 2500 kg/m 3 ).

Figure 8 .

 8 Figure 8. Model validation using data of Lee [13] for case 5 corresponding to the category of horizontal non-buoyant jets in stationary ambient for particles with large diameter and low density (d 50 = 621 and 716 µm, ρ p = 1140 and 1160 kg/m 3 ).

Nomenclature