Hélène Thuret-Benoist

Virginie Pallier

Geneviève Feuillade-Cathalifaud

QUANTIFICATION OF MICROCYSTINS IN NATURAL WATERS BY HPLC-UV AFTER A PRE-CONCENTRATION STEP: VALIDATION OF THE ANALYTICAL PERFORMANCES AND STUDY OF THE INTERFERENCES

Keywords: Cyanobacteria, Microcystins, Organic Matter, HPLC-UV/PDA, Preconcentration on SPE

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

Figure 2: Comparison between the standard mobile phase gradient (ISO 20179: 2005) and the optimized mobile phase gradient.

Figure 3: HPLC-UV/PDA separation of a solution of ultra-pure grade water spiked with three microcystins:

1. MC-RR, 2. MC-LR and 3.MC-YR. Data were recorded at 238 nm. Analyse by HPLC-UV/PDA at 238 nm.

Figure 5: SPE protocol adapted to literature. In black and bold, the optimized steps. (UPW = Ultra-Pure grade Water).

Figure 6: Recovery percentages of MCs from a standard mix containing 1µg/L of variants (-RR, -YR, -LR).

Extraction performed using OASIS HLB cartridge followed by HPLC-UV/PDA, data acquisition at 238 nm.

Figure 7: Recovery percentages of MCs from a standard mix containing 1µg/L of variants (-RR, -YR, -LR).

Extraction performed using OASIS HLB cartridge followed by HPLC-UV/PDA, data acquisition at 238nm.

INTRODUCTION

Over the last decades, each year, more and more water resources are forbidden to recreational activities because of cyanobacteria proliferation. Cyanobacterial blooms are geographically spread and concern 58% of the European aquatic ecosystems, 45% of the North America aquatic ecosystems [START_REF] Pinay | Eutrophisation: Manifestations, Causes, Conséquences et Prédictibilité[END_REF] and also major water resources like Victoria lake (Africa), Taihu lake (China) and Baltic Sea (North Europe) [START_REF] Smith | Eutrophication Science: Where Do We Go from Here?[END_REF][START_REF] Paerl | Controlling Harmful Cyanobacterial Blooms in a World Experiencing Anthropogenic and Climatic-Induced Change[END_REF]. In France, 56.6% of the aquatic ecosystems are in a "bad ecological state" (Eau France, 2015), and in the French department Haute-Vienne (87), 81%

of water resources used for recreational activities are in a worrying situation. Warning levels (1, 2 or 3) of the water resources were defined to limit recreational and fishing activities [START_REF] Chorus | Toxic Cyanobacteria in Water: A guide to their public health consequences, monitoring and management Determination of Organic Compounds in Natural and Treated Waters[END_REF].

Between 2014-2017, the warning level started at 56% for level 1 (> 20 000 cells/mL) and 24% for level 2 (> 100 000 cells/mL) (ARS Nouvelle-Aquitaine, 2017).

Cyanobacteria blooms cause ecological troubles, affect the quality of the water resources and consequently the efficiency of the water treatment processes and can threat animal and human health, specifically when cyanobacteria species produce cyanotoxins. Over 2 000 cyanobacteria species, around 40 can produce cyanotoxins or taste-and -odor compounds [START_REF] Graham | Cyanotoxin mixtures and taste -and-odor compounds in cyanobacterial blooms from the midwestern united states[END_REF][START_REF] Briand | Health Hazards for Terrestrial Vertebrates from Toxic Cyanobacteria in Surface Water Ecosystems[END_REF]Merel et al., 2013 a). Even if the toxin-producing cyanobacteria are in minority, there are found in 60 to 70% of the observed cyanobacteria blooms [START_REF] Fawell | Blue-green algae and their toxins-analysis, toxicity, treatment and environmental control[END_REF][START_REF] Sivonen | Toxic cyanobacteria in water[END_REF].

Skin irritation, gastrointestinal illness, dizziness are the main symptoms attributed to cyanotoxins and in the worst case, the consumption of polluted water can lead to death [START_REF] Jochimsen | Liver Failure and Death after Exposure to Microcystins at a Hemodialysis Center in Brazil[END_REF][START_REF] Pouria | Fatal microcystin intoxication in haemodialysis unit Caruaru, Brazil[END_REF]. Nowadays, five cyanotoxins' groups, classified according to their mode of action, are considered as priority hazardous substances [START_REF] Codd | Cyanobacterial Toxins: Risk Management for Health Protection[END_REF]: anatoxins (ATXs), cylindrospermopsin (CYLs), microcystins (MCs), nodularins (NODs) and saxitoxins (STXs). The MCs are the most quantified and studied cyanotoxins [START_REF] Merel | Spatial and thematic distribution of research on cyanotoxins[END_REF], produced by many species like Dolichospermum (ex Anabaena), Microcystis, Oscillatoria, and Planktothrix. The structure of this cyclic heptapeptide is presented Figure 1. The X and Z components are variable amino acids and more than 90 variants of MCs have been identified since 1980 [START_REF] Chorus | Toxic Cyanobacteria in Water: A guide to their public health consequences, monitoring and management Determination of Organic Compounds in Natural and Treated Waters[END_REF]. The most studied and toxic variant is the MC-LR (Leucine-Arginine) [START_REF] Meriluoto | Cyanotoxins: sampling, sample processing and toxin uptake[END_REF][START_REF] Merel | Spatial and thematic distribution of research on cyanotoxins[END_REF].

Figure 1

Humans are exposed to cyanotoxins through contact with contaminated water, consumption of contaminated fish and shells or drinking water produced from water resources exposed to cyanobacterial proliferation (80% of the human exposure to cyanotoxins). To protect human health, the World Health Organization (WHO) fixed a guideline value of 1 µg/L (in equivalent MC-LR) as the maximum concentration in drinking water [START_REF] Who | Guidelines for drinking water quality[END_REF]. The other toxins (ATX-a, CYL, NODs …) are excluded of the WHO guideline because of insufficient relevant toxicological data. However, some countries fixed their own health advisories (Health Canada, 2002 ;[START_REF] Hoeger | Occurrence and elimination of cyanobacterial toxins in drinking water treatment plants[END_REF][START_REF] Chorus | Current approaches to Cyanotoxin risk assess-ment, risk management and regulations in different countries[END_REF]. Health and societal impacts of MCs require to progress on cyanotoxins detection, toxicity analyses and toxins removal in drinking water in order to respect the actual safety standards and make new recommandations [START_REF] Devasurendra | Solid-Phase Extraction, Quantification, and Selective Determination of Microcystins in Water with a Gold-Polypyrrole Nanocomposite Sorbent Material[END_REF].

Even if several detection methods were developed and optimized, detection of MCs at low concentration in natural waters is still challenging because of matrix interferences like salts and dissolved Organic matter (OM). Indeed, high levels of dissolved OM may clog the cartridge during extraction step and OM compounds may be eluted with the toxins [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF]. OM in the sample matrix negatively influences the MCs determination by High Performance Liquid Chromatography with UV/PDA detection (HPLC-UV/PDA) (baseline drift) and over-estimates the MCs concentration [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF]. Thus, the sample preparation is an essential step to optimize MCs detection.

Several methods are mentioned in litterature: dispersive liquid-liquid microextraction (DLLME) [START_REF] Yu | Rapid and Sensitive Analysis of Microcystins Using Ionic Liquid-Based in Situ Dispersive Liquid-Liquid Microextraction[END_REF], solid-phase microextraction (SPME) [START_REF] Poon | Determination of Microcystins in Cyanobacterial Blooms by Solid-Phase Microextraction: High-Performance Liquid Chromatography[END_REF] and Solid-Phase Extraction (SPE) (Palagam et al., 2017). SPE is the most frequently used method, adviced by ISO standard, useful for concentrating micropollutants, minimizing the use of organic solvents, and decreasing the time consuming [START_REF] Andrade-Eiroa | Solid-Phase Extraction of Organic Compounds: A Critical Review[END_REF]. An hydrophilic-lipophilic balanced cartridge (OASIS HLB) promotes good recoveries of several MCs variants [START_REF] Rapala | Detection of microcystins with protein phosphatase inhibition assay, high-performance liquid chromatography-UV detection and enzyme-linked immunosorbent assays-comparison of method[END_REF]. It was designed for concentration of organic compounds with a large polarity spectrum and for the entire pH range [START_REF] Andrade-Eiroa | Solid-Phase Extraction of Organic Compounds: A Critical Review[END_REF].

The objectives of this research work were thus to: 1) develop and optimize an HPLC-UV/PDA method to quantify MCs in natural waters, 2) improve the detection and quantification limits by applying a concentration step on SPE before quantification on HPLC-UV/PDA and 3) test the interferences of the samples' matrix on the concentration and detection steps (pH, conductivity, OM content and origin…). (Equation III).

MATERIALS AND METHODS

Reagents

Solid-Phase Extraction (SPE)

The SPE concentration was operated on the GX-271 ASPEC® automated device (Gilson). The SPE system consisted in a OASIS HLB cartridge (3 cc, 60 mg adsorbent, 30µm particles size, Waters, France). The MCs concentration protocol is based on Waters preconisations. However, few parameters were optimized: the sample volume (from 10 to 100 mL), the percentage of MeOH used for the washing step (between 0% and 30%), the sample and elution solution flow rate (between 10 and 50 mL/min), the cartridge drying duration (from 10 to 45 minutes) and the final transfer step to vial (recovery volume, rincing step). The SPE cartridge was pre-conditioned with 3 mL of MeOH followed by 6mL of ultra pure grade water. A volume of sample was then filtered on a 1.2 µm glass microfiber GF/C filter (Ø=47mm, Whatman) and the residual liquid fraction, whose pH was fixed between 6 and 8, was passed through the cartridge. The filtration on GF/C 1.2 µm allow separating intra cellular toxins (on the filter) and extra cellular toxins (in the filtrate). To ensure that there is no loss on the filter, 200 mL of ultra pure grade water were spiked with MCs at 2 µg/L and filtered on GF/C before SPE concentration. The toxins were not adsorbed on the filter, as shown by the %RE: 99% for MC-RR, 98% for -LR and 97% for YR (results not shown).

After MCs extraction on the solid phase, the cartridge was washed, to removed unwanted compounds (OM, proteins, …), then dried under vacuum before being eluted by 5 mL of MeOH. Glass tubes were used to store the elution solution, which was then dried with a nitrogen stream. When the volume of the eluted solution was reduced to about 0.5 mL, the solution was transferred in a glass vial. The tube was rinced with 0.5 mL of MeOH which was transferred in the same vial. The 1 mL solution in the vial was completely dried under nitrogen stream. The residue in the vial was dissolved in 100 µL of ultra pure grade water.

Interferences on SPE-HPLC-UV/PDA

The water characteristics evolve during the year because of climate and phytoplankton development, as phytoplankton proliferation increases with temperature. This proliferation modifies Dissolved Organic Carbon (DOC) content and OM characteristics [START_REF] Leloup | Organic matter produced by algae and cyanobacteria: Quantitative and qualitative characterization[END_REF] and increase pH by CO2 consumption and NO3 -assimilation [START_REF] Granum | A photobioreactor with pH control: demonstration by growth of the marine diatom Skeletonema costatum[END_REF]. Besides, the run-off rain contributes to increase the salts concentration and thus the water conductivity. Therefore, between an oligotrophic and an eutrophic pond or between an oligotrophic pond in winter and the same pond in summer, various chemical and physico-chemical parameters, as water conductivity, pH and DOC content, may affect the MCs analysis. Thus, after method development and optimization, interferences of the samples's matrix on SPE concentration were evaluated.

To evaluate the significance of the interferences tests, statistical analyses were performed on average SPE recovery and MCs concentration. To determine if the means were significantly different, student's t-test were perfomed with α = 0.05

Tests on ultra pure grade water

The interferences of pH, conductivity and OM content on MCs quantification by SPE-HPLC-UV/PDA were tested on ultra pure water spiked with MC-LR, -RR and -YR at a concentration of 0.5 µg/L each. The prepared solution were systematically mixed during 12 hours before extraction of 5

replicates on SPE and analyses on HPLC-UV/PDA.

pH interference was tested for two pH (5 and 9). pH was fixed by addition of HCl 0.1 M or NaOH 0.1 M in 250 mL of ultra pure grade water. These pH conditions were choosen because pH of natural waters depends on soils characteristics (granitic or limestone) and natural and anthropic activities and phenomenom and because drinking water pH must ranged between 6.5 and 9.

The interference of samples's conductivity was tested by adding NaNO3 in ultra pure grade water to fix conductivity at 200 µS/cm, the minimal conductivity required for drinking water at 25°C.

OM interference on analytical method was tested by adding known amounts (2.5 or 5 mg C/L) of fulvic Acid (FA) and hydrophobic compounds (HPO) in ultra pure grade water. These DOC concentrations were choosen because the French drinking water regulations set maximum DOC concentrations of 8 mg C/L and 2 mg C/L in resource water and drinking water respectively. FA (2S101F)

were extracted from the Suwanee River (provided by the International Humic Substances Society (IHSS))

and HPO compounds were extracted from lab culture of Microcystis aeruginosa according to the protocol of [START_REF] Aiken | Isolation of Hydrophilic Organic Acids from Water Using Nonionic Macroporous Resins[END_REF] and Malcolm & MacCarthy (1992), by using DAX-8 and XAD-4 resins in series.

The fractionation protocol allowed separating OM in three fractions, according to their hydrophobicity:

HPO, transphilic (TPH) and hydrophilic (HPI) fractions and the organic fractions were purified according to the protocol of [START_REF] Leloup | Organic matter produced by algae and cyanobacteria: Quantitative and qualitative characterization[END_REF]. Such OM compounds were choosen because this cyanobacteria specie is frequently found in eutrophic freshwater pond and its Algal Organic Matter (AOM) is characteristics of OM from natural water subjected to eutrophication. Besides, the HPO fraction represents the major fraction of natural water non-subject to eutrophication; either oligotrophic water or under winter conditions.

Tests on synthetic water

Experiments were also performed on synthetic water [START_REF] Lenoble | Dynamic arsenic removal on a MnO2-loaded resin[END_REF], characteristic of natural underground water from granitic soils: comparable major ions concentrations (ionic chromatography, 930 Compact IC Flex from Metrohm ) and pH (Table 1). Matrix interferences were analyzed by measuring the recoveries of MC-LR : 250 mL of synthetic water were spiked with MC-LR at 1 µg/L and filtered on SPE before HPLC-UV/PDA analyses.

Table 1 Tests on natural water

To test the applicability of the SPE and HPLC-UV/PDA methods , natural water was sampled at Pigeard pond, an artificial shallow pond (maximum depth 2.30 m, area 3.2 ha) located at latitude 45°54'N and longitude 1°11'E, near Limoges (87), France. Water quality of this eutrophic pond was monitored during 21 months (from April 2017 to January 2019). Once a month, bio-physicochemical analyses were performed: pH, conductivity, redox potential, temperature and dissolved oxygen with a multi-parameters probe (3430 IDS by WTW), OM was quantified and qualified: DOC (Shimadzu TOC-L, precision ± 2%, detection limit = 50 µg C/L), UV254 (UV-visible Shimadzu Pharmaspec 1700, precision ± 0,005) and hydrophobic fractionation [START_REF] Aiken | Isolation of Hydrophilic Organic Acids from Water Using Nonionic Macroporous Resins[END_REF] and Malcolm & MacCarthy (1992) protocol), phytoplankton was characterized: species identification and counting (Malassez cell and microscope Nikon Eclipse 2000), chlorophyll-a content (standard NF T 90-117) and toxins, as MCs, were identified and quantified. After filtration on GF/C filter, the filtrate, containing the extracellular toxins, were stored at -18°C until analysis. Besides, to confirm the developed method is suitable for natural water analysis and to ensure good data quality, one natural sample per season was spiked with MC-LR at 2 µg/L before analysis. The MCs concentration before and after spiking were compared.

RESULTS AND DISCUSSION

HPLC-UV/PDA method optimization

The ISO gradient elution was optimized in order to separate both correctly and quickly the 3 MCs variants, -LR, -RR and -YR. Different gradient programs were thus tested to hasten the retention time of the MCs variants and decrease the method duration while maintaining a proper distinction of peak variants. The flexible parameters were: the initial ratio %A / %B, the %A increasing slope to speed the toxins output, the %A decreasing slope. The chosen gradient was approximately faster by half than the ISO gradient (Figure 2).

Figure 2

Figure 3 With this gradient elution program combined with a 0.6 mL/min flow rate and a 15 µL injection volume, the recorded retention time, in ultra pure water, were 8.247 min, 9.225 min and 9.407 min respectively for MC-RR, -LR and -YR at 500 µg/L each (Figure 3).

The reproducibility of the method was verified by analyzing ten times a sample of MC-LR at 500 µg/L in ultra pure water and confirmed by a variation factor lower than 10%: 460 µg/L ± 35 µg/L (7.7% of variation).

Performance parameters for the HPLC-UV/PDA method are listed in Table 2. The characteristics were comparable for the 3 studied MCs and the correlation coefficient (r²) were better than 0.990. The ILOD for analytical standards in ultra pure grade water were ten times better than the ILOD obtained by Aranda-Rodriguez et al., 2003 (ILOD = 80 -30 and 40 µg/L respectively for MC-RR, -LR and -YR).

Conductivity effect on MCs analyses by HPLC-UV/PDA was studied by comparison of calibration curve's slope in ultra pure grade water and synthetic water (70 µS/cm). Synthetic water samples were spiked with increasing concentrations of MC-LR (from 150 to 5 000 µg/L). The calibration curve's slope obtained was fairly similar than those obtained with ultra pure grade water (less than 10% of difference) (Figure 4). Thus, the proposed HPLC-UV/PDA method was validated by assessment of linearity, reproducibility and ILOD -ILOQ.

Table 2 Figure

Evaluation of SPE efficiency

The aim of SPE protocol is to concentrate the extracellular toxins. The initial protocol was adapted from literature (Figure 5) and modifications (sample volume, MeOH percentage for washing, sample elution flow rate, drying duration, final transfer to vial) were realized on ultra pure grade water spiked with MCs at 2 000 µg/L.

The use of the GX-271 ASPEC® device provided a good reproducibility of the duration steps and flow rates. They were fixed in order to obtain a proper drop by drop extraction and elution. To limit the method time, several drying duration (between 10 and 45 minutes) were tested until getting a total column drying in a limited time.

After the sample loading step, various percentages of MeOH in the washing solution were tested.

The objective of this step is to remove undesirable molecules without loosing molecules of interest. A washing solution containing more than 25% of MeOH was not suitable because of MCs elution: the percentage of recovery (%RE) droped to less than 50% with MeOH at 50%, to 72% with MeOH at 30% and 89% with MeOH at 25%. To purify the sample without loosing MCs, a 20% methanol-water solution was chosen (98 ± 2% of recovery).

At the end of the protocol, once the MCs are in the 5 mL MeOH in the tube, the first protocol consisted in evaporating under dryness, dissolving into 100 µL ultra pure grade water and transferring to a vial. This protocol gave poor %RE probably because of MCs loss. The protocol was optimized by additional rincing step: 4.5 mL of MeOH were evaporated and the remaining 0.5 mL were transferred to a vial. The tube was rinsing with 0.5 mL of MeOH and this volume was added to the vial. The solution in the vial was evaporated to dryness and the MCs were dissolved into 100 µL of ultra pure grade water.

According to the cartridge volume (3 mL), a sample volume between 1 mL and 250 mL was adviced (Sigma-Aldrich, 1998). Eutrophic water can be highly concentrated in dissolved organic carbon.

In order to avoid clogging of the cartridge by OM and thus lost of SPE efficiency [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF], a 50 mL sample volume was defined. This volume is the average volume defined in literature [START_REF] Poon | Determination of Microcystins in Cyanobacterial Blooms by Solid-Phase Microextraction: High-Performance Liquid Chromatography[END_REF][START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF]ISO 20179, 2005;[START_REF] Cong | Determination of trace amount of microcystins in water samples using liquid chromatography coupled with triple quadrupole mass spectrometry[END_REF]. As the concentration factor was fixed at 500-times [START_REF] Poon | Determination of Microcystins in Cyanobacterial Blooms by Solid-Phase Microextraction: High-Performance Liquid Chromatography[END_REF][START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF]ISO 20179, 2005;[START_REF] Cong | Determination of trace amount of microcystins in water samples using liquid chromatography coupled with triple quadrupole mass spectrometry[END_REF], a 100 µL re-dissolved solution was used.

According to the SPE optimized method, extracellular MCs can be measured in water for concentrations between 0.1 µg/L and 10 µg/L (Table 3). The method limit of detection (MDL) is comparable to [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF] but superior than the 0.07 µg/L obtained by [START_REF] Nicholson | Evaluation of Analytical Methods for Detection and Quantification of Cyanotoxins in Relation to Australian Drinking Water Guidelines[END_REF]

Table 3

The average %RE for extraction of MC-RR, -LR and -YR analytical standards in ultra pure grade water, from 0.1 to 10 µg/L, using OASIS HLB cartridge, were greater than or equal to 95% (Table ).

These results are comparable to those obtained by [START_REF] Cong | Determination of trace amount of microcystins in water samples using liquid chromatography coupled with triple quadrupole mass spectrometry[END_REF]: 98.7 ± 5.6 % for MC-LR and 95.4 ± 4.7 % for MC-RR. They are 10% higher to those obtained by [START_REF] Rapala | Detection of microcystins with protein phosphatase inhibition assay, high-performance liquid chromatography-UV detection and enzyme-linked immunosorbent assays-comparison of method[END_REF] and [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF]. The difference can be explained by the characteristics of the tested sample: ultra pure grade water in our study unlike natural samples for the others.

The optimized SPE method is presented Figure 5: the SPE cartridge is pre-conditioned with 3 mL of MeOH (15 mL/min) and 6 mL of ultra pure grade water (40 mL/min). 100 mL of sample is filtered on a 1.2 µm glass microfiber GF/C filter (Ø=47mm, Whatman). Then, 50 mL of sample are passed through the cartridge at a flow rate of 40 mL/min. After extraction, the cartridge is washed with 3 mL of ultra pure grade water (6 mL/min) and 5 mL of 20% methanol-water solution (15 mL/min), dried under vacuum for 20 min (30 mL/min) and eluted with 5 mL of MeOH at 15 mL/min.

The proposed SPE method was validated by assessment of accuracy, specificity to MCs, precision, repeatability and MDL and meet validation criteria for use in trace MCs concentrated water.

Figure 5

Matrix interferences on SPE concentration

Effect of pH

In Limousin area, water pH are acid because of granitic soils but may increase following cyanobacterial blooms. The effect of pH on MCs concentration on SPE was thus studied for pH 5 and 9

and compared to the neutral pH of ultra pure grade water. As presented on Figure 6, the average recoveries of MCs at high pH (pH 9) were 106 ± 5% and was significantly higher (Student's t-test, p-value = 0.015 < 5%) than those obtained at neutral pH (97 ± 2%). At low pH (pH 5), the average %RE was significantly much lower (68 ± 9%) (Student's t-test, p-value = 2.10 -4 < 5%).

Figure 6

To limit pH effect, it is recommended to fix the sample pH between 6 and 8 before SPE to ensure the best %RE and allow MCs concentration comparison throughout the seasons. The result is in accordance with [START_REF] Kaloudis | Determination of Microcystins and Nodularin (Cyanobacterial Toxins) in Water by LC-MS/MS. Monitoring of Lake Marathonas, a Water Reservoir of Athens, Greece[END_REF] who fixed the pH between 5 and 8 and with [START_REF] Zervou | New SPE-LC-MS/MS method for simultaneous determination of multi-class cyanobacterial and algal toxins[END_REF] who adviced a neutral pH for MCs treatment on OASIS HLB.

Effect of conductivity

In Limousin area, water are slightly mineralized because of grainitic soils. The average conductivity is around 50 -120 µS/cm. The %RE of MCs after concentration on SPE was then studied for conductivity of 200 µS/cm and compare to the zero conductivity of ultra pure grade water. At 200 µS/cm, the %RE were 101%, 99% and 100 ± 2% respectely for MC-RR, -YR and -LR (Figure 7) and were not significantly different than those obtained in ultra pure grade water (p-value = 0.13 (Student's t-test)).

Figure 7

Figure 8 Comparable results were obtained on synthetic water with a %RE of 103 ± 7% for MC-LR (Figure 7). The increase of ionic strength did not impact, neither the %RE of MC-LR extraction by SPE (p-value = 0.067 (Student's t-test)), nor the analyses on HPLC-UV as shown on chromatograms on Figure 8. Thus, it is not necessary to control conductivity before SPE preconcentration and this SPE-HPLC-UV/PDA method can be used all year long whatever the water conductivity.

Effect of organic matter:

DOC content and OM characteristics in ressource water for drinking water production vary according to climate. The concentrations increase because of runoff water and with phytoplanckton development. The %RE of MCs and the chromatograms shape were compared in ultra pure grade water spiked with both 2.5 mg C/L and 5 mg C/L of HPO from M. aeruginosa and FA from Suwanee River.

Despite the purification step on SPE, the presence of OM increased significantly the MC-LR %RE (Student's t-test, p-value < 5%) (Figure 9), which is consistent with [START_REF] Aranda-Rodriguez | Extraction of 15 Microcystins and Nodularin Using Immunoaffinity Columns[END_REF] The deviation between theorical and experimental MCs concentration were -3 ± 2% %, +18 ± 2%, +15 ± 3% and +24 ± 4% % for respectively ultra pure grade water, HPO at 2.5 mg C/L and FA at 2.5 mg C/L and 5 mg C/L.

The characteristics of OM did not significantly impact (HPO and AF 2.5 mg C/L: p-value = 0.39 and AF 2.5 and 5 mg C/L : p-value = 0.08 (Student's t-test)) unlike the concentration.

Application of the SPE -HPLC-UV/PDA method on natural water samples: Pigeard pond's monitoring

Pigeard pond is an hyper-eutrophic pond with total phosphorus concentration between 20 -170 µg/L, total nitrogen concentrations between 0.6 -3.6 mg/L and chlorophyll-a higher than 100 µg/L in summer. Under high temperatures, phytoplanckton, mostly cyanobacteria, developped in the pond (Figure 11) and during summer, their concentration ranged between 0.5.10 6 and 6.5.10 6 cell/mL. Blooms were observed on May 2018 and October 2018, with repectively 6.5.10 6 cells/mL (Planktolyngbia) and 11.10 6 cells/mL (M. wesenbergii). Phytoplankton developments increase DOC concentration and HPI percentage (Figure 12): in summer, the average DOC content was 9 ± 2 mg C/L, with 55 ± 6 % of HPI while in winter, the average DOC content was 5.2 ± 0.7 mg C/L, with 40 ± 3 % of HPI. In these later conditions, the OM content is mostly explain by more hydrophobic runoff water inputs (Figure 12).

Figure 11

Figure 12 As mentioned during the study of the interferences on the SPE and HPLC-UV/PDA methods, the presence of OM over-estimated the MCs concentration, even after sample purification on SPE. In order to ensure good data quality, four samples (one at each season) from Pigeard pond were spiked with MC-LR at 2 µg/L. The recoveries were all between 105 and 118% which is consistent with Yen et al., 2011 (100 -120%) (Table 4).

Table 4

The developed method was thus validated on natural samples and used to investigate the occurrence of microcystins MC-LR, -RR and -YR in Pigeard pond (87).

The three studied MCs (-LR, -RR and -YR) were detected in the samples collected between June and December 2017 and between June and November 2018, which correlated with high water temperatures and cyanobacteria development. Their concentrations ranged from <LOQ to 34.4 µg/L (total microcystins) with a maximum of 18.5 µg/L of extracellular MCs. Among all detected toxins, MC-LR was the most abundant variant. As presented on Figure 13, the MCs detection on the sample is well correlated with the presence of potentially toxic species (D. heterospora (ex Anabaena), P. agardhii, M.

aeruginosa, and M. wesenbergii).

Figure 13

4.

CONCLUSION

An analytical method coupling concentration by SPE and detection by HPLC-UV/PDA was developed and optimized to concentrate, purificate and detect the MC-LR, -RR and -YR in natural water samples. After optimization on ultrapure grade water, a MDL of 0.1 µg/L for MCs was obtained.

Interferences of pH, conductivity and OM content and characterisitics were tested. The presence of OMnatural or algal organic matter -overestimated the MCs concentration: recoveries on ultra pure grade water and ultra pure grade water spiked with OM of 92-101% and 96-130% respectively. However, no interference of the OM characteristics were underlined. The method can thus be used all year long. The method was then successfully applied on 19 water samples collected in an eutrophic pond between June 2017 and December 2018 and for each season, one sample of Pigeard was spiked with MC-LR.

Recoveries ranged from 105 to 118%. The analytical method developed is thus appropriate for the monitoring of MCs in an eutrophic lake.

Table 2: HPLC-UV/PDA instrument performances using XBridge C18 (3.5µm -4.6x100mm) and optimized gradient.

Figure 1 :

 1 Figure 1: General structure of microcystins.

Figure 4 :

 4 Figure 4: Comparison of calibration curves of MC-LR in ultra-pure grade water and synthetic water.

Figure 8 :

 8 Figure 8: HPLC-UV chromatogram for MC-LR in ultra-pure grade water or synthetic water after SPE preconcentration (initial concentration 1µg/L).

Figure 9 :

 9 Figure 9: Recovery percentages of MCs from an individual standard of MC-LR at 1µg/L. Extraction performed using OASIS HLB cartridge followed by HPLC-UV/PDA.

Figure 10 :

 10 Figure 10: HPLC-UV chromatogram for MC-LR in ultra-pure grade water spiked with HPO 2.5mg C/L.

Figure 11 :

 11 Figure 11: Influence of the water temperature on the development of cyanobacteria.

Figure 12 :

 12 Figure 12: Characteristics and concentration of OM in Pigeard pond according to the season. Respective average air temperature for each season: 18 ± 4°C -11 ± 4°C -4 ± 3°C -14 ± 4°C.

Figure 13 :

 13 Figure 13: Correlation between toxins producers species and MCs concentrations in Pigeard pond.

  MC-LR, MC-RR and MC-YR were purchased from Novakits (France). The three MCs were conditioned in methanol (MeOH) at a concentration of 10 mg/L, with a purity > 95%. To prepare the stock solutions, the MeOH was evaporated under nitrogen stream and the toxins were dissolved in ultra pure grade water. HPLC grade acetonitrile and MeOH were respectively obtained from Carlo Erba (Paris, France) and VWR Chemical (France), while the trifluoroacetic acid (TFA) was obtained from Thermo Fisher. The water used for dilution was ultra pure grade water produced by a Gradient A10 Milli-Q system.The stock solutions were stored at -20°C before use in tinted glass vial. The stability of MCs concentration during storage was checked by measuring the same sample at 1000 µg/L of MC-LR in ultra pure grade water every two weeks during 6 months. The stability was confirmed with an average concentration of 915 µg/L ± 66 µg/L (less than 10% loss).Liquid chromatography coupled with UV/PDA detectionHPLC-UV/PDA and SPE methods were optimized by using ultra pure grade water spiked with MCs standards. Linearity plots were constructed for HPLC-UV/PDA detection by analysis of standard solutions at eight concentrations in the range 20 -5000 µg/L. A full validation study of the method was carried out -evaluation of specificity, accuracy, repeatability, precision, limits of detection and robustness -by analyzing ten times a sample spiked with MC-LR.The liquid chromatography (model LC 1220 Infinity, Agilent Technology, USA) is equipped with a dual-channel gradient pump and a reverse phase C18 analytical column (XBridge C18 -3.5 µm -4.6 x 100 mm, Waters) thermostated at 35°C. A UV photodiode was used as detector. UV-spectra were drawn from 200 to 300 nm and data were recorded at 238 nm because this wavelength corresponds to the maximum absorption of the MC's Adda group. The retention time by HPLC-UV/PDA of the three MCs variants were identified by using the analytical standards. The chromatographic parameters were inspired from ISO 20179:2005. The mobile phase A was composed of 0.05% trifluoroacetic acid (TFA) in acetonitrile (ACN) and the mobile phase B of 0.05% TFA in ultra pure grade water. The objective of the optimization was to decrease the analysis duration while keeping a good MCs variants separation. The gradient elution program (ratio %A / %B evolution in function of the time), the flow rate (from 0.3 to 1.0 mL/min) and the injection volume (from 10 to 30 µL) were thus adapted to the column characteristics.Before each sequence, the column was equilibrated for 15 minutes at the initial conditions. The concentration of extracellular MCs was calculated as follows : of each individual MC, µg/L : re-dissolving volume of the sample after SPE, mL : volume of water sample applied on SPE cartridge, L : slope of the calibration curve, : intercept with y-axis, area : pic area, milli absorbance unit To determine the instrument limit of quantification (ILOQ), successive dilutions of the standard solution were analyzed until a concentration that presented a chromatogram comparable to ultrapure water. 10 replicates of the lowest concentration that presented a detectable peak were then quantified and the ILOQ was calculated as the average concentration of these ten replicates containing MCs at this concentration. ILOQ was then determined by: = ∑(" # ,… ," #& ) '( (Equation II) where n is the concentration of each replicate. The instrument limit of detection (ILOD) was determined as ) = *+,-.

  or 0.05 µg/L fromLévi et al., (2006) and much more superior than those obtained by HPLC-MS/MS (0.01 µg/L(Lévi et al., 2006), 0.005 µg/L[START_REF] Nicholson | Evaluation of Analytical Methods for Detection and Quantification of Cyanotoxins in Relation to Australian Drinking Water Guidelines[END_REF]).

Figure 9 Figure 10 Figure 10

 91010 Figure 9Figure10

Table 3 :

 3 Method performances obtained for OASIS HLB preconcentration and HPLC-UV/PDA detection at 238nm in ultra pure grade water.

Table 4 :

 4 The results of matrix spike recovery (sample from Pigeard pond).

Table 1 :

 1 Synthetic water characteristics (concentrations in mg/L).

	Calcium	3,6 ± 0,2	Sulphate	4,0 ± 0,4
	Magnesium	1,5 ± 0,1	Chloride	8,6 ± 0,6
	Sodium	7,0 ± 0,5	Nitrate	10,9 ± 0,5
	Potassium	0,9 ± 0,1	Hydrogen carbonate	10,35
	pH	6,5	Turbidity	0,6 ± 0,1 NTU
	DOC	< 0,5 mg C.L -1

Table 2 :

 2 HPLC-UV/PDA instrument performances using XBridge C18 (3.5µm -4.6x100mm) and optimized gradient elution.

		MC-RR MC-YR MC-LR
	Slope (a)	42.87	51.57	58.88
	Intercept with y-axis (b)	-2175	-1852	-528
	RSD	0.7	0.8	0.9
	r²	0.996	0.998	0.998
	ILOQ (µg/L)	9	13	12
	ILOD (µg/L)	3	4	4

Table 3 :

 3 Method performances obtained for OASIS HLB preconcentration and HPLC-UV/PDA detection at 238nm in ultra pure grade water.

		Range (µg/L) MDL (µg/L) Recovery (%) RSD (%)
	MC-RR	0.1-10	0.1	95	3
	MC-LR	0.1-10	0.1	98	3
	MC-YR	0.1-10	0.1	97

ACKNOWLEDGMENTS

The autors thank the FEDER (European Found for Regional Development) for their financial support. The autors are grateful to WATERS Company for the donation of the chromatographic column.

Sample

Initial concentration


S Amir Bahrani

Luc Humberset

Rémy Osipian

Laurent Royon

Kamel Azzouz

André Bontemps

How thermally efficient are chaotic advection mixers ? An experimental assessment

Keywords: Chaotic advection, Heat transfer, Friction factor, Enhancement techniques, Energy efficiency

Chaotic Laminar Mixers (CLMs) are static mixers whose concept uses chaotic advection based on baker's transformation. The present work is an attempt to study the CLMs from the viewpoint of heat transfer efficiency and global energy efficiency, and to compare the CLMs with helical heat exchangers. The influence of the number of bends and of the orientation of curvature planes was studied to bring out the role of regular and alternate Dean flow. An experimental investigation using water as inner hot fluid was carried out. It is shown that for the studied range of Reynolds numbers , CLMs have a heat transfer efficiency two-times better than helical heat exchangers. However taking into account pressure losses, helical exchangers have better global energy efficiency than CLMs. For laminar flows, CLMs might be good heat exchangers when only mixing and heat transfer are the main requests.

Introduction

The efficiency of convective heat transfer with a flow in laminar regime is a major concern in industrial 2 applications due to fluid physical properties (high viscosities), mechanical behavior (velocity profile, no 3 fluid mixing) and device geometry (mini and microfluidic devices). In such systems, in the absence of 4 a turbulent flow regime, heat transfer between the fluid and the wall occurs by molecular diffusion. In 5 order to increase the heat and mass flow rate, several means can be used. It is usual to distinguish two 6 types of enhancement techniques, passive or active [START_REF] Bergles | Current progress and new developments in enhanced heat and mass transfer[END_REF][START_REF] Bergles | Enhanced heat transfer: endless frontier, or mature and routine?[END_REF].

7

Passive techniques are those which do not necessitate an external energy source other than the energy 8 Email address: seyed-amir.bahrani@univ-paris-diderot.fr (S. Amir Bahrani) needed to circulate the fluids through the heat exchanger. In active techniques an external energy source is needed to modify the main flow. These last techniques penalize the global performance of a system because of the added energy cost. Many articles have been devoted to describe and analyze the most used techniques [START_REF] Ghani | Hydrothermal performance of microchannel heat sink: The effect of channel design[END_REF][START_REF] Léal | An overview of heat transfer enhancement methods and new perspectives: Focus on active methods using electroactive materials[END_REF][START_REF] Siddique | Recent advances in heat transfer enhancements: A review report[END_REF][START_REF] Dewan | Review of passive heat transfer augmentation techniques[END_REF][START_REF] Steinke | Review of single-phase heat transfer enhancement techniques for application in microchannels, minichannels and microdevices[END_REF][START_REF] Ligrani | Comparison of heat transfer augmentation techniques[END_REF][START_REF] Tao | A unified analysis on enhancing single phase convective heat transfer with field synergy principle[END_REF] In passive techniques, the heat transfer rate can be improved in creating some disturbance in the fluid flow. However, this can induce a significant increase of the pumping power and finally of the pumping cost [START_REF] Dewan | Review of passive heat transfer augmentation techniques[END_REF][START_REF] Bergles | Enhanced heat transfer: endless frontier, or mature and routine?[END_REF]. To achieve the desired heat transfer rate at an economic pumping power, several techniques have been proposed. Several types of device have been implemented to create an extension of the heat transfer surface and/or to provoke some flow modification. In laminar regime the heat transfer coefficient in very large at the entrance of ducts and decreases with the increasing distance down to the final value for fully developed flow [START_REF] Bejan | Convection heat transfer[END_REF]. Flow inserts like fins or ribs interrupts this development and acts as a new entrance thus increasing the local heat transfer coefficient. Another way is to generate a secondary flow to mix the stream lines and/or to drive the core flow to the walls. Such a secondary flow can be produced by modifying the channel geometry in creating secondary channels to induce mixing [START_REF] Steinke | Review of single-phase heat transfer enhancement techniques for application in microchannels, minichannels and microdevices[END_REF] or in combining secondary channels and ribs [START_REF] Ghani | Heat transfer enhancement in microchannel heat sink using hybrid technique of ribs and secondary channels[END_REF]. This secondary flow also can appear by modifying the channel cross section [START_REF] Siddique | Recent advances in heat transfer enhancements: A review report[END_REF] for example in making successive alternating wall deformations of the internal and external walls of an annular heat exchanger [START_REF] Zambaux | The effect of successive alternating wall deformation on the performance of an annular heat exchanger[END_REF]. Another technique is to insert vortex generators which can take various cross-sectional shapes and forms such as protrusions, wings, inclined blocks, winglets, fins, and ribs [START_REF] Lemenand | Vorticity and convective heat transfer downstream of a vortex generator[END_REF][START_REF] Zhou | Experimental investigations of heat transfer enhancement by plane and curved winglet type vortex generators with punched holes[END_REF][START_REF] Habchi | Chaotic mixing by longitudinal vorticity[END_REF][START_REF] Habchi | Enhancing heat transfer in vortex generator-type multifunctional heat exchangers[END_REF]. Secondary flows can also be produced in changing the cross section orientation for non-circular channels and heat transfer improvement has been observed [START_REF] Keklikcioglu | Experimental investigation on heat transfer enhancement in a circular tube with equilateral triangle cross sectioned coiled-wire inserts[END_REF][START_REF] Filimonov | Numerical study on the effect of cross-section orientation on fluid flow and heat transfer in a periodic serpentine triangular microchannel[END_REF]. In their review, Ghani et al. [START_REF] Ghani | Hydrothermal performance of microchannel heat sink: The effect of channel design[END_REF] have underlined the role of two phenomena namely Dean vortices and chaotic advection. In this paper, in order to increase the heat transfer coefficient, we are particularly interested in a passive technique by using a phenomenon known as chaotic advection. In curved pipes, due to the secondary flow generated by centrifugal forces (see figure 1), transverse displacements of fluid particles are provoked and consequently the axial flow decreases leading to fluid mixing [START_REF] Dean | note on the motion of fluid in a curved pipe[END_REF]. The Dean roll-cells, formed in the secondary flow, act as internal agitators which homogenize the flow. This mixing process is improved in separating the flow in two or several parts and in mixing them again together after. This is produced by the physical realization of a mathematical transformation known as the "baker's transformation".

A practical realization of this transformation, which allows the exchange surface to be maximized in a laminar regime, is the split and recombine (SAR) exchanger/mixer (called here Chaotic Laminar Mixers CLM). This geometry has been proposed for the first time by Gray et al. [START_REF] Gray | Drie Novel interconnection technologies for integrated microfluidic systems1paper presented as part of the ssaw-98 workshop.1[END_REF] and Chen & Meiners [START_REF] Chen | Topologic mixing on a microfluidic chip[END_REF].

The CLM concept is based on passive division of the flow, then a rotation in a curved pipe of opposite chirality and finally recombination for stretching and squeezing following the baker's transformation.

From a Lagrangian point of view, the chaos can be quantified using the Lyapunov Exponent (LE). As mentioned by Carrière [START_REF] Carrière | On a three-dimensional implementation of the baker's transformation[END_REF] the value obtained for the Lyapunov exponent is very close to the theoretical value of ln 2 predicted by the baker's map. This specific flow regime was first introduced by Aref [START_REF] Aref | Stirring by chaotic advection[END_REF] and then received considerable attention for mixing [START_REF] Habibi | Some observations on the spatiotemporal orbits structure and heat transfer enhancement in pulsating flow[END_REF][START_REF] Jarrahi | Mixing enhancement by pulsating chaotic advection[END_REF][START_REF] Timité | Mass transfer and mixing by pulsatile three-dimensional chaotic flow in alternating curved pipes[END_REF] and heat transfer [START_REF] Anxionnaz-Minvielle | Implementation of 'chaotic' advection for viscous fluids in heat exchanger/reactors[END_REF][START_REF] Castelain | Experimental study of the thermal performance of chaotic geometries for their use in pem fuel cells[END_REF][START_REF] Peerhossaini | Heat exchanger design based on chaotic advection[END_REF] applications. The enhancement of transport phenomena by means of chaotic advection in a twisted curved channel has been experimentally shown by Peerhossaini et al. [START_REF] Peerhossaini | Heat exchanger design based on chaotic advection[END_REF]. Recently, Creyssels et al. [START_REF] Creyssels | Laminar heat transfer in the mllm static mixer[END_REF] presented, numerically and experimentally, the influence of chaotic advection on heat transfer in a multi-level laminating mixer (MLLM). The MLLM is composed of 8 successive elements with the geometry early proposed by Gray et al. [START_REF] Gray | Drie Novel interconnection technologies for integrated microfluidic systems1paper presented as part of the ssaw-98 workshop.1[END_REF]. The authors reported that the Nusselt number averaged over each basic element forming the MLLM remains approximately constant whatever the element location, a behavior which relates to the cutting/stacking mechanism.

Anxionnaz-Minvielle et al. [START_REF] Anxionnaz-Minvielle | Implementation of 'chaotic' advection for viscous fluids in heat exchanger/reactors[END_REF] experimentally compared the performances of the Gray's and Chen's exchanger-mixer to a plate-type heat exchanger/reactor with a corrugated pattern. The authors mentioned that the more viscous the fluid, the more the energy efficiency of the SAR design increases compared to the corrugated design because of the balance between advection and diffusion mechanisms.

A large increase in the internal convective heat transfer coefficient for the chaotic geometries compared to the straight tube is reported by Castelain et al. [START_REF] Castelain | Experimental study of the thermal performance of chaotic geometries for their use in pem fuel cells[END_REF] in the bipolar plates for PEM fuel cells.

Consequently, a comparative study by Raynal & Gence [START_REF] Raynal | Energy saving in chaotic laminar mixing[END_REF] reported that the mixing in globally chaotic Stokes flow is more efficient than turbulent mixing in considering the energy dissipated by the mixing time.

The aim of the present study is to experimentally investigate the enhancement of heat transfer induced by chaotic advection in heat exchanger-mixers. In the present work, we propose two new CLM geometries alongside with the two classical geometries of Gray and Chen. We particularly focus on the effects of pipe curvature, number of bends and pipe orientations. In this context a quantitative study of the role of regular and alternated Dean flow, through four configurations of CLMs, has been performed to investigate the enhancement of heat transfer.

A systematic comparison has been carried out with helical heat exchangers, which are commonly used in industry, in considering the same exchange surface. We have defined power-law correlations in the form of N u = aP e b . The pressure drop has been determined allowing us to calculate the Performance Evaluation Criterion (PEC) in order to assess the thermal-hydraulic performances. Together with thermal performance, the PEC was used to determine advantages and disadvantages of chaotic heat exchangers compared to helical heat exchangers.

The paper is organized as follows: Sec. 2 is devoted to a presentation of the chaotic advection.

The experimental set-up, the different geometry of CLMs and of helical heat exchangers as well as the experimental procedure and measurements are described in sec. 3. The methodology used to obtain the convective heat transfer coefficient and pressure drop is presented in sec. 4. In sec. 5 we firstly propose to compare heat transfer performance of one of our CLMs with the same geometry as Creyssels et al. [START_REF] Creyssels | Laminar heat transfer in the mllm static mixer[END_REF]. In this section are presented the experimental results for the different configurations of CLMs with comparison with two helical heat exchangers. Finally, Sec. 6 is devoted to a concluding discussion.

Chaotic advection

Dean vortices

If a fluid is moving along a curved pipe, two opposed forces apply on fluid particles perpendicularly of the direction of the main flow: centrifugal force due to the pipe curvature and force generated by pressure gradient. By naming "inner wall" (iw) the closest wall from the center of curvature and "outer wall" (ow) the farthest from this center (Figure 1), centrifugal force acts following the direction from inner wall to outer wall whereas pressure force acts on the opposite direction. On the median plane, centrifugal force gets the largest of pressure force thus fluid particles move towards outer wall. Particles movement slows down close to outer wall because of viscous forces. To insure momentum conservation, fluid particles return towards inner wall going close of upper and lower walls where velocities are lower. At this location, pressure forces are higher than centrifugal forces. Thereby competition between centrifugal force and pressure force gives rise to a secondary motion superimposed on the primary flow, and this secondary motion is expected to appear as a pair of counter-rotating cells, which are called Dean vortices [START_REF] Dean | note on the motion of fluid in a curved pipe[END_REF]. It is named after the british scientist W. R. Dean [START_REF] Dean | note on the motion of fluid in a curved pipe[END_REF], who was the first to provide a theoretical solution of the fluid motion through curved pipes for laminar flow by using a perturbation procedure from a Poiseuille flow in a straight pipe to a flow in a pipe with very small curvature.

Alternated Dean flow and baker's transformation

As it is shown on figure 1, Dean vortices have an elliptic form. These vortices are not favorable for mixing fluid particles in a quantitative way and they do not have a chaotic feature. To increase mixing, one solution is to form a sequence of curved pipes by changing the orientation of the curvature plane of each curved pipe. With each change of orientation of plane, positions of centers of Dean vortices and their directions of rotation are modified (see figure 1). Fluid particle trajectories in this flow become chaotic [START_REF] Jones | Chaotic advection by laminar flow in a twisted pipe[END_REF].

To better describe the effects from orientation of curvature plane, we call χ the pitch angle between 2 successive curved pipes (figure 1). [START_REF] Jones | Chaotic advection by laminar flow in a twisted pipe[END_REF] [START_REF] Jones | Chaotic advection by laminar flow in a twisted pipe[END_REF] have studied effects of χ angle on chaotic advection in a twisted pipe. Their numerical experiments give qualitative guidelines on how to tune the geometry of a pipe for maximum mixing efficiency. For χ = 0 • and χ = 180 • , that is a toroidal or helical geometry, the flow is regular and mixing is low. For small deviations from χ= 0 • or χ = 90 • , regularity of trajectories begins to decrease and a chaotic behavior is observed (moreover small deviations from χ = 0 • have a more profound impact on mixing than a comparable deviation from χ = 180 o ). When χ angle is 90 • , the chaotic behaviour is at its maximum level thus maximum mixing is reached [START_REF] Peerhossaini | Heat exchanger design based on chaotic advection[END_REF] [START_REF] Jones | Chaotic advection by laminar flow in a twisted pipe[END_REF]. On this experimental study, we focus on this specific geometry (χ = 90 • ) and we use only the two values χ = 0 • and χ = 90 • in order to compare their effects on heat transfer. Chaotic advection by Dean flow appears at very low Reynolds number so in laminar flow what is very interesting. Indeed, several heat transfers must be done at low Reynolds numbers as it is explained is section 3 and they are limited by the laminar nature of the flow. Using Dean flow could lead to a homogeneous and efficient heat transfer for low Reynolds number application. Given its several advantages, heat transfer by Dean flow has received a particular attention and has been subject to several studies, especially experimental and numerical studies. Therefore, CLM 4 has been constructed because it has less elbows than CLM 3 with the same number of OCPs than CLM 3, so by comparing CLM 3 and CLM 4 , effects of number of elbows might be observed.

Helical Heat Exchangers (HHEs)

We have compared the four studied CLMs with two Helical Heat Exchangers (HHEs) (see Figure 4). They are often used in industry, so this comparison could inform us on the possibility to use CLMs

Experimental set-up

Inside the CLMs, and HHEs water circulated thanks to a pump and was heated by a constanttemperature bath (Huber Ministat 125, Germany) fixed at 45 • C (see figure 5). Mass flow rate was varied over a range from 0.5 to 5 (g/s) and was measured using a Coriolis mass flow controller (FIC, mini Cori-Flow, Bronkhorst High-Tech B.V., Ruurlo, NL) providing accuracy of ± 0.2% of rate. A pressure transmitter (AST 5100, USA) was used to measure the differential pressure between the input and output of CLMs (with an uncertainty of ± 1%).

Experimental procedure and measurements

For each experiment, we have measured the several quantities as presented on figure 6. Measurements were carried out when a stationary state was reached. To have accurate values and to reduce uncertainties, we have recorded measurements on a long period, at least 10 times the dynamical period time. Then we have done a data average during the stationary state. From all these measurements we have deduced parameters of interest. Water properties like density or viscosity depends on water temperature. Because temperature water flowing in the heat exchanger decreases along the exchanger, we have fixed a reference for simplification reasons. For each experiment, we have chosen inlet temperature to determine water properties inside the exchanger. During experiments it has been noted that the wall temperatures T wi and T wo were approximately constant (±0.2 • C). To deduce the useful quantities we have assumed that T wi = T wo = T w .

Data reduction

Heat transfer

The heat flow rate Q was determined from the measured mass flow rate ṁ and the inlet and outlet temperatures of the fluid T f i , T f o inside the heat exchanger:

Q = ṁC p (T f i -T f o ) (1)
From the heat flow rate, the internal heat transfer coefficient h between the fluid and the wall, can be derived from the expression:

Q = hA   T f i -T f o ln T f i -Tw T f o -Tw   (2)
A being the heat exchange surface area.

In CLMs, a problem can raise due to division of the main flow in two parts followed by remixing: what mass flow rates and what heat exchange surface areas must be used? As shown in the Appendix A, we can use the total mass flow rate and we can consider that the heat exchange surface area is the area of a single tube with d i diameter and L length and we obtain A = πd i L. The heat transfer coefficient can be written as a function of the Nusselt number N u by:

h = N uλ d i (3)
With the expression of the heat transfer rate and, introducing the Reynolds and Prandtl numbers

Re = ρV d i µ ( 4
) P r = µC p λ ( 5
)
where ρ and µ are the mass density and the dynamic viscosity of the fluid respectively. V is the mean flow velocity. Introducing the Péclet number Pe, which is defined by:

P e = ReP r (6)
the Nusselt number becomes:

N u = d i P e 4L eq ln T f i -T w T f o -T w (7)
where L eq is the developed length of the CLMs. This number was extracted from measurements.

Pressure drop

The pressure drop inside the pipes was directly measured and compared with the Darcy-Weisbach equation:

∆p = Λ L eq d i ρ V 2 2 ( 8
)
where Λ is the Darcy friction factor. The Λ factor was extracted from measurements and compared to the Poiseuille law obtained for laminar flow in a smooth tube: follow a comparable variation of the form N u ∼ P e 1/2 . We notice that the Creyssel's results are the same as ours for their second element and lower for the first element. By fitting the experimental points with straight lines in logarithmic coordinates we can find out correlations of the form N u = a P e b .The obtained values are given in Table 1.

Λ = 64 Re (9

Thermal comparison of CLMs

Due to different equivalent lengths L eq it is difficult to compare directly the Nusselt numbers of the four CLMs. We have chosen to rescale them by the Nusselt number of a straight pipe which would have the same equivalent length. Nusselt number evolution for a straight pipe with constant wall temperature is known as the Graetz's problem [START_REF] Graetz | Ueber die warmeleitungsfahigkeit von flussigkeiten[END_REF]. For a straight pipe of length L eq and a flow characterized by the Péclet number P e, the Nusselt number for an established dynamical regime is given by N u straight pipe = 3.66 + 0.127

L * + 0.0635L * 1/3 (10)
where

L * = 2L eq P e d i (11)
So, we define a reduced Nusselt number by

N u red = N u N u straight pipe (12)
The reduced Nusselt numbers N u red are presented on Figures 8a and 8b as a function of P e and Re respectively. Several comments can be done: Firstly, it is observed that the shown experimental points are clearly distinct from one CLM to another. For each CLM they are mainly outside the range of error bars of its neighboring. Second, compared to a straight tube with the same exchange surface area, the heat transfer enhancement reaches more than 200 % for CLM 1 and more than 400% for CLM 2, 3 and 4 . One of the reasons of the heat transfer enhancement in the CLMs is the chaotic effect of the flow. Indeed, the flow paths are not parallel as in a straight tube but rapidly diverge, which results that hot particles located in the center region move in the cold region close to the wall. Consequently, the heat transfer is enhanced and the Nusselt number is increased.

Third, CLM 2 seems to be more performing than CLM 3 and 4 , and these three CLMs are more performing than CLM 1 . Knowing differences of geometries between CLMs (see figure 3), one can assume that it is a consequence of the number of elbows and number of OCPs. CLM 1 and CLM 2 have the same organization sequence (all χ angles equal to 90 • ), thus an increase of elbow number leads to more alternating Dean vortices and a better heat transfer. CLM 1 has only one OCP, CLM 3 and 4 have 2 OCPs and CLM 2 has 3; looking at N u red results, one can note that OCP is clearly beneficial for heat transfer and mixing. Moreover CLM 3 and CLM 4 have the same number of OCPs but not the same number of elbows and not the same organization, and one note that heat transfer is quite similar.

Experimental results exhibit a kind of plateau for all CLMs. CLM 2, 3 and 4 exhibit a plateau for P e= 1700 or Re = 300, whereas for CLM 3 , a large plateau is observed when 3000 ≤ P e ≤ 6000 or 500 ≤ Re ≤ 1200. No physical interpretation is known to this day in order to explain these plateaus apart from the fact that there is clearly some reorganization of the flow and the temperature fields. At last, no significant changes are noted between Re representation and Pe representation. Indeed, Prandtl number P r is quite constant for all experiments (close to 7). For next results, only Re representation will be used.

Thermal comparison of CLMs with helical heat exchangers

As CLM 2 seems to be the most performing we only have compared its results with the two previously described helical heat exchangers. In Figure 9 are reported the Nusselt number values for the two used helical heat exchangers and no significant difference is observed between the two heat exchangers up to Re ≈ 1500 (see Fig. 9) but beyond this value a maximum is seen for the heat exchanger which has the most number of spires. These values have been compared to those given by the Manlapaz and Churchill (MC) correlation [START_REF] Manlapaz | Fully developed laminar convection from helical coil[END_REF]. It appears that up to Reynolds numbers of about 1000 the obtained values are very close to those of MC due to the fact that their correlation is essentially based upon low Reynolds number values (Re ≤ 1000). We note a difference beyond this value, our results tending to a maximum. The reduced Nusselt numbers also have been calculated and we observe Fig. 10 that helical heat exchangers have a Nusselt number greater than 1 as expected. They have been compared with those of the CLM 2 heat exchanger which are the highest values among the CLMs. The interesting point is that CLM 2 has a higher Nusselt number than both helical heat exchangers. CLMs might be a better choice than HHE to improve heat transfer. The Λ values seem to be linked to the number of (elbows plus OCP) even though the gap between them is small. However, all values are about ten times those of a smooth straight tube. The presence of elbows, split and recombination structures causes singular losses which explain the huge pressure drop observed. However, the CLMs pressure drop obeys roughly to the same power law as a straight tube (Re -1 ) in laminar regime.

Comparison of CLMs pressure drop with helical heat exchangers

On Figure 11b are reported Darcy coefficient values for the two HHEs together with those obtained with CLM 2 which is the most thermally performing. The Darcy coefficient is lower for HHEs than for CLMs due to absence of recombination structures. It must be remarked that, the flow regime is laminar, the Reynolds number being lower than the critical Reynolds, Re crit . According to different authors, this critical Reynolds number is between 7000 and 7300 for HHE 1 and between 8700 and 9100 for HHE 2 [START_REF] Ito | Friction factors for turbulent flow in curved pipes[END_REF][START_REF] Schmidt | Warmeubergang und druckverlust in rohrschlangen[END_REF].

Performance Evaluation Criterion (PEC)

As already employed in many studies [START_REF] Bergles | Recent developments in enhanced heat transfer[END_REF][START_REF] Bergles | Survey and evaluation of techniques to augment convective heat and mass transfer[END_REF] we have used the Performance Energy Criterion, (PEC) which is based on an energy global approach. It is defined as the ratio of the transferred heat flow rate to the required pumping power for the fluid circulation in the test section.

PEC =

Heat flow rate Pumping power

= ṁc p (T f i -T f o ) Q v ∆p (13)
Q v being the volume flow rate. If the transferred thermal power is greater than the mechanical power, PEC > 1.

From the data measurements, PEC was determined for CLMs and HHEs. As well as for the Nusselt number we have rescaled the actual PEC with PEC of a straight pipe of equivalent length, delivering the same thermal power. We have noted δ this ratio: In Figure 12a, are presented PECs for the four CLMs. It is observed that the PECs have a very low value (from 0.01 to about 0.12) due to the high value of the pressure drop. We note that the PECs increase regularly with Re. The comparison with helical heat exchangers is shown in the inset of Figure 12b. It is clearly seen that the helical heat exchangers have a better PEC than CLMs. On a global energy approach, helical heat exchangers have a better energy efficiency than CLMs.

δ = PEC PEC Straight pipe (14

Conclusion

To enhance heat transfer at low Reynolds, we have used the chaotic advection based on baker's transformation. This latter finds its origin through the Dean flow and the split and-recombination structure.

To observe effects of Dean flow on heat transfer, we have constructed different Chaotic Laminar Mixers (CLMs) with different geometrical characteristics. Number of elbows has been modified as well as number of OCPs representing organization and structure of the CLMs: CLM 1 has only one OCP, CLMs 3 and 4 have 2 OCPs and CLM 2 has 3. Results show that heat transfer is improved when number of OCPs increases while the pressure drop is quite the same. Then, we have compared our CLMs with helical exchangers in order to determine if our CLMs could be used in a global energy approach.

CLMs have two-times better heat transfer than helical exchangers. Concerning pressure drops, CLMs are about three-times less efficient than helical exchangers. This implies that helical exchangers have a better efficiency than CLMs. This efficiency has been quantified through a Performance Energy Criterion (PEC).

As a consequence, CLMs can be recommended in the case where mixing and heat transfer only are the main specification requests. Moreover, between CLMs, CLM 2 is the best solution for mixing at industrial scale. Indeed, for a higher quality mixing, CLM 2 has less elbows than CLM 3 and 4 , so that implies a diminution of costs. The heat exchanger consists of several units with two equivalent branches and its total length is L t .

The equivalent length of a unit is L. Neglecting the straight part at the inlet and outlet, the Reynolds number must be calculated with the ṁ/2 mass flow rate in each branch.

The power transferred to (or from) the tube wall by (or from) the fluid in each branch j is (Figure

Figure 1 :

 1 Figure 1: Basic unit of a curved pipe inducing Dean-roll cells. θ is the angle between xz and yz planes and χ is the angle between xy and yz planes (in this particular case χ equal 90 • ).

3 .Figure 2 :

 32 Figure 2: View of the four studied heat exchangers: (a) CLM 1 (b) CLM 2 (c) CLM 3 (d) CLM 4 .

Figure 3 :

 3 Figure 3: Breakdown of elements in one branch of CLMs.

Figure 4 :

 4 Figure 4: Helical Heat Exchangers: (a) HHE 1 : D = 10.5 cm and p = 5.4, (b): HHE 2 : D = 5 cm and p = 2.6 and (c) Definition of geometrical parameters.

Figure 5 :

 5 Figure 5: Schematic of the experimental loop.

Figure 6 :

 6 Figure 6: Summary of measured quantities in the test section.

) 5 .

 5 Results and discussions 5.1. Heat transfer 5.1.1. Nusselt number evolution Nusselt numbers have been deduced using formula 7. As an example, we give on figure 7 values of N u as a function of P e obtained with CLM 2 based on Gray geometry. For each measurement error bars are shown. The uncertainty has been determined with the method of error propagation described in annex B. On the same figure these results have been compared with those of Creyssels et al. [30] obtained with an analogue geometry. It is seen that results are very close especially when P e ≥ 1700. Both results

Figure 7 :

 7 Figure 7: Variation of the Nusselt number as a function of the Péclet number for CLM 2 . Comparison with Creyssel's results.

Table 1 :

 1 Coefficients a and b obtained from the correlation N u = a P e b .

Figure 8 :

 8 Figure 8: Variation of the reduced Nusselt number as a function of Péclet and Reynolds numbers.

Figure 9 :

 9 Figure 9: Evolution of the Nusselt numbers of the two studied helical heat exchangers with the Reynolds number. Comparison with the Manlapaz and Churchill correlation [34].

Figure 10 :

 10 Figure 10: Comparison of the reduced Nusselt number of Helical Heat Exchangers with CLM 2 .

Figure 11 :

 11 Figure 11: Darcy coefficients in function of the Reynolds number (a) for CLMs (b) comparison of CLM 2 with Helical Heat Exchangers.

Figure 12 :

 12 Figure 12: Evolution of the ratio δ in function of the Reynolds number. (a) for CLMs (b) for HHEs compared to CLM 2 .

  Appendix A. Calculation of the Nusselt number in the studied Chaotic Heat Exchangers In the expression of the Nusselt number given in formula 7 we have used the total mass flow rate and an equivalent heat exchange area to calculate the Péclet number. An elementary unit of flow separation and remixing in a chaotic heat exchanger can be schematically represented on Figure A.13.

Figure A. 13 :

 13 Figure A.13: (a) Flow paths in the first part of a unit of the chaotic heat exchanger (b) Simplified representation used to extract quantities of interest.

A.13a):

Where A j = πd i L and where h is calculated with the help of the Nusselt number which depends on a Reynolds number. The mean logarithmic difference is given by:

Where T i and T o are the fluid temperatures at the inlet and the outlet of the unit respectively.

In one branch, the Reynolds number is:

And the Nusselt number and the heat transfer coefficient become:

If ṁ is the total mass flow rate (at the heat exchanger inlet, for example), the total power transferred by the two branches is:

Assuming that only one branch would be existing in which the whole flow circulates with the mass flow rate ṁ, in this unique branch the Reynolds number is:

The associate Nusselt number can be written:

Then, the heat transfer coefficient is:

Taking into account

The Nusselt number deduced from the equation 7 can be used to determine the heat transfer coefficient.

Appendix B. Measurement uncertainty

The estimation of the measurement uncertainty is based on the method of error propagation described by Moffat [START_REF] Moffat | Describing the uncertainties in experimental results[END_REF]. For a y function depending on N independent parameters, the uncertainty is given by:

Assuming that there is no error on the physical properties and on the geometrical parameters, from the following Nusselt expression:

We can write: