Yao-Yin Lou

F Geneste

I Soutrel

A Amrane

F Fourcade

Alachlor dechlorination prior to an electro-Fenton process: Influence on the biodegradability of the treated solution

Keywords: Alachlor, Electro-Fenton, Electro-reduction, Biodegradability, combined processes

This study investigates alachlor herbicide removal by electro-Fenton (EF) process with and without a previous dechlorination step by electro-reduction (ER-EF). The objective is to evaluate the relevance of dechlorination before electro-Fenton according to the biodegradability evolution and the energy consumption. The influence of the applied current, the ferrous ions concentration and the air flow rate on the production of hydrogen peroxide and on the general behavior of alachlor removal by EF oxidation was studied and optimized EF conditions were chosen. Scavenger tests were performed to determine the contribution of hydroxyl radicals (•OH), superoxide radicals (•O2 -) and sulfate radicals ( • SO4 -) during alachlor degradation. Some intermediate products formed during degradation by EF of alachlor and of the electroreduced solution were identified and the evolution of small organic acids was examined. Possible pathways of alachlor degradation and of deschloroalachlor, the mean byproduct from ER, were proposed on the basis of the EF reaction. EF treatment significantly improved the biodegradability of electrolyzed solutions with BOD5/COD ratio increasing from 0 to 0.4 after 0.5 h oxidation and can be further enhanced by the application of ER prior to EF, leading to a maximum value for the BOD5/COD ratio of 0.7 that can be due to the absence of chloroacetic acid found during the EF treatment. The energy consumption of the different electrochemical processes was also evaluated.

Introduction

Alachlor, 2-chloro-(2',6'-diethyl-N-(methoxymethyl)acetanilide), has been one of the mostly used herbicides to remove annual grasses and broadleaf weeds and promote crops yield in the last few decades [START_REF] Qin | Protocatechuic acid promoted alachlor degradation in Fe (III)/H2O2 Fenton system[END_REF][START_REF] Carlson | Influence of surface composition on the kinetics of alachlor reduction by iron pyrite[END_REF]. The excess use of alachlor has led to contaminations in surface water and farming soil [START_REF] Pérez | Comparative Degradation of Alachlor Using Photocatalysis and Photo-Fenton[END_REF]. Alachlor and some of its metabolites have also been detected in vitro in human liver microsomes and in urine [START_REF] Chevrier | Environmental determinants of the urinary concentrations of herbicides during pregnancy: The PELAGIE mother-child cohort (France)[END_REF][START_REF] Lee | Biotransformation and molecular docking of cyazofamid by human liver microsomes and cDNA-expressed human recombinant P450s[END_REF]. To avoid this potential threat to human via drinking water, alachlor has a maximum contaminant level of 2.0 g L -1 set by US EPA [START_REF]National primary drinking water regulations: Long Term 1 Enhanced Surface Water Treatment Rule. Final rule[END_REF]. More strict control at 0.1 g L -1 for any particular pesticides is regulated by the European Union (European Union, 2007).

Considering its high toxicity and poor biodegradability, alachlor negatively impacts the activity of the activated sludge, which indicates the unfeasibility of utilizing municipal sewage treatment process to treat wastewaters containing alachlor [START_REF] Zhu | Improving alachlor biodegradability by ferrate oxidation[END_REF]. It has been shown that the presence of chlorine atoms in the chlorinated organic compounds structure is considered to be the main cause of their toxic properties [START_REF] Chen | Electrochemically codeposited palladium/molybdenum oxide electrode for electrocatalytic reductive dechlorination of 4-chlorophenol[END_REF]. To reduce toxicity, electroreduction (ER) has been chosen as a pretreatment before the biological process because of its high selectivity of dechlorination on catalyst-modified cathodes, which can enhance the pollutants biodegradability [START_REF] Fontmorin | Reductive dehalogenation of 1, 3-dichloropropane by a [Ni (tetramethylcyclam)] Br2-Nafion® modified electrode[END_REF][START_REF] Arellano-González | Mineralization of 2-chlorophenol by sequential electrochemical reductive dechlorination and biological processes[END_REF]. Hence, some previous works about ER pretreatment of alachlor have been attempted, including Co complex-supported catalyst [START_REF] He | Reductive dechlorination of a chloroacetanilide herbicide in water by a Co complex-supported catalyst[END_REF][START_REF] He | A new bipyridyl cobalt complex for reductive dechlorination of pesticides[END_REF] and nanoparticle Ag-modified electrodes [START_REF] Verlato | Preparation of Silver-Modified Nickel Foams by Galvanic Displacement and Their Use as Cathodes for the Reductive Dechlorination of Herbicides[END_REF][START_REF] He | Reductive dehalogenation of a chloroacetanilide herbicide in a flow electrochemical cell fitted with Ag-modified Ni foams[END_REF]. After ER pretreatment on nanoparticle Agmodified cathode, alachlor has been completely degraded with a dechlorination yield of 77% and its dechlorinated derivative (deschloroalachlor) has been formed with a yield of 65%. Higher selectivity toward the dechlorination process has been obtained on Cocomplex-modified cathode with a dechlorination yield of 95% and 86% yield of deschloroalachlor. However, BOD5 measurements have shown that the main by-product deschloroalachlor is also not biodegradable [START_REF] He | Reductive dechlorination of a chloroacetanilide herbicide in water by a Co complex-supported catalyst[END_REF]. This result is in accordance with the work of Zhang et al. [START_REF] Zhang | Biodegradation of Chloroacetamide Herbicides by Paracoccus sp. FLY-8 in Vitro[END_REF] who found that the amide nitrogen's alkoxymethyl group in chloroacetamide organics influences significantly and negatively their biodegradability.

Therefore, some other technologies that can degrade the amide nitrogen's alkoxymethyl group are necessary.

A c c e p t e d m a n u s c r i p t

Various kinds of techniques have been put forward to remove alachlor from aquatic environment. Advanced oxidation processes (AOPs) have attracted considerable interests owing to the generated reactive oxidant radicals •OH, especially the Fenton reaction (equation ( 1)) combined with UV [START_REF] Katsumata | Photo-Fenton degradation of alachlor in the presence of citrate solution[END_REF] or sonication [START_REF] Wang | Degradation of alachlor using an enhanced sono-Fenton process with efficient Fenton's reagent dosages[END_REF], the peroxone process [START_REF] Qiang | Degradation mechanism of alachlor during direct ozonation and O3/H2O2 advanced oxidation process[END_REF], photocatalysis [START_REF] Pérez | Comparative Degradation of Alachlor Using Photocatalysis and Photo-Fenton[END_REF][START_REF] Zheng | Preparation of graphene/TiO 2 nanotube array photoelectrodes and their photocatalytic activity for the degradation of alachlor[END_REF][START_REF] Bhoi | Photocatalytic degradation of alachlor using type-II CuS/BiFeO3 heterojunctions as novel photocatalyst under visible light irradiation[END_REF] and electrochemical processes [START_REF] Pipi | Total removal of alachlor from water by electrochemical processes[END_REF]. Among AOPs, electro-Fenton (EF) was considered in this study because of its advantage of self-generation of H2O2 by reduction of O2 (E° = 0.695 V/SHE), as shown in equation [START_REF] Carlson | Influence of surface composition on the kinetics of alachlor reduction by iron pyrite[END_REF], which avoids the transportation and storage of H2O2.

Fe 2+ + H 2 O 2 → Fe 3+ +• OH + OH - (1)
O 2 + 2H + + 2e -→ H 2 O 2 (2)
Instead of complete mineralization, the partial oxidation of toxic compounds by EF can be used to enhance biodegradability cost [START_REF] Chamarro | Use of Fenton reagent to improve organic chemical biodegradability[END_REF][START_REF] Mansour | Mineralization of synthetic and industrial pharmaceutical effluent containing trimethoprim by combining electro-Fenton and activated sludge treatment[END_REF][START_REF] Dalle | Efficiency of DMSO as hydroxyl radical probe in an Electrochemical Advanced Oxidation Process-Reactive oxygen species monitoring and impact of the current density[END_REF][START_REF] Aboudalle | Reactive oxygen and iron species monitoring to investigate the electro-Fenton performances. Impact of the electrochemical process on the biodegradability of metronidazole and its byproducts[END_REF], in order to save energy and decrease the treatment cost. In this work, a succession of ER and EF was considered as a pretreatment prior to a cost-efficiency biological treatment. The first objective of this combined system is to avoid the formation of short-chain chlorinated alkane species and carboxylic acids, which have resistance to oxidation by the Fenton reaction and may flow into the biological process and hinder the activity of micro-organisms [START_REF] Bigda | Consider Fentons chemistry for wastewater treatment[END_REF]. The comparison of EF with the combination of ER and EF in terms of improvement of alachlor biodegradability and energy consumption was performed. We first optimized the EF parameters such as current, ferrous concentration and air flow rate. To go further in the understanding of the mechanism involved and the by-products formed, the radicals contribution was also examined by scavenger tests and the formation of high-molecular-weight (HMW) degradation by-products and low-molecular-weight by-products, including small organic acids and inorganic anions, was studied. The biodegradability improvement in different conditions of electrochemical treatment was also evaluated.

A c c e p t e d m a n u s c r i p t 2 Materials and Methods

Chemicals products

All chemicals used were of analytical grade and used without further purification. Alachlor, deschloroalachlor, ferrous sulfate (FeSO4), sodium hydroxide (NaOH) and sulfuric acid (H2SO4) were obtained from Sigma-Aldrich. The initial pH of the solutions was adjusted to 3 by adding analytical grade H2SO4 purchased from Acros Organics. Anhydrous sodium sulfate (Na2SO4) was from Acros Organics. Isopropyl alcohol (IPA, (CH3)2CHOH, >99.5%), tertbutyl alcohol (TBA, (CH3)3OH, >99.0%) and 1, 4benzoquinone (BQ, C6H4O2, >97%) were purchased from Sigma-Aldrich. Acetonitrile (HPLC-grade) was purchased from Fisher Scientific (Loughborough, UK). Ultra-pure water obtained from ELGA Purelab Option-Q DV 25 system was utilized for the preparation of all working solutions, as well as HPLC and LC-MS/MS mobile phases.

Electrochemical process

The electrodechlorination processes were conducted as described in our previous work [START_REF] Verlato | Preparation of Silver-Modified Nickel Foams by Galvanic Displacement and Their Use as Cathodes for the Reductive Dechlorination of Herbicides[END_REF][START_REF] He | Reductive dehalogenation of a chloroacetanilide herbicide in a flow electrochemical cell fitted with Ag-modified Ni foams[END_REF][START_REF] Lou | Ni-coated graphite felt modified with Ag nanoparticles: a new electrode material for electro-reductive dechlorination[END_REF] chosen, because it has been shown to be the optimal pH for the Fenton's reaction [START_REF] Brillas | Electro-Fenton process and related electrochemical technologies based on Fenton's reaction chemistry[END_REF]. All solutions were vigorously stirred (300 rpm) with a magnetic bar during treatment.

Biodegradability estimation

Biochemical oxygen demand in 5 days (BOD5) was considered to evaluate the biodegradability of the studied solutions [START_REF] Ferrag-Siagh | Tetracycline degradation and mineralization by the coupling of an electro -Fenton pretreatment and a biological process[END_REF]. BOD5 measurements were carried out in NANOCOLOR® BOD5-TT test tubes (from Macherey-Nagel, German) at 20.0±0.5 o C, pH 7 and in obscurity during 5 days. For inoculation, an initial activated sludge concentration of 0.05 g L -1 was targeted. A control sample containing 150 mg L -1 glutamic acid and glucose known as biodegradable compounds was conducted to check the viability of the activity sludge. A blank solution containing pure water was performed to deduce the biochemical oxygen demand corresponding to the endogeneous respiration. 120 μL of a mineral solution was also added, containing 5.625 g L -1 MgSO4•7H2O, 6.875 g L -1 CaCl2, 0.375 g L -1 FeCl3, 0.5 g L -1 NH4Cl. BOD5/COD value was introduced to evaluate solutions' biodegradability. Above a threshold value of 0.4, the solution is considered as easily biodegradable [START_REF] Ferrag-Siagh | Tetracycline degradation and mineralization by the coupling of an electro -Fenton pretreatment and a biological process[END_REF].

Biological treatment

Biological treatments were conducted in duplicate for 21 days at 25C o and in 500 mL

Erlenmeyer flasks containing 250 mL solution, magnetically stirred at 200 rpm, closed by a cellulose cap to guarrantee oxygenation. Activated sludge was inoculated to achieve an initial concentration of 0.5 g L -1 .The following mineral solution was added (mg L -1 ): Under these conditions, many peaks of the byproducts appeared at lower retention times.

Detection was performed with a photodiode array detector Waters 996 at 196 nm.

UPLC-MS analysis

To identify the by-products obtained during the alachlor and the electroreduced solution degradation, several samples were analyzed by ultra-high pressure liquid chromatography (Acquity UPLC -Waters) coupled to mass spectrometry Tandem (Triple Quad Quattro Premier Waters). The analytes were separated by the Waters Acquity UPLC system consisting of an Acquity UPLC binary solvent manager, an Acquity UPLC sample manager and an Acquity UPLC column heater equipped with a Waters Acquity UPLC BEH C18 column (2.1 × 100 mm, 1.7 μm particle size) (Milford, MA, USA). Isocratic LC elution was performed with acetonitrile quality LC-MS as mobile phase A and an ultrapure water 9:1 acetonitrile (v/v) mixture as mobile phase B. Separation of the analytes on the column was performed at 0.4 mL min -1 flow rate.

Other analytical methods

NH4 + -N, and NO3 --N were measured via colorimetric methods (APHA) using a UV-visible spectrophotometer (DR5000, HACH, Colorado) [START_REF] Lou | Occurrence and ecological risks of veterinary antibiotics in struvite recovered from swine wastewater[END_REF]. The mineralization of the organic compounds was monitored by measuring the non-purgeable organic carbon (NPOC) abatement by TOC-VCPH/CPN Total Organic Carbon Analyzer Schimadzu. The hydrogen peroxide (H2O2) concentration was measured by titration with a solution of sodium thiosulfate (Na2S2O3) [START_REF] Klassen | H2O2 determination by the I3-method and by KMnO4 titration[END_REF]. Chemical oxygen demand (COD) was determined using NANOCOLOR® COD 160 kit (from Macherey-Nagel, Germany). Low-molecular-weight A c c e p t e d m a n u s c r i p t organic acid and inorganic anions were quantified by ion exclusion chromatography using a Dionex 900 ion chromatograph (IC, Thermo, USA) equipped with a conductivity detector.

An Ionpac (4 mm × 250 mm) was used as anion exchange column. The eluent was ultrapure water at a flow rate of 1.0 mL min -1 .

Results and discussion

Optimization of the EF oxidation

Effect of the current

The current is a key parameter that influences the EF process [START_REF] Brillas | Electro-Fenton process and related electrochemical technologies based on Fenton's reaction chemistry[END_REF][START_REF] Moreira | Electrochemical advanced oxidation processes: a review on their application to synthetic and real wastewaters[END_REF]. To find the optimal current to be applied, cathodic current from -15 to -300 mA were investigated. Current of -30 mA corresponded to a potential around -0.5 V/SCE in our experimental system (data not shown), which is the theoretical optimal cathodic potential for the generation of H2O2 [START_REF] Qiang | Electrochemical generation of hydrogen peroxide from dissolved oxygen in acidic solutions[END_REF].

A maximum accumulated H2O2 concentration of 5.92 ± 0.33 mmol L -1 was obtained at a current of -200 mA after 3 h of electrolysis, as shown in Figure 1(a). According to equation

(2), a more negative current is expected to improve the production of H2O2 [START_REF] Rezgui | Electro-Fenton catalyzed with magnetic chitosan beads for the removal of Chlordimeform insecticide[END_REF] at the cathode and the production of hydroxyl radicals at the Pt anode (Pt( • OH)) [START_REF] Steter | On the selection of the anode material for the electrochemical removal of methylparaben from different aqueous media[END_REF][START_REF] Coria | Influence of the anode material on the degradation of naproxen by Fenton-based electrochemical processes[END_REF].

However, beyond -200 mA, the opposite trend was observed. It can be explained by the competition with the four-electron reduction of O2 (E° = 1.229 V/SHE), the reduction of H2O2 into H2O (E° = 1.763 V/SHE), and the hydrogen evolution reaction (E° = 0 V/SHE) which are favored when a high current density is used as shown in equation ( 3), ( 4) and ( 5) [START_REF] Zhou | Highly efficient H2O2 electrogeneration from O2 reduction by pulsed current: Facilitated release of H2O2 from porous cathode to bulk[END_REF][START_REF] Zhou | Activated carbon as effective cathode material in iron-free Electro-Fenton process: Integrated H2O2 electrogeneration, activation, and pollutants adsorption[END_REF][START_REF] Sirés | Electrochemical advanced oxidation processes: today and tomorrow[END_REF][START_REF] Zhou | Electrogeneration of hydrogen peroxide for electro-Fenton system by oxygen reduction using chemically modified graphite felt cathode[END_REF]. Meanwhile, an enhanced current could promote parasitic reactions at the anode, according to equations (6) (E°= 1.440 V/SHE) and ( 7) [START_REF] Sirés | Catalytic behavior of the Fe3+/Fe2+ system in the electro-Fenton degradation of the antimicrobial chlorophene[END_REF], leading to the consumption of H2O2.

O2 + 4H + + 4e -→ 2H2O (3)
H2O2 + 2H + + 2e -→ 2H2O (4) 2H3O + + 2e -→ H2 + 2H2O (5) H2O2 → HO2• + H + + e - (6)
HO2• → O2(g) + H + + e - (7)
A c c e p t e d m a n u s c r i p t

Oxidant radicals, such as •OH, are produced by the activation of the electro-generated H2O2 in the presence of the ferrous catalyst (equation ( 1)). Consequently, an increase of the applied current led to a significant enhancement of the kinetic of alachlor removal and mineralization (Figures 1(b) and 1(c)). However and according to the maximum amount of H2O2 electro-generated, maximum degradation and mineralization yields were obtained for an applied current of -200 mA and 0.1 mM of ferrous ions concentration. It can be observed that both the removal of the herbicide and the mineralization were found to follow a pseudo-first order kinetic model with maximum kinetic rate constants (kapp) of 0.451 ± 0.09 min -1 (Supplementary material Table S1) and 0.0137 ± 0.0007 min -1 (Supplementary material Table S2), respectively. Hence, as discussed above, the optimal applied current of -200 mA was selected and considered thereafter.

Effect of the ferrous ions concentration

The effect of Fe(II) concentration on the degradation of the target molecule was investigated in the presence of 50 mg L -1 of alachlor and for an applied constant current of -200 mA; the corresponding results are displayed in Figure 2. According to our previous work on the degradation of enoxacin [START_REF] Annabi | Degradation of enoxacin antibiotic by the electro-Fenton process: Optimization, biodegradability improvement and degradation mechanism[END_REF] and metronidazole [START_REF] Aboudalle | Reactive oxygen and iron species monitoring to investigate the electro-Fenton performances. Impact of the electrochemical process on the biodegradability of metronidazole and its byproducts[END_REF], the optimal Fe(II) concentration is around 0.1-0.2 mmol L -1 . Hence, a range of Fe(II) concentrations, from 0.02 to 1.0 mmol L -1 , was investigated in this study. The percentage of alachlor conversion increased with the catalyst concentration up to 100% within 10 min EF oxidation, as shown in Figure 2(a). It should be observed that increasing the catalyst concentration beyond 0.05 mmol L -1 did not have a significant impact on the degradation rate. The alachlor degradation versus time followed a pseudo-first order kinetic model with increased kapp from 0.033 ± 0.002 min -1 to 0.56 ± 0.07 min -1 as Fe(II) concentration increased from 0.02 to 0.1 mmol L -1 (Supplementary material Table S1). On the other hand, alachlor degradation was also observed in the absence of Fe(II), with 77.3% degradation after 1 h electrolysis, showing the contribution of the electrochemical oxidation at the Pt anode or/and reduction on graphite felt to alachlor degradation. Indeed, it was previously shown that alachlor can be reduced to deschloroalachlor on graphite felt electrode [START_REF] He | A new bipyridyl cobalt complex for reductive dechlorination of pesticides[END_REF]. Moreover, a reaction between alachlor and the produced hydrogen peroxide can also occur in solution [START_REF] Bagal | Sonochemical degradation of alachlor in the presence of process intensifying additives[END_REF]. Maximum mineralization yield was 91.8 ± 0.8%, obtained for 0.05 mmol L -1 Fe(II) 8) with a rate constant of 3.2 10 8 L mol -1 s -1 [START_REF] Sirés | Catalytic behavior of the Fe3+/Fe2+ system in the electro-Fenton degradation of the antimicrobial chlorophene[END_REF][START_REF] Annabi | Degradation of enoxacin antibiotic by the electro-Fenton process: Optimization, biodegradability improvement and degradation mechanism[END_REF]. [START_REF] Zhou | Influence of a reagents addition strategy on the Fenton oxidation of rhodamine B: control of the competitive reaction of• • OH[END_REF]. As for target compound degradation, mineralization also followed a pseudo first order kinetic model, and maximum kapp was found to be 0.014 ± 0.002 min -1 for a Fe(II) concentration of 0.05 mmol L -1 . As a result, 0.05 mmol L -1 was the optimal catalyst concentration and was considered thereafter.

Fe 2+ + •OH →Fe 3+ + OH -•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••(8)

Effect of the air flow rate

The conductive air pump does not only provide sufficient dissolved O2 for electrogeneration of H2O2 but also enhances the mass transfer; so that the air flow rate is also an interesting parameter to be investigated. As illustrated in Figure 3(a), the accumulated H2O2 reached a maximum of 3.56 ± 0.06 mmol L -1 for an air flow rate of 0.3 L min -1 , compared to 0.1 and 0.5 L min -1 . Although the air flow rate did not show significant influence on dissolved O2 (DO) content, which was 7.1 ± 0.6 mg L -1 (close to the limit of solubility of O2 in water, which is around 9 mg L -1 at 20 °C) for all flow rates, increasing the air flow rate enhances the mass transfer in the solution. However, overpumped air could result in an excessive production of bubbles, leading to a heterogeneous distribution of current density inside the graphite felt and to an increase in the electric resistance. This phenomenon would explain the decrease of the H2O2 concentration when an air flow rate of 0.5 L min -1 was used. Indeed, a potential around -1.5 V/SCE was measured at the working electrode for a flow rate of 0.5 L min -1 . At this potential, the four-electron reduction of O2 (equation ( 3)) becomes predominant, decreasing the amount of formed H2O2. Another side-reaction that could occur at -1.5 V/SCE is the decomposition of H2O2 into water, according to equation (4) [START_REF] Brillas | Electro-Fenton process and related electrochemical technologies based on Fenton's reaction chemistry[END_REF][START_REF] Zhou | Electrogeneration of hydrogen peroxide for electro-Fenton system by oxygen reduction using chemically modified graphite felt cathode[END_REF]. For lower air flow rates, the potential was found to be -0.75 V/SCE, which is in favor of H2O2 formation. Similarly, Zhou et al. [START_REF] Zhou | Electrogeneration of hydrogen peroxide for electro-Fenton system by oxygen reduction using chemically modified graphite felt cathode[END_REF] have observed 10% decrease of the accumulated H2O2 in the EF process with hydrazine hydrate chemically modified graphite felt as the cathode after increasing the O2 flow rate A c c e p t e d m a n u s c r i p t from 0.4 to 0.6 L min -1 and found that the optimal potential to form H2O2 was -0.75 V/SCE.

H2O2 also became easily decomposed into water in the case of 0.5 L min -1 , according to equation (4). For 0.1, 0.3, and 0.5 L min -1 , mineralization yields were 84% ± 4%, 92% ± 2% and 82% ± 2%, respectively, after 3 h EF (Figure 3(c)). The mineralization followed a pseudo first order kinetic model with kapp values of 0.013 ± 0.001 min -1 , 0.014 ± 0.002 min - 1 and 0.009 ± 0.001 min -1 for 0.1, 0.3 and 0.5 L min -1 , respectively (Supplementary material Table S2). Alachlor degradation increased with the air flow rate up to 100% within 10 min EF oxidation, as shown in Figure 3(b). The alachlor degradation with time followed a pseudo-first order kinetic model with increased kapp from 0.19 ± 0.09 min -1 to 0.54 ± 0.07 min -1 as air flow rate increased from 0.1 to 0.5 L min -1 (Supplementary material Table S1).

From the above results, 0.3 L min -1 was therefore chosen as the optimal air flow rate and was therefore considered thereafter. If the mineralization yield was in accordance with the hydrogen peroxide production, the behavior of the degradation yield was different since it increased from 0.1 to 0.5 L min -1 . If the electrochemical reaction of alachlor at the electrode surface is mainly responsible for its degradation, an increase of air flow rate and then a better mass transport of alachlor toward the electrode surface could explain this trend.

Possible mechanism of alachlor degradation

By-products identification

LC/MS analysis was considered to investigate the intermediates generated during EF oxidation of pure alachlor and of the electroreduced solution. In order to identify a maximum of intermediates, the EF oxidations were performed at 50 mA. In total, 18 aromatic and/or cyclic molecules were identified as the primary transformation byproducts (compounds 2 to 11 for alachlor and compounds 12 to 19 for the electroreduced solution considering deschloroalachlor as the main product of alachlor dehalogenation) (Supplementary material Table S3 and Table S4).

Alachlor oxidation

On the basis of these intermediates and the related literatures [START_REF] Katsumata | Photo-Fenton degradation of alachlor in the presence of citrate solution[END_REF][START_REF] Qiang | Degradation mechanism of alachlor during direct ozonation and O3/H2O2 advanced oxidation process[END_REF][START_REF] Bhoi | Photocatalytic degradation of alachlor using type-II CuS/BiFeO3 heterojunctions as novel photocatalyst under visible light irradiation[END_REF][START_REF] Pipi | Total removal of alachlor from water by electrochemical processes[END_REF][START_REF] Vanraes | Removal of alachlor, diuron and isoproturon in water in a falling film dielectric barrier discharge (DBD) reactor combined with adsorption on activated carbon textile: Reaction mechanisms and oxidation by-products[END_REF][START_REF] Liu | Hydrothermal synthesis of FeS2 as a high-efficiency Fenton reagent to degrade alachlor via superoxide-mediated Fe (II)/Fe (III) cycle[END_REF][START_REF] Hladik | Removal of neutral chloroacetamide herbicide degradates during simulated unit processes for drinking water treatment[END_REF], we proposed that alachlor degradation mechanism involved alkylic oxidation, cleavage of C-N, C-Cl, C-O, and/or C-C bonds, cyclization, and dealkylation (Figure 4). First, compound been previously observed in photo-Fenton oxidation [START_REF] Katsumata | Photo-Fenton degradation of alachlor in the presence of citrate solution[END_REF]. Compound 9 would be generated from compound 5 by dehalogenation and dealkylation. Subsequently, cyclization of compounds 2 and 6 generate heterocyclic compounds 10 and 11 with one aromatic ring, respectively, as it has been also identified in O3/H2O2 treatment [START_REF] Qiang | Degradation mechanism of alachlor during direct ozonation and O3/H2O2 advanced oxidation process[END_REF]. In the meantime, compound 3 was formed by direct scission of the C-Cl bond of alachlor, and was further oxidized to compounds 8 and 7, as reported in other AOPs [START_REF] Qiang | Degradation mechanism of alachlor during direct ozonation and O3/H2O2 advanced oxidation process[END_REF][START_REF] Vanraes | Removal of alachlor, diuron and isoproturon in water in a falling film dielectric barrier discharge (DBD) reactor combined with adsorption on activated carbon textile: Reaction mechanisms and oxidation by-products[END_REF][START_REF] Liu | Hydrothermal synthesis of FeS2 as a high-efficiency Fenton reagent to degrade alachlor via superoxide-mediated Fe (II)/Fe (III) cycle[END_REF]. The cleavage of the C-N bond occurring by α/β scission of the bond and hydroxylation generate compound 4, which could be oxidized via the further cleavage of the C-Cl bond and hydrogen abstraction to form 8, as also reported in BDD(•OH) oxidation [START_REF] Pipi | Total removal of alachlor from water by electrochemical processes[END_REF]. The last step involved oxidative opening of the aromatic ring, leading to small organic ions and inorganic species.

Deschloroalachlor oxidation

As deschloroalachlor was the main by-product of alachlor electroreduction, compounds identified after oxidation of the electroreduced solution were considered as intermediates of deschloroalachlor. The mechanism suggested from the by-products identification showed high similarities with those of alachlor (Figure 5). For example, the compound 13 corresponded to compound 2 without chlorine. The compound 15 was structurally closed to the compound 5. The compound 10 was identified during the oxidation of alachlor and during the oxidation of the electroreduced solution. The compound 16 was already identified by Pipi et al. [START_REF] Pipi | Total removal of alachlor from water by electrochemical processes[END_REF] in their study on alachlor oxidation. These high similarities between the identified by-products showed that the two mechanisms were analogous and that the presence of a chlorine atom in the molecule did not change the sites of radical attack.

Inorganic ions evolution

From the above results, optimal alachlor degradation (100% conversion within 15 min) and mineralization (over 90% after 180 min) can be reached in the following conditions (named as opt-condition): a current of 200 mA, in the presence of 0.05 mmol L -1 of Fe(II) catalyst, with an air oxygen rate of 0.3 L min -1 . EF treatment was performed in these optimal A c c e p t e d m a n u s c r i p t conditions for the non-pretreated alachlor solution (solution alachlor ) and an electroreduced solution of alachlor (solution alachlor-ER ) prior to biodegradability evaluation.

Ions chromatography (IC) was then used to identify and quantify the low-molecular-weight organic acids and inorganic anions generated during the alachlor degradation process (Figure 6). The concentrations of Cl -, NH4 + , and NO3 -were monitored during EF process; while NO2 -was not detected. The release of chloride ions and nitrogenous ions at the early stages of the electrolysis proved that alachlor was readily removed in the EF process and that previously identified intermediates were decomposed quickly. A significant decrease of the total nitrogen was detected after 0.5 h, along with NH4 + concentration decrease after 0.5 h and NO3 -concentration decrease after 1.5 h. The decrease of the total nitrogen content could be explained by the release of N2 after the oxidation of NH4 + into NO3 - [START_REF] Pipi | Total removal of alachlor from water by electrochemical processes[END_REF][START_REF] Yahiat | Photocatalysis as a pre-treatment prior to a biological degradation of cyproconazole[END_REF].

After 2h of electrolysis, the concentration of chloride ions reached 99% ± 8%, showing that alachlor was totally dechlorinated. The slight decrease of the percentage in solution to 91% ± 7% after 3h of electrolysis was not significant regarding the measurement uncertainties. The increase of the nitrogen from NH4 + and NO3 -, which reached a maximum after 0.5h of EF treatment, was faster than the increase of Cl -content. This suggested that the cleavage of the C-N bond occurred prior to the scission of the C-Cl bond, leading to the formation of organo-chloride intermediates in solution.

Contribution of free radicals to alachlor mineralization

The reactive oxidants, which could be formed during the EF process, are •OH and/or superoxide radicals (•O2 -), the conjugate base of peroxide radicals (HO2•) (HO2• ↔ H + + •O2 -), and/or sulfate radical •SO4 -thanks to •OH oxidation (•OH + SO4 2-→ HO -+ •SO4 -) [START_REF] Nidheesh | Magnetite as a heterogeneous electro Fenton catalyst for the removal of Rhodamine B from aqueous solution[END_REF]. The role of radicals involved in the EF process was determined using three radical scavengers, including isopropyl alcohol IPA (•OH and •SO4 -scavenger), tert-butyl alcohol TBA (•OH scavenger, but not for •SO4 -) and benzoquinone BQ (•O2 -scavenger) [START_REF] Zhang | Comparative study of three solid oxidants as substitutes of H2O2 used in Fe (III)-oxalate complex mediated Fenton system for photocatalytic elimination of reactive azo dye[END_REF]. A control test was also performed in the absence of Fe(II) in order to determine the electrooxidation or/and electroreduction contribution, and the results are presented in Figure 7. In the optimal conditions (previously named as 'opt-condition'), alachlor conversion was almost 100% within 15 min. 89% ± 2% alachlor conversion was obtained catalyst, only 81% ± 5% alachlor conversion after 60 min and 15.2% ± 0.5% mineralization after 3 h were obtained. Since a possible reaction between alachlor and hydrogen peroxide can occur in solution [START_REF] Bagal | Sonochemical degradation of alachlor in the presence of process intensifying additives[END_REF], the presence of deschloroalachlor (19.68 mg L -1 at 100 min)

indicated that alachlor underwent electroreduction on the graphite felt in these conditions (Supplementary material Figure S1). The Direct oxidation of alachlor did not take place on the Pt anode since no signal for alachlor oxidation was observed by cyclic voltammetry (Data not shown). According to these results, •OH was the main radical species involved in the alachlor degradation.

Comparison of the EF process with the coupling of electroreduction and electro-

Fenton treatment (ER-EF)

Biodegradability and biodegradation of alachlor before and after electroreduction

An efficient method to evaluate the biodegradability of a solution is to use the ratio of Biological Oxygen Demand (BOD5) and Carbon Oxygen Demand (COD) over 5 days.

Indeed, it has been demonstrated that an effluent can be considered as easily biodegradable if its BOD5/COD ratio is above 0.4 [START_REF] Sarria | Recent developments in the coupling of photoassisted and aerobic biological processes for the treatment of biorecalcitrant compounds[END_REF]. We have previously reported that this ratio was lower than 0.02 after electroreduction of alachlor on Ni foams modified with Ag nanoparticles [START_REF] He | Reductive dehalogenation of a chloroacetanilide herbicide in a flow electrochemical cell fitted with Ag-modified Ni foams[END_REF]. To go further in the biodegradability estimation of alachlor solution after ER (solution alachlor-ER ), a biological treatment was implemented during 21 days with pure alachlor (solution alachlor ) and with the solution alachlor-ER . Whereas, the solution alachlor did not show any increase of the mineralization yield, a value of 46% was obtained for the solution alachlor-ER after one day of culture, indicating the presence of some biodegradable by-products generated during the ER process (Figure S2(a)). A control test with sterilized sludge was performed to assess for possible biosorption of the solution alachlor-ER during the . About 11% TOC decrease can be attributed to the biosorption onto activated sludge and hence 35% of mineralization corresponded to the biodegradation of the by-products from ER. However, as observed in Figure S2(c), a constant concentration of alachlor in solution alachlor and deschloroalachlor in solution alachlor- ER were observed during the 21 days of culture, confirming that alachlor and deschloroalachlor were biocalcitrant.

Biodegradability improvement with electro-Fenton

The evolution of biodegradability was then examined thanks to the BOD5/COD ratio during the EF treatment of a solution alachlor and a solution alachlor-ER . In both cases, the initial biodegradability was negligible and increased with the EF oxidation time, showing a significant biodegradability improvement by the EF process. Moreover, biodegradability was often higher with the solution resulting from the combination of ER and EF (ER-EF treatment), compared to EF alone (Table 1). This indicates that ER pretreatment had an impact on biodegradability improvement. The highest biodegradability was observed after 1 h of oxidation, with BOD5/COD ratios of 0.65 and 0.70, for EF and ER-EF treatments, respectively. The decrease of biodegradability after 1 h of oxidation could be explained by about 50% decrease of available organic carbon source for microorganisms.

Interestingly, after 0.25h of oxidation, the BOD5/COD value increased to 0.16 for the ER-EF treatment whereas it was still not measurable for EF. This could be explained by the presence of organo-chlorinated compounds after 0.25h of EF treatment since 40% of the chlorine from alachlor were found as Cl -ions in solution against 80% for the combined process (Figure 8a). This is in agreement with the study on the suggested EF mechanism, which underlined a preference for a radical attack of the C-N and C-O bonds instead of the C-Cl bond. This phenomenon is likely to results in the formation of organo-chlorinated compounds. Higher TOC values were observed in the case of the coupling of ER and EF.

The presence of a higher concentration of Cl -in the solution alachlor-ER could lowered the efficiency of the EF process, since Cl -has a scavenging effect on •OH (equations ( 8) and ( 9)) [START_REF] Nidheesh | Magnetite as a heterogeneous electro Fenton catalyst for the removal of Rhodamine B from aqueous solution[END_REF][START_REF] Zhang | Comparative study of three solid oxidants as substitutes of H2O2 used in Fe (III)-oxalate complex mediated Fenton system for photocatalytic elimination of reactive azo dye[END_REF]. As a result of higher TOC values, higher organic carbon remained available for microbial growth.

A c c e p t e d m a n u s c r i p t

•OH + Cl -→ •ClOH - (8)
•

ClOH -+ Cl -→ •Cl 2 -+ OH - (9)
Acetic, formic and oxalic acids were analyzed (Figure 8b) since they are low-molecularweight organic acids known to be formed during EF treatment and to be beneficial to microbial growth [START_REF] Annabi | Degradation of enoxacin antibiotic by the electro-Fenton process: Optimization, biodegradability improvement and degradation mechanism[END_REF]. Acetic acid is oxidized to oxalic and formic acids which are directly transformed into CO2 [START_REF] Randazzo | Comparative electrochemical treatments of two chlorinated aliphatic hydrocarbons. Time course of the main reaction by-products[END_REF].The significant higher content of these organic acids for the ER-EF treatment, compared to the EF treatment, is probably related to the better biodegradability obtained. Furthermore, these organic acids do not easily react with radicals, which also partly accounted for the higher TOC values observed in ER-EF treatment [START_REF] Bigda | Consider Fentons chemistry for wastewater treatment[END_REF].

For the EF treatment, the maximum production of acetic and oxalic acid was always reached earlier than for the ER-EF treatment. It is necessary to point out that a small amount of chloroacetic acid was detected in the case of the EF pretreatment, but was never observed during the ER-EF treatment. Chloroacetic acid has been classified as priority pollutant in environment because of its phytotoxic and carcinogenic effect and its Predicted Natural Environmental Concentration in water is about 0.58 μg L -1 [START_REF] Sala | Degradation of Monochloroacetic acid by aluminium modified Fenton process[END_REF]. Finally, in the ER-EF treatment, a slower mineralization, a higher amount of small organic acids, and the absence of chlorinated intermediates can explain the higher biodegradability observed during the electrolysis.

Energy consumption

According to these results, alachlor degradation can be achieved by different processes.

Firstly, electro-Fenton treatment alone is able to degrade alachlor with a mineralization yield of 92% after 3h and a concentration of Cl -ions around 95% of the chlorine content of alachlor. This process requires a charge of 2160 C to treat 12.5 mg of alachlor (173 kC/g of alachlor), corresponding to a consumed energy of about 48 kWh/kg of alachlor for a difference of potential around 1 V. Secondly, a coupling between electro-Fenton and a biological treatment is also possible if the solution is biodegradable with BOD5/COD > 0.4. This is achieved after 0.5 h of EF treatment of the solution alachlor (Table 1). The charge is then 29 kC/g of alachlor and the energy consumed is 8 kWh/kg of alachlor, underlining the possible interest of the coupling process compared with EF treatment alone. Finally, the coupling between the ER-EF pretreatment and a biological process can also be envisaged.

Since the BOD5/COD ratio is 0.16 after only 0.25 h of EF treatment on solution alachlor-ER , an increase of the biodegradability can be expected between 0.25 h and 0.5 h of electrolysis, as experimentally confirmed (Table 1). A charge of 2 kC/g of alachlor corresponding to an energy of 1.6 kWh/kg of alachlor is consumed to do the electroreduction of alachlor since the current efficiency has been previously estimated to be about 36 % [START_REF] Lou | Ni-coated graphite felt modified with Ag nanoparticles: a new electrode material for electro-reductive dechlorination[END_REF]. Thus, ER-EF pretreatment could be interesting if the total energy that it consumed is lower than 29 kC/g alachlor, which corresponds to a time of 28 min for the EF treatment in these operating conditions. Thus, if the time of the electro-Fenton process is reduced by only 2 min, in these operating conditions, the ER-EF pretreatment begins to be less energy-consuming, owing to the higher energy consumption of EF compared with ER. However, these calculus were made on the basis of experiments performed at lab scale and without taking into account the price of the electrode material for example. Therefore, it is difficult to conclude on the interest of ER-EF pretreament for alachlor degradation in these conditions. This strategy should be assessed at higher scale to confirm its relevance.

Conclusions

The sequential ER and EF processes as pretreatment prior to biological treatment toward decontamination of alachlor were presented and compared to EF pretreatment alone. The EF pretreatment was performed in galvanostatic mode on graphite felt cathode with air feeding to promote the generation of H2O2 through two-electron reduction. Complete

6 cm 2 )

 62 modified as follow: 25 mL alachlor (50 mg L -1 ) was electro-dechlorinated on a homemade electrochemical cell with a Ni layer covered support modified by Ag nanoparticles as the cathode (volume: 0.13 cm 3 ), at -1.6 V/MSE in 0.05 mol L -1 NaOH. Then the pH of the electrolyzed solution (named as solution ER ) was adjusted to 3 for the subsequent EF treatment and then to 7 for the biodegradability estimation and the biological treatment. The EF experiments were performed at ambient temperature in an undivided cylindrical glass cell containing 250 mL of solution ER or of a solution of 50 mg L -1 alachlor (named as solution alachlor ) in 0.1 mol L -1 Na2SO4 . The cell was equipped with two electrodes: one 3-dimensional graphite felt (GF) piece (8.5 cm × 5.0 cm × 1.0 cm) as cathode (Mersen; Paris La Defense, France) and a cylindrical platinum (Pt) electrode (34.as anode. Continuous saturation of O2 was ensured by bubbling compressed air flow rate of 0.1-0.5 liter per minute, starting 20 min before electrolysis. The EF process was conducted in galvanostatic mode at a current in the range 15-300 mA, with a ferrous ions solution in the range 0-1.0 mmol L -1 at pH 3.0 adjusted with H2SO4. A pH value of 3.0 was A c c e p t e d m a n u s c r i p t

A c c e

  p t e d m a n u s c r i p t within 3 h EF oxidation, as shown in Figure 2(b). The low mineralization observed in the absence of the ferrous catalyst (Figure 2(b)) suggested that radicals are the main contributors in the mineralization of alachlor. The negative effect of the Fe(II) amount beyond 0.1 mmol L -1 should be most likely attributed to a competitive reaction occurring between the •OH generated and the excess of Fe(II) according to equation (

A c c e p t e d m a n u s c r i p t 2

 2 was generated by dealkylation of alachlor upon the attack by •OH and then further oxidized to compounds 6 and 5 by scission of the R-N bond and hydroxylation, as it has

A c c e p t e d m a n u s c r i p t within 15

 15 min in the presence of BQ indicated that 11% of alachlor conversion can be attributed to the oxidation by •O2 -/ •HO2 -. When TBA was added in the solution, alachlor conversion was only 20.6 % ± 0.5% within 15 min instead of 99%, underlining the important role of • OH in the degradation process. The comparison between the experiments performed with TBA and IPA after 60 min, showed a contribution to alachlor conversion of 63% and 12% for •OH and •SO4 -radicals, respectively. Without Fe(II)

A c c e p t e d m a n u s c r i p t

  setout of culture (Figure S2(b))

A c c e p t e d m a n u s c r i p t

  degradation and over 91% mineralization were achieved within 3 h EF oxidation after optimization of the current, the ferrous ions concentration and the air flow rate. The pseudo-first order kinetic model can well describe the alachlor degradation through the EF process. The radicals, including •OH, •O2 -and •SO4 -, were the main reactive oxidants in this EF treatment, especially •OH with about 63% contribution to alachlor mineralization.The analysis of the intermediate products after EF oxidation of alachlor and the electroreduced solution allowed proposing similar mechanisms for the degradation of alachlor and deschloroalachlor, the main by-product of electroreduction. It showed that the presence of a chlorine atom in the molecule did not change the sites of the radical attack.

A c c e p t e d m a n u s c r i p t

  Biodegradability improvement was shown on the basis of the BOD5/COD ratio for EF and ER-EF processes. The lower BOD5/COD ratio observed at the beginning of the EF treatment (<0.5h) can be attributed to the presence of organo-chloride compounds since the Cl -ions concentration remained still low. The slower mineralization and the higher content in low-molecular weight organic acids found in the case of the ER-EF treatment were in favor of microbial growth and can explain the higher biodegradability observed after 0.5h of treatment. The presence of residual organo-chloride compounds such as chloroacetic acid identified during the EF process would also have an effect on the BOD5/COD ratio. A comparison of the energy consumption of the different processes underlines the possible interest of coupling the electrochemical pretreatment (electro-Fenton or electroreduction followed by electro-Fenton) with a biological treatment, but further studies especially at pilot scale are necessary to be able to conclude on this point.

A c c e p t e d m a n u s c r i p t A c c e p t e d m a n u s c r i p t Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Effect of [Fe(II)] on (a) alachlor degradation and (b) mineralization. Experimental conditions: C0(alachlor) = 50 mg L -1 , applied current = -200 mA, air flow rate = 0.3 L min -1 , pH = 3.0, [Na2SO4] = 100 mmol L -1 , V = 250 mL.

A c c e p t e d m a n u s c r i p tFigure 3 .

 3 Figure 3. Effect of the air flow rate on (a) the generation of H2O2, (b) alachlor degradation, (c) mineralization. Experimental conditions: C0(alachlor)=50 mg L -1 , applied current = -200 mA, [Fe(II)] = 0.05 mmol L -1 , pH = 3.0, [Na2SO4] = 100 mmol L -1 , V = 250 mL.

Figure 4 .Figure 5 .Figure 6 .Figure 7 .

 4567 Figure 4. Proposed pathways for alachlor degradation by EF oxidation

Figure 8 .

 8 Figure 8. a) Dechlorination yield and b) Concentration of acetic acid (red square □), formic acid (blue cycle ⃝ ), and oxalic acid (green triangle Δ) during the EF treatment (dash line and open symbols) and the ER-EF treatment (solid line and symbols).

  conditions: C0(alachlor)=50 mg L -1 , applied current = -200 mA, [Fe(II)] = 0.05 mmol L -1 , pH = 3.0, air flow rate=0.3 L min -1 , [Na2SO4] = 100 mmol L -1 , V = 250 mL.

  Fig 1a A c c e p t e d m a n u s c r i p t

Fig 6 Fig 7 A

 67 Fig 6

Table Time

 Time

	0.5	23.5 (±0.8) 68 (±0)	26 (±2)	0.38 (±0.03)
	1	19 (±1)	66.5 (±1)	47 (±2)	0.70 (±0.02)
	1.5	14 (±2)	57 (±1)	39 (±2)	0.68 (±0.02)
	2	10 (±2)	42 (±2)	26.5 (±0.7) 0.64 (±0.05)
				m a n u s c r i p t
	(h) solution alachlor 0 0.25 0.5 1 1.5 A c c e p t e d TOC (mg L -1 ) COD (mg O2 L -1 ) BOD5 (mg O2 L -1 ) 35.0 (±0.1) 105 (±0) ----77 (±1) --21.7 (±0.7) 58 (±1) 223 (±4) 15 (±2) 48 (±0) 31 (±0) 9.3 (±0.1) 43 (±2) 26 (±4)	BOD5/COD ----0.39 (±0.05) 0.65 (±0.00) 0.60 (±0.05)
	2	6.1 (±0.9)	29 (±1)	13 (±4)	0.4 (±0.1)
	solution alachlor-ER
	0	30 (±2)	102 (±2)	--	--
	0.25	--	74 (±1)	11.8 (±2)	0.16 (±0.03)

Table 1 .

 1 Biodegradability of by-products from EF and ER-EF treatments. Experimental


D Lebrun

D Allano

F Walle

F Corbin

SIZE NUCLEI MEASUREMENT IN A CAVITATION TUNNEL BY DIGITAL IN-LINE HOLOGRAPHY

Digital in-line

is used to measure size and concentration of small bubbles (6-100 µm) in hydrodynamic facilities. The forward diffraction pattern produced by small objects (bubbles, droplets, particles) illuminated by a laser diode is directly recorded by a camera without objective lens. From this pattern, each image plane can be reconstructed by applying backpropagation formalism (Huygens-Fresnel Integral). Then, after having reconstructed the whole volume, the 3-D location and size of each particle can be measured. Here the wavelet transform is used for the implementation of Fresnel Integral.

In the present case, nuclei are measured by a sampling probe specially designed for DIH measurements and equipped with transparent sections. A diverging beam coming from a fiber coupled laser diode (=635 nm, P=12 mW) illuminates the sample volume and the hologram is recorded by a 1024 1280  CMOS camera. From each hologram the volume can be reconstructed slice by slice. We present here the method used for obtaining the size nuclei distribution extracted from hologram analysis. Statistical results (5000 holograms are recorded and processed) obtained under different pressures (P= 567, 927 and 1287 mbars) are compared and discussed.

Introduction

Digital in-line holography (DIH) can be efficiently used for particle diagnostics in small volumes. When a magnification is wanted, particles images can be imaged close to the camera by using a couple of lenses for obtaining a magnification higher than 1 during the reconstruction stage. Such systems are interesting when the 2D sensor (CCD or CMOS camera) cannot be placed near the sample to be studied [START_REF] Malek | Digital In-line holography system for 3D-3C Particle Tracking Velocimetry[END_REF]. In more convenient situations a magnification factor can also be directly obtained by illuminating the sample volume with a diverging beam coming from a pinhole or a laser coupled in an optical fiber. This enables to spread the diffraction pattern over a larger area. Furthermore, the image sensor can be brought closer to the objects to be recorded. Consequently, the numerical aperture (NA) of the recording system is increased and a significant magnification of the reconstructed images is observed. Numerous papers have been published under this configuration also called Digital In-line Holographic Microscopy (DIHM). For example, the authors of Ref. [START_REF] Garcia-Sucerquia | Immersion Digital in-line Holographic microscopy[END_REF] have shown that a resolution of order of the wavelength can be reached. Two decades ago, Vikram et al. [START_REF] Vikram | Some salient features if in-line Fraunhofer holography with divergent beams[END_REF] , where e z is the recording distance), the authors of Ref. [3] concluded that the problem can be exactly formulated as if the hologram were recorded with a plane wave. In other terms, the equation describing intensity distribution in the camera is nothing but the intensity distribution of an equivalent magnified object recorded at an equivalent magnified distance from the camera. As a result, digital holograms can be simply processed as a common in-line hologram that would have been recorded with a collimated plane wave. This configuration is used here to measure the size and position of small bubbles in a cavitation tunnel. Thus, the size distribution obtained from thousands of holograms can be estimated under different pressures. The objective of this communication is to describe the method used for choosing the best configuration of the diverging recording wave in the diameter range (5-140 µm) . In Section 2, the expression of the intensity recorded by holograms is recalled and the resulting magnification factor is expressed. Here the hologram pattern is sampled by a digital camera (CMOS). This means that the spatial sampling conditions must be checked. According to this sampling constraint, the discussions of Section 3 lead to the optimal curvature radius of the recording wave that is needed for obtaining the wanted spatial resolution in the reconstruction image plane. The digital hologram reconstruction principle is recalled in section 4. A transparent pipe has been specially designed for recording holograms of nuclei collected from the cavitation tunnel. The experimental setup and the diameter measurement method are described in sections 5 and 6. Here, statistical results are expected and thousands of holograms have been recorded leading to an enormous volume of data (100 Mbytes/hologram). The automatic processing of holograms and the measured size distributions are described in section 7 and a conclusion is given in section 8.

Digital holography with a spherical recording wave

The optical configuration of in-line holography is given by figure 1. A single laser beam coming from a point source S illuminates the particle and a 2D detector records the interferences produced by the superposition of the direct beam and the wave scattered by the bubble. The point source and the object are located respectively at the distances z s and z e from the camera.

 y

Consider that the input function in the     , plane is :

      e s 2 2 z z i 0 e O 1 ) , ( A           (1)
Under Fresnel approximation, the amplitude distribution in the (x,y) plane is [START_REF] Tyler | Fraunhofer holography Applied to Particle Size Analysis: A Reassessment[END_REF] :

                       d d e e O z
2         (2)
Assuming that the far-field conditions are checked

            1 z . e . i
where

         1 2 2 J r F  (4)
and

e s s z z z K   (5)
The intensity distribution in the camera plane is deduced from (3) by the relation

) ( ). ( ) ( r A r A r I e z e z e z 
where . denotes the complex conjugate :

      r F Kz r F Kz
                 (6)
                 (7)
As a result, a single equation is sufficient to describe the intensity distribution of a particle hologram whatever the divergence of the recording beam. K can be seen as a magnification factor and is a function of the distance object camera z e . In other words, equation [START_REF] Kreis | Handbook of Holographic Interferometry, optical and Digital Methods[END_REF] shows that the diffraction pattern produced by an object of diameter d illuminated by a spherical wave with a curvature radius z s and recorded at a distance z e can be simply expressed as the intensity distribution produced by an object of diameter Kd illuminated by a plane wave and located at a distance Kz e from the camera. This result is very convenient because it lead to a very simple way for the processing of digital holograms. It means that the diffraction pattern of a given object can be processed exactly as if the hologram were recorded with a plane wave and all the conditions (spatial sampling, recording distance, spatial resolution) can be expressed in the equivalent magnified space. This point will be developed in sections 3 and 4.

Note that the magnification factor K can also be written as a function of eq z by replacing e z by K / z eq in equation ( 5):

s eq s z z z K   (8)

Hologram recording conditions

Spatial sampling

Classically, in digital holography the sampling conditions need at least 2 pixels of size p per fringe period. When this condition is not checked, it may give rise to moiré effects and an optical low-pass filter should be applied before spatial sampling the diffraction pattern [START_REF] Nicolas | Suppression of the moiré effect in subpicosecond digital in-line holography[END_REF]. In order to avoid such unwanted effects, the angle between the recording wave and the object wave must be lower than [START_REF] Picart | General theoretical formulation of image formation in digital Fresnel holography[END_REF]. Considering the case where a centred particle is recorded with a plane wave, the above condition can be approximated by p    max where max  is the maximum collecting angle by the camera (i.e. angle viewed from the object). For a digital camera composed of N N  pixels, this condition is easily checked when the recording distance e z is higher than an optimal distance equal to  2 Np [START_REF] Kreis | Handbook of Holographic Interferometry, optical and Digital Methods[END_REF][START_REF] Zhang | Influence of some recording parameters on digital holographic particle image velocimetry[END_REF].

        4p λ 2arcsin
In the present work, a diverging beam is used. Thus, the above condition must not applied to the working distance e z but to the equivalent distance e eq Kz z 

. It follows that the sampling condition leads to

 2 Np Kz e 
. By using the definition of K (equation ( 5)), the recording distance e z should respect the following inequality:

1 2 2 1            s e z Np Np z   . (9)
Eq. ( 9) shows the conditions needed for a convenient spatial sampling of the interference fringes by the camera when an object is illuminated by a spherical wave. This result also means that by using a diverging beam (i.e. by decreasing the value of s z ), the camera can be moved closer to the studied objects without braking in the spatial sampling conditions. As a result, the numerical aperture (NA) can be increased and smaller objects can be studied. This point is detailed in the next subsection.

Spatial resolution

From authors of ref [START_REF] Garcia-Sucerquia | Immersion Digital in-line Holographic microscopy[END_REF], the spatial resolution is  related to the numerical aperture (NA) of the hologram. It can be given by the ratio

  NA 2 /    where      2 / 1 2 2 2 / 2 / e z Np Np NA  
. The highest NA is obtained for the optimal recording optimal distance

 2 1 Np K z opt 
. Then, we deduce the best spatial resolution that can be expected for a given magnification factor K :

2 p 2 K 1 K p             (10)
The sampling step is generally much greater than the product  K . Consequently, equation (10) shows that the spatial resolution is roughly improved by a 1/K factor with a divergent beam.

Note also that in the optimal case as regards to the sampling condition (i.e.

opt e z z 
), equation ( 5) gives the optimal distance source-camera s z that should be used for a given magnification K :

 ) 1 K ( Np z 2 s   (11)



is used, equation [START_REF] Verrier | Digital in-line holography in thick optical systems: application to visualization in pipes[END_REF] indicates that the distance source-sensor must be lower to a limit distance mm z s 4 . 72  for safely recording holograms with a magnification K higher than 2 .

Case of DIH with a relay lens

Another way for magnifying holographic particle images is to use a relay lens. Let us describe the case where an object is illuminated by a plane wave and imaged near the CCD sensor by using an objective lens with a focal length f. This configuration, not used in the present case, is shown in figure II.

Fig. II -Optical configuration of recording in-line holograms with an imaging lens

With this configuration, assuming that well-known geometrical optics laws can be used, a given object is imaged in the     , plane with the magnification:

f z z e s     . ( 12
)
This geometric image can be considered as an object placed in a diverging beam coming from the focal point. As a result, using the conclusions of section 2, the intensity distribution recorded on the

  y , x
plane can be seen as the diffraction pattern produced by a magnified object (of factor K ) illuminated by a plane wave. The resulting magnification is simply given by the product  K . By using ( 5) and [START_REF] Malek | Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter[END_REF], the total magnification is rewritten:

f z K s    (13)
Consequently, if we assume that the far-field conditions are fulfilled, the holographic magnification given by the curvature radius counterbalances exactly the geometrical magnification given by an imaging lens. Therefore, the total magnification is not dependent on the axial location of the objects e z but depends only on the ratio f z s . The 3D particle volume can be reconstructed and analyzed without introducing any correction factor. This result is in good accordance with the formulation given in Ref [START_REF] Sheng | Digital holographic microscope for measuring threedimensional particle distributions and motions[END_REF] for Digital holographic microscopy. Although this configuration offers the advantage of invariance of the magnification, we have preferred to directly illuminate the objects by a diverging beam (see Fig. I). In this way, the number of optical elements is reduced and geometrical aberrations, often observed when a microscope objective is used, are avoided.

Reconstruction of magnified particle images

As said in section 2, the holograms are processed as if they were recorded by a plane wave. Let us recall the principle of the recording and reconstruction of digital holograms. Consider a particle located at a distance e z from the recording plane. Under far-field approximation, the intensity distribution recorded by the camera can also be described by the following convolution:

    ) , ( * * 1 ) , ( y x h h O y x I e e e z z z    (14)
where

) y , x ( O 1 
is the object transmission function (here a bubble) and

          2 2 1 y x z i exp z i ) y , x ( h e e z e   
the Fresnel Kernel.

As for the recording step, the intensity distribution in a reconstructed image located at a distance z r from the camera is also calculated by a convolution operation:

    ) y , x ( h h * * I ) y , x ( R r r e z z z   (15)
It is easy to show that when the best focus plane is reached (i.e. when z r =z e =z), we obtain :

                ) y , x ( h h * * ) y , x ( O y , x O ) y , x ( R z z 2 2 2 1 1 2 (16)
A shown by eq [START_REF] Salah | Application of multiple exposure digital in-line holography to particle tracking in a Benard-von Karman vortex flow[END_REF], the reconstructed image

) y , x ( O 1  is surrounded by the unwanted fringes   ) y , x ( h h * * ) y , x ( O 2 1 z 2 z 2 
. In our case (far-field conditions), this fringes due to the « twin image » located at a distance 2z does not disturb the particle image. The wavelet method described in Ref.10 has been used for implementing the calculation of ) , ( y x R (see subsection 6.1).

Experimental setup

The system used for recording holograms is shown on figure III. The sample volume is illuminated by a diverging beam coming from a single mode optical fiber with a 5 µm core. The source is a modulated laser diode emitting at nm 635 



. The image sensor is a 1024 1280  CMOS camera with 6.7 µm pixels. The curvature radius (taking into account that the wave passes through media of different indices) is set to mm z s 7 . 79  , leading from eq. ( 11) to an optimal magnification K = 1.9. Note that a direct measurement in the hydrodynamic test section (cross section of 2mx1,35m) would have been difficult. Then, an optical probe has been specially designed for these tests. The flow sampling hydraulic loop includes an optical pipe which has an internal square section in order to have two planar optical perpex windows (see fig. IV). A cylindrical pipe, which would have been easier to manufacture, could have been used for these tests. However, the processing of digital holograms is not straightforward even if we have shown that the Fractional Fourier Transform has to be used in this case to reconstruct images [START_REF] Verrier | Digital in-line holography in thick optical systems: application to visualization in pipes[END_REF]. Each hologram is reconstructed plane by plane by applying by a Gaussian shape wavelet formalism described in ref. [START_REF] Buraga | Application of wavelet transform to hologram analysis : three dimensional location of particles[END_REF]. This enables to adapt the working aperture  for hologram reconstruction and leads to an extended the depth of diameter measurement. Indeed, when a collimated beam is used (K=1), the authors of reference [START_REF] Malek | Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter[END_REF], have shown that the point-spread function is invariant in the 3D space and its width is theoretically equal to

  3 . 2  th L
. Here, the aperture has been reduced to Linéaire (T: 80) Linéaire (q: 54) Linéaire (T: 34) sensitivity (pixel/µm)

 = 80 mrad = 55 mrad  = 34 mrad
Note here that for smallest objects, the image diameter becomes invariant and tends toward a limit image diameter (slightly higher than th L ). This observation is confirmed by Fig. V(b) where the predicted sensitivity (image size evolution for a increasing of 1 µm of the object size) is plotted versus the object diameter for different wavelet apertures. This graph shows that by selecting mrad 55   it is would be possible to build a histogram of particle diameter by step of 4 µm, provided that the image size can be estimated with an accuracy of 0.08 pixel. Here, it must be recalled that the graphs of Figure V have been plotted in the equivalent space (plane wave configuration) mentioned in section 2. Moreover, we have shown that a particle image can be measured with accuracy better than 0.1 pixel. Thus, knowing that the magnification K is higher than 2 (see tab I), a classification of nuclei by intervals of 2 µm in the diameter range [5-25 µm] can be expected.

Focusing

The method used for searching the best focus plane depends on the diameter range that is investigated. For the range (5-25 µm), the z-coordinate of a particle image ( eq z ), has been estimated by searching the reconstructed plane that leads to a maximum image contrast. However, as described in [START_REF] Pu | Particle field characterization by digital in-line holography: 3D location and sizing[END_REF], this criterion is not valid for big particles and the Bexon method has been used for the focusing the biggest particles of the upper range (12-140 µm) [START_REF] Bexon | Automatic assessment of aerosol holograms[END_REF]. It must be noted that the density of small bubbles is two orders of magnitude higher than the density of bigger bubbles. This is the reason why the size of the interrogation volume has been adapted for each diameter range (see tab. I). Figure VI gives an example of bubbles reconstructed under this configuration. As described in section 2, equation [START_REF] Zhang | Influence of some recording parameters on digital holographic particle image velocimetry[END_REF] gives the correction factor K that must be applied to z eq for recovering the right axial coordinate z e in the sample volume. Note also the background disturbance surrounding the image of small bubble. It is commonly admitted that a particle image have to be reconstructed with a signal-tonoise ratio (SNR) higher 5 [START_REF] Meng | Holographic particle image velocimetry: from film to digital recording[END_REF][START_REF] Salah | Application of multiple exposure digital in-line holography to particle tracking in a Benard-von Karman vortex flow[END_REF]. Here we have removed particle images under 8dB (SNR=6.3). This fixes the lower limit of detection. For the configuration presented in this paper, the depth location of each bubble is known with an accuracy better than 0.1 mm. For this study, all the particles have been located within a measurement volume V meas = 59 mm 3

Diameter measurement and calibration of the technique

From the best focus reconstructed plane, the particle size is simply determined by counting the pixels whose grey-level are below a 50% threshold [START_REF] Pu | Particle field characterization by digital in-line holography: 3D location and sizing[END_REF]. After having estimated the diameter eq d , the magnification factor K (that depends on the depth coordinate eq z ) is applied to estimate the actual particle diameter. The curvature radius of the recording wave is s z evaluated by using the known distance separating the input and output planar optical window. The estimation of this distance by holography leads to a satisfactory knowledge of the axial magnification ratio. The sizing method has been calibrated on particle images reconstructed by simulated holograms in the range of [5-140 µm]. Then, this method has been validated by using a particle size standard composed of 27 opaque disks deposited by a microlithography technique on a quartz substrate in the range [2 µm, 1000 µm]. Fig. Va shows that the experimental measured diameters are in good accordance with the simulations for diameters d eq of 20 and 30 µm. For higher diameters, we have shown that the particle diameter d eq can be measured with an accuracy better than 10% in the range [40-200 µm].

Automatic processing of holograms and experimental results

After having recorded holograms in-situ (Facilities of Techniques Hydrodynamiques, formerly Bassin d'Essai des Carènes), the post-processing is realized at CORIA laboratory. Here, 5000 holograms have been processed by a fully automatic process developed at CORIA. The computational time needed for extracting the 3D location and size of nuclei is about 2 min/hologram with a 8 processors computer. The results for each pressure condition in the tunnel and for both nuclei diameter range are presented in tab. II. The processing method and the results are summarized in the following subsections.

Range 6-25 µm

The reliability of diameter measurement is strongly dependent on the capability of depth-coordinate estimation. As described in [START_REF] Malek | Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter[END_REF], the 3D invariance of the PSF is only applicable when the particle image is well-focused. However, it has been shown in ref. [START_REF] Pu | Particle field characterization by digital in-line holography: 3D location and sizing[END_REF], that the focusing problem is easy to solve in the range [5-25 µm]. In that case, the depth coordinate is estimated with accuracy better than 100 µm. The size distribution over this range is presented on fig. VII. Note that the results are quite similar for the three pressures conditions.

Fig. VII -Size distribution of nuclei measured by DIH in the range 5-25 µm

It must be pointed out that these distributions have been obtained by assuming the bubbles to be spherical. In fact, due to the circular shape of the point spread function (PSF) [START_REF] Pu | Particle field characterization by digital in-line holography: 3D location and sizing[END_REF] and keeping in mind that the width of the PSF is roughly about 2 pixels, both non-spherical and spherical particles are seen as circular shape images. So, it is highly probable that other particles such as solid particles could wrongly have been identified as bubbles. This may lead to an overestimation of the concentration of small bubbles. This is good accordance with the conclusions of reference [START_REF] Méès | Development of interferometric techniques for nuclei size measurement in cavitation tunnel[END_REF].

Conclusion

Digital in-line holography is applied to the measurement of bubble size in a cavitation tunnel. The optical magnification has been adapted to the size-range to be investigated (5-140 µm). A specific transparent pipe has been designed for this experiment. With this equipment, more than 5000 of holograms have been recorded and automatically processed by home-made software. Note that the focusing process differs as small or big particles are observed. This is why the ranges [5-25 µm] and [12-140 µm] have been studied separately. Concerning the upper range, non-spherical particles (like solid particles or fibers) can be detected and removed from the results. This work is to our knowledge the first study concerning statistical results of size measurement of bubbles by digital holography and processed by a fully automatic process. This makes possible a comparison with others (optical and non optical) measurement techniques.

  studied the gain obtained by recording the holograms with a divergent beam. Under far-field condition (i.e. when the object size d verifies the

Fig. I -

 I Fig. I -Optical configuration of recording in-line holograms of bubbles with a divergent beam. S : Laser source,     , : object plane (x,y) : 2D detector plane

2 ,

 2 object can be approximated by an opaque disk of diameter d. the calculus of integral (2) gives[START_REF] Tyler | Fraunhofer holography Applied to Particle Size Analysis: A Reassessment[END_REF] :

Fig

  Fig. III -Hologram recording for size nuclei measurement. CCD : Camera, LD :modulated laser diode, F : single mode optical fiber, SV : Sample volume.

Fig. IV - 1 .

 1 Fig. IV -Optical pipe used for holography

Fig

  Fig. V-Influence of the wavelet aperture  on diameter measurement in the equivalent space (plane wave configuration) (a) Simulated reconstructed image diameter versus equivalent object diameter, mrad 55  

Fig

  Fig. VI -Example of image bubble reconstructed at different depth.(a) z e = 44 mm (d=10 µm) , (b) z e = 50 mm (d=85 µm) For the configuration presented in this paper, the depth location of each bubble is known with an accuracy better than 0.1 mm. For this study, all the particles have been located within a measurement

7. 2 .Fig

 2 Fig. VIII -Images of bubbles reconstructed automatically from holograms in the range [12-140 µm] (a) P = 567 mb, 1000 holograms (b), P = 927 mb, 2000 holograms and (c) P = 1287 mb, 2000 holograms

Fig

  Fig. IX -Examples of non-spherical particles automatically extracted from the series

Fig X -

 - Fig X -Size nuclei distribution in the optical pipe for different flow pressures