Fabien Robert-Peillard
email: fabien.robert-peillard@univ-amu.fr

Edwin Palacio Barco

Marco Ciulu

Carine Demelas

F Théraulaz1

J.-L Boudenne

Bruno Coulomb

Frédéric Théraulaz

Jean-Luc Boudenne

High throughput determination of ammonium and primary amine compounds in environmental and food samples

Keywords: ammonium, primary amine, microplate, reagents stability

In this paper, an improved spectrofluorimetric method for the simultaneous and direct determination of ammonium and primary amine compounds is presented. The method is based on the derivatization with o-phthaldialdehyde (OPA) / N-acetylcysteine (NAC) reagent using high throughput microplates, and OPA/NAC ratio has been optimized in order to suppress interference of ammonium on primary amine determination. Direct measurement of these two parameters is therefore possible with a global procedure time that does not exceed ten minutes. Excellent limits of detection of 1.32 µM and 0.55 µM have been achieved for ammonium and primary amines, respectively. Reagent stability issues have also been addressed and formulation of reagents solution is described for improved reagents shelf life.

The proposed protocol was finally applied and validated on real samples such as wine samples, compost extracts and wastewater.

Introduction

Amino compounds are widely distributed in the environment and essentially result from metabolic processes of degradation, hydrolysis and excretion at different levels of the food chains. Soil organic matter thus contains about 30% of its nitrogen pool as amino acids [START_REF] Stevenson | Humus chemistry: Genesis, composition, reactions[END_REF], and a significant proportion of NH 4 + can be released from organic matter by microbial hydrolysis [START_REF] Barraclough | The direct or MIT route for nitrogen immobilization: A 15 N mirror image study with leucine and glycine[END_REF]. Anthropogenic activities also contribute to the presence of these compounds and ammonium in the environment, mainly attributed to the incineration of waste [START_REF] Seeber | Determination of airborne, volatile amines from polyurethane foams by sorption onto a high-capacity cation-exchange resin based on poly(succinic acid)[END_REF] and the discharges of waste waters from chemical industry and wastewater treatment plants [START_REF] Seeber | Determination of airborne, volatile amines from polyurethane foams by sorption onto a high-capacity cation-exchange resin based on poly(succinic acid)[END_REF][START_REF] Skarping | Determination of toluenediamine isomers by capillary gas chromatography and chemical ionization mass spectrometry with special reference to the biological monitoring of 2,4-and 2,6-toluene diisocyanate[END_REF].

Among the nitrogen pool, primary amino compounds determination is a significant parameter in the food processing or drinking-water treatment industry as it can react with nitrites or nitrates to form nitrosamines which are classified as "probably carcinogenic to human" [START_REF] Hureiki | Chlorination studies of free and combined amino acids[END_REF][START_REF] Brosillon | Chlorination studies of free and combined amino acids[END_REF].

Primary amino compounds (mainly primary amino acids) are also very important regarding the nitrogen management in some specific fields such as wine industry [START_REF] Ugliano | Nitrogen management is critical for wine fl avour and style[END_REF]. Indeed, assaying the total primary amino acids concentration is often considered to be the most convenient method to measure assimilable nitrogen, which is critical for wine flavour and style.

Regarding ammonium, its determination in environmental samples is highly relevant, due to its important micronutrient function in aquatic systems or as an important index in composting process studies. As example, high concentration in a water body can be an indicator of the environmental impact of human activities, with strong effects on microbiological activities that can potentially lead to eutrophication events [START_REF] Zamparas | Nitrogen management is critical for wine flavour and style[END_REF]. In the composting field, low ammonium concentration coupled to low N-NH 4 + /N-NO 3 -ratio has been proposed as indicators of a compost stability [START_REF] Bernal | Influence of sewage sludge compost stability and maturity on carbon and nitrogen mineralization in soil[END_REF].

Several methods have been proposed for the analysis of ammonium [START_REF] Molins-Legua | Influence of sewage sludge compost stability and maturity on carbon and nitrogen mineralization in soil[END_REF], such as spectrophotometry [START_REF] Marina | Flow-injection determination of low levels of ammonium ions in natural waters employing preconcentration with a cation-exchange resin[END_REF][START_REF] Oms | Gas diffusion techniques coupled sequential injection analysis for selective determination of ammonium[END_REF][START_REF] Jeong | Determination of NH 4 + in environmental water with interfering substances using the modified Nessler method[END_REF], ion selective electrode [START_REF] Meseguer-Lloret | Ammonium determination in water samples by using OPA-NAC reagent: a comparative study with Nessler and ammonium selective electrode methods[END_REF], fluorimetry [START_REF] Meseguer-Lloret | Determination of ammonia and primary amine compounds and Kjeldahl nitrogen in water samples with a modified Roth's fluorimetric method[END_REF][START_REF] Cao | A new fluorescence method for determination of ammonium nitrogen in aquatic environment using derivatization with benzyl chloride[END_REF] or ion chromatography [START_REF] Shen | The application of a chemical sensor array detector in ion chromatography for the determination of Na + , NH 4 + , K + , Mg 2+ and Ca 2+ in water samples[END_REF]. Primary amines/amino acids are generally analyzed individually by liquid chromatography [START_REF] Krumpochova | Amino acid analysis using chromatography-mass spectrometry: an inter platform comparison study[END_REF][START_REF] Rigas | Post-column labeling techniques in amino acid analysis by liquid chromatography[END_REF], but methods have also been developed to measure the total concentrations of these compounds in order to have a rapid and global assay of these important nitrogen compounds. This can be done for example by spectrophotometric measurements after reaction with ninhydrin [START_REF] Moore | A modified ninhydrin reagent for the photometric determination of amino acids and related compounds[END_REF] or by fluorimetry after reaction with ophthaldialdehyde (OPA) and a thiol compound [START_REF] Jones | Simple method to enable the high resolution determination of total free amino acids in soil solutions and soil extracts[END_REF].

The numerous advantages of the combination of this OPA-thiol reagent (reaction with ammonium and amines, sensitivity, selectivity, low toxicity and price of reagents...) has led to the development of simultaneous determination methods for ammonium and primary amino compounds. Meseguer Lloret et al. [START_REF] Meseguer-Lloret | Ammonium determination in water samples by using OPA-NAC reagent: a comparative study with Nessler and ammonium selective electrode methods[END_REF] used solution derivatization with OPA-NAC reagent (NAC: N-acetylcysteine), two different excitation and emission fluorescence wavelengths and statistical analysis by multivariate Principal Component Regression in order to separate the responses of ammonium and amine under selected experimental conditions [START_REF] Meseguer-Lloret | Determination of ammonia and primary amine compounds and Kjeldahl nitrogen in water samples with a modified Roth's fluorimetric method[END_REF]. Darrouzet-Nardi et al. [START_REF] Darrouzet-Nardi | Fluorescent microplate analysis of amino acids and other primary amines in soils[END_REF] developed a fluorescent assay with OPA and β-mercaptoethanol for analysis of primary amino compounds, by taking into account potential interference of ammonium.

The main drawback of this method was the necessity to use a 1-h incubation time in order to reduce interference from ammonium.

The aim of the present study is to develop a fast, simple and efficient method for ammonium and primary amino compounds analysis, with no need of statistical analysis, direct measurement from calibration curves and a global procedure time that does not exceed ten minutes. Moreover, this method has been developed as a potential routine analytical method applicable to the large number of samples that an analytical laboratory typically has to deal with (especially for ammonium). Therefore, a high-throughput microplate method based on OPA-NAC reagent was used, with special care on reagents stability which is a key point for routine analysis development (shelf life of at least 3 months without deterioration of analytical performances). The final goal of this study was to conduct a strong validation on complex samples like compost extracts or wastewaters by comparison with a chromatographic reference method, in order to have a robust method for routine analysis of ammonium and primary amino compounds.

Ion exchange chromatography for primary amines determination

Primary amino acid compounds in selected wines were determined by an external laboratory using an automatic amino acid analyzer (Biochrom 30+, Cambridge, England). Wine samples were initially diluted in a sodium citrate buffer (pH 2.2). All amino acids were spectrophotometrically detected after post-column derivatization with ninhydrin reagent at 570 nm. Concentrations of amino acid compounds in unknown samples were determined by comparison with standard peak areas (Sigma-Aldrich amino acid standard kit) and by using norleucine as internal standard. Ion-exchange chromatography analyses on real wine samples were performed on the same day as microplate analyses for validation purposes. 2.3 Analytical protocol for primary amines and ammonium determination 100 µL of sample or standard solution were dispensed into the wells of the microplate, where 30 µL of 13 mM OPA in ethanol-0.15 M carbonate buffer pH 10.5 (10:90, v/v) and 20 µL of a solution of 20 mM NAC and 1.5 mM TCEP in 0.1 M HCl were added. The plate was shaken for 10 min and fluorescence intensity was then recorded, with excitation and emission wavelengths set at at λ ex =335 nm / λ em =455 nm and at λ ex =415 nm / λ em =485 nm for total primary amines and ammonium determination respectively. Concentrations in unknown samples were determined using the linear calibration curves obtained with standards. All experiments were performed in duplicate.

Results

Optimization of analytical method 3.1.1 OPA/NAC concentration and pH

Initially derivatization of amino acids by OPA-NAC reagent developed by Aswad [START_REF] Aswad | Determination of D-and L-Aspartate in amino acid mixtures by High-Performance Liquid Chromatography after derivatization with a chiral adduct of o-Phthaldialdehyde[END_REF] was carried out with an OPA/NAC ratio of 1:2. Even if the reaction rate and the fluorescence yield are not dependent on the OPA/NAC ratio [START_REF] Zhao | Determination of a-dialkylamino acids and their enantiomers in geological samples by high-performance liquid chromatography after derivatization with a chiral adduct of o-phthaldialdehyde[END_REF], it is nevertheless necessary to use an OPA concentration higher than targeted amino acid concentration [START_REF] Svedas | The interaction of amino acids with o-Phthaldialdehyde: a kinetic study and spectrophotometric assay of the reaction product[END_REF]. In past years OPA/NAC 1:1 ratio solution has often been used as pre-column derivatization reagent for HPLC or capillary electrophoresis separation of amino acids or biological amines.

More recently, this method was adapted for the determination of total primary amine compounds and ammonium in environmental samples by Meseguer Lloret et al. [START_REF] Meseguer-Lloret | Determination of ammonia and primary amine compounds and Kjeldahl nitrogen in water samples with a modified Roth's fluorimetric method[END_REF] with a fluorescence measurement at two  ex / em couples of wavelengths to separate the response of the primary amines with that of ammonium. However, this method was based on the use of a This reaction time is longer than the one used by Meseguer-Lloret et al. [START_REF] Meseguer-Lloret | Determination of ammonia and primary amine compounds and Kjeldahl nitrogen in water samples with a modified Roth's fluorimetric method[END_REF] (120 and 300 seconds respectively for amines and ammonia) but greatly simplifies the calibration process by avoiding the use of statistical tools. The reaction time also depends on the pH used for the derivatization reaction. Fig. 2 shows the fluorescence intensity of the OPA-NAC-ammonium adduct as a function of pH and reaction time. The reaction time previously set at 600 seconds for the simultaneous measurement of ammonium and primary amines is sufficient to obtain a high and stable fluorescence signal for ammonium derivatization by OPA/NAC 8mM/8mM at pH = 10.5. This reaction time is significantly lower than that proposed by Darrouzet-Nardi et al. (60 minutes) for a OPA/mercaptoethanol (ME) procedure developed in order to limit interference of ammonium on the measurement of primary amines in soils [START_REF] Darrouzet-Nardi | Fluorescent microplate analysis of amino acids and other primary amines in soils[END_REF].

Buffer

Sodium or potassium tetraborate are certainly the most commonly used buffers for derivatization of ammonia or amines with OPA and NAC or ME in alkaline conditions [START_REF] Meseguer-Lloret | Ammonium determination in water samples by using OPA-NAC reagent: a comparative study with Nessler and ammonium selective electrode methods[END_REF][START_REF] Meseguer-Lloret | Determination of ammonia and primary amine compounds and Kjeldahl nitrogen in water samples with a modified Roth's fluorimetric method[END_REF][START_REF] Jones | Simple method to enable the high resolution determination of total free amino acids in soil solutions and soil extracts[END_REF][START_REF] Darrouzet-Nardi | Fluorescent microplate analysis of amino acids and other primary amines in soils[END_REF][START_REF] Aswad | Determination of D-and L-Aspartate in amino acid mixtures by High-Performance Liquid Chromatography after derivatization with a chiral adduct of o-Phthaldialdehyde[END_REF][START_REF] Zhao | Determination of a-dialkylamino acids and their enantiomers in geological samples by high-performance liquid chromatography after derivatization with a chiral adduct of o-phthaldialdehyde[END_REF][START_REF] Svedas | The interaction of amino acids with o-Phthaldialdehyde: a kinetic study and spectrophotometric assay of the reaction product[END_REF]. However, tetraborate salts have been classified as toxic for reproduction (category 1B) by European regulations since 2008 [START_REF]Parliament and of the council of 16 December 2008 on classification, labelling and packaging of substances and mixtures[END_REF]. Substitution of these products is therefore recommended, especially for analytical procedures that are developed as potential routine methods with high frequency of use for the reagent solutions.

In this study, we replaced the borate buffer solution with a carbonate or CAPS buffer which have pKa values compatible with the pH used in the derivatization reaction. Experiments showed that a carbonate buffer could replace the borate buffer but the fluorescence signal obtained decreased by 40%. Nevertheless, despite this significant decrease of fluorescence intensity, the analytical features obtained with the carbonate buffer fit with expected values of ammonium and amines in environmental samples (see 3.3). CAPS, on the other hand, lead to a very significant decrease in the fluorescence signal by 90% (Sup. Fig. 1).

Conservation of reagents 3.2.1 Reducing agent

It is well known that thiol group can easily be oxidized and form disulfide bond. This oxidation reaction will quickly limit NAC reactivity and therefore inhibit derivatization of ammonium or amines by OPA. This usually leads the authors to prepare OPA/NAC solutions daily. However, it may be interesting in an analytical laboratory to keep OPA and NAC solutions for several days, several weeks or even a few months, again especially for analytical methods that are used routinely.

Three reducing agents conventionally used in analytical procedures have been studied: 2,2thiodiethanol (TDE), ascorbic acid and tris(2-carboxyethyl) phosphine hydrochloride (TCEP).

Fluorescence intensity of an ammonium standard adduct (100 μM) was measured over a period of 60 days (Fig. 3). Derivatization was carried out with OPA/NAC solution comprising one of the reducing agent mentioned above at a concentration of 1 mM (TCEP) or 10 mM (ascorbic acid, TDE).

We can observe with data of Fig. 3 that ascorbic acid did not enable good preservation of OPA/NAC solutions. TDE and TCEP reduced degradation of OPA/NAC solution with approximately 14% decrease in fluorescence intensity after 30 days in both cases. TCEP was preferred for subsequent experiments because TDE is unpleasant to use due to its malodorous properties. The optimization of the concentration of TCEP was then carried out (fig . 4). Data showed that TCEP concentration of 1 mM was sufficient to improve the conservation of OPA/NAC reagent. Higher concentrations lead to an increase in the blank signal. Similar results have been obtained for amino compounds derivatization (glycine as a reference).

Conservation mode of reagents

The optimization of the preservation of reagents was finally optimized by studying the conservation mode of the reagents: OPA and NAC solutions can be stored in a mixture or separately. It is well known that a formulation at low pH can be used to prevent oxidation of N-acetylcysteine [START_REF] Pearlman | Formulation, characterization, and stability of protein drugs: case histories[END_REF]. We have thus studied the evolution of the slope of calibration curves over time (up to 6 months) either with the two liquid reagents prepared together (condition called 'mixed reagents' on Fig. 5A) or with the two liquid reagents stored separately (condition called 'separated liquid reagents' on Fig. 5B), and also with solid NAC deposited in microplate wells and liquid OPA reagent stored separately (condition called 'solid NAC + liquid OPA' on Fig. 5C). For this last preservation condition of the reagents, NAC was solubilized in acetone and then introduced into microplate wells. Acetone was evaporated at room temperature, then the plate was sealed with a polyethylene film. The OPA reagent was similar to the previous condition (in carbonate buffer at pH 10.5). All the solutions or microplates used in this study were stored in the dark at 4 °C.

For each experimental condition, confidence interval (CI) of slope value was determined at initial time (0 day) from the standard deviation of the b-slope value of the calibration curve s(b), depending on the residual standard deviation of the regression (n=5, P=0.05) [START_REF] Afnor | Protocole d'évaluation d'une méthode alternative d'analyse physico-chimique quantitative par rapport à une méthode de référence[END_REF].

Calculated values of (b±UM), with UM the uncertainty of measurement, for separated liquid reagents, mixed reagents and solid NAC/liquid OPA were 58.1±8.1, 54.6±1.6 and 49.1±9.2, respectively. On figure 5, CI limits are noticed by dotted lines. We can observe that the slope remained inside CI for separated liquid reagents up to 4 months, on contrary to mixed reagents only after 7 days. For solid NAC/liquid OPA condition, a great variability of slope value during experimental period was noticed and one data was outside CI after only 4 weeks.

These results prompted us to use separated liquid reagents condition.

Analytical features 3.3.1 Screening of primary amines

Screening of some biogenic amines and primary amino acids (25 µM) that could be likely present in environmental or food samples was performed using OPA/NAC optimized analytical protocol (Fig. 6). The fluorescence intensity of the different adducts was standardized over that of the glycine adduct (reference 100).

A great diversity of amines and primary amino acids can therefore be detected by the developed method, although their responses are not all similar. Secondary amines (proline) and primary amines involved in a conjugated system (creatine, urea, creatinine) do not react. The method allows for example the control of amino compounds in raw waters at the inlet of treatment plants. Brosillon et al. [6] found that alanine, valine and tyrosine were the main amino acids at the origin of disinfection by-products in drinking water during chlorination.

These 3 amino acids exhibit responses of 103, 82 and 78% compared to glycine. Although individual concentrations of amino acids in raw waters range from 0.2 to 0.9 nM depending on the season, the method is sensitive enough to quantify the total amount of amino compounds. Likewise, the most frequently measured primary amino acids in wine samples (alanine, glutamic acid, arginine) all lead to responses comparable with that of glycine, and a global measurement based on a glycine standard is therefore relevant for this study.

Cross-interference and other interferences

In this section, a compound was considered as interferent when its presence resulted in more than 5% modification of the pure ammonium (100 µM) or glycine (as reference amino acid; 100 µM) response.

The cross-interference of amines over ammonium (λ ex =415 nm / λ em =485 nm) and inversely ammonium over amines (λ ex =335 nm / λ em =455 nm) was evaluated. The results showed that ammonium could be quantified in the presence of a 1000-fold excess of glycine and that primary amines could be quantified in the presence of a 100-fold excess of ammonium.

The interference of various metal cations has also been studied. The presence of Fe 3+ or Cu 2+ at 15 µM resulted in an interference of more than 5%. The addition of 50 mM EDTA to the reaction mixture reduced this interference. Ammonium could thus be quantified in the presence of 750 µM of Fe 3+ or Cu 2+ and the amines could be quantified in the presence of 180 µM of Fe 3+ and 450 µM of Cu 2+ . The other metallic elements tested (Al 3+ , Cd 2+ , Co 2+ , Ni 2+ , Pb 2+ , Zn 2+ ) did not interfere up to 1 mM.

Performance and validation of the analytical method

The developed method was characterized and validated according to the AFNOR procedure XP T 90-210 [START_REF] Afnor | Protocole d'évaluation d'une méthode alternative d'analyse physico-chimique quantitative par rapport à une méthode de référence[END_REF]. Regarding analytical features, calibration curves for ammoniacal nitrogen and amine compounds were constructed with several standards (respectively, n=6 and n=5)

with triplicate measurements for each, and have been obtained for each compound by linear regression of the fluorescence intensity against the concentrations of standards. The calibration range lies between the limit of quantification and a maximum concentration depending on the concentration range allowing to keep linearity between instrumental signal and standard concentrations. The limit of detection (LOD) of the analytical procedure is defined as the lowest amount of analyte in a sample that can be detected and considered as different from the blank value but not necessarily quantified as an exact value, whereas the limit of quantification (LOQ) is the lowest amount of analyte in a sample which can be quantitatively determined with the analytical procedure with a defined variability. The LOD and LOQ were evaluated from the residual standard deviation of the regression (linearity study method) as LOD= 3.s(a)/b and LOQ= 10.s(a)/b, where s(a) is the standard deviation of the a-intercept and b is the slope of the calibration curve.

The accuracy of an analytical procedure is defined as the closeness of agreement between the conventional "true" value (obtained by the reference analytical procedure) and the measured value. The accuracy of our microplate procedure with fluorescence detection was assessed by analyzing a great number of samples from various origins. The calculation of the existing difference (d) between the measured value and the value issue from cationic chromatography, for each sample, and the calculation of the absolute value of their mean (|d||) and the standard deviation (s) of all calculated data, is used to evaluate the good accuracy by check of the normal distribution of these data around zero (w=|d||/s < 3; P=0.01) [START_REF] Afnor | Protocole d'évaluation d'une méthode alternative d'analyse physico-chimique quantitative par rapport à une méthode de référence[END_REF].

The repeatability, i.e. the precision, of analytical procedures was assessed by calculating the standard deviation of repeatability taking into account each replicate measurement (n=3) for each sample. A comparison of variance of repeatability obtained with the two analytical methods on the same multiple samples as previously is realized in order to determine their potential significative difference or not (Fisher-test, P=0.01) [START_REF] Afnor | Protocole d'évaluation d'une méthode alternative d'analyse physico-chimique quantitative par rapport à une méthode de référence[END_REF].

Ammonium

The calibration curve (y=57.076x+623.96) was linear up to 100 µM with a correlation coefficient of 0.997 (n=6). A LOD of 1.32 µM and a LOQ of 4.41 µM have been obtained.

The working range of this analytical method is then 4.4-100 µM. The relative standard deviation evaluated from a sample containing 50 µM (n=6) was 1.58%.

Validation of the analytical method requires satisfactory results for the accuracy and the repeatability. No significant differences (Fisher-test, n=54, P=0.01) were noticed between variance of repeatability of our new analytical method and cationic chromatography, and the closeness of agreement of results proved a good accuracy (w=0.16 < 3; P=0.01). Figure 7 shows regression line obtained by comparison of results of 54 samples (surface water, wastewater, water extracts of compost). Slope of regression line is 0.96±0.05 and intercept were 1.13±1.88. Result was satisfactory for the intercept and slope as confidence intervals of their value included 0 and 1 respectively, in accordance with previous statistical test for accuracy. The analytical range and the low limit of quantification allow the determination of ammonium in various types of samples as natural waters, raw or treated wastewaters, aqueous extracts of soils or wastes.

Primary amines

For primary amines, the calibration curve (y=153.94x+374.89) was linear up to 100 µM with a correlation coefficient of 0.995 (n=5). A LOD of 0.55 µM and a LOQ of 1.84 µM have been obtained. The working range of this analytical method is then 0.55-100 µM. The relative standard deviation evaluated from a sample containing 50 µM (n=6) was 1.25%.

As for ammoniacal nitrogen, the accuracy and the repeatability for amine compounds gave satisfactory results. No significant difference (Fisher-test, n=13, P=0.01) was noticed between variance of repeatability of the developed analytical method and cationic chromatography, and the closeness of agreement of results proved a good accuracy (w=0.22 < 3; P=0.01).

Figure 8 shows regression line obtained by comparison of results of 13 samples (various samples of wines). Slope of regression line is 0.94±0.23 and intercept were 178.7±535.2.

Confidence intervals for the intercept and slope were relatively wide, essentially due to higher residual standard deviation of the regression, including however 0 and 1 respectively, equally in accordance with previous statistical test for accuracy. The analytical range and the low limit of quantification allow the determination of primary amines in various types of samples as natural waters or food samples for example.

Conclusion

In this study, we presented the development and validation of a method for the determination of ammonium and primary amine compounds in various environmental and food samples.

Optimization of reagents ratio and pH buffer enables fast and stable responses with no cross interferences between these two structurally close analytes. Reagent storage conditions were also evaluated in order to improve reagents shelf life, and we showed that separated storage of OPA and NAC solutions was the best option. Regarding analytical features, excellent limits of detection of 1.32 µM and 0.55 µM have been achieved for ammonium and primary amines, respectively, with RSD below 2%. Validation on various real samples by comparison with reference methods resulted in very good accuracies, proving the efficiency of this methodology for routine analysis of these nitrogen compounds. [OPA]: 8 mM; [NAC]: 8 mM; carbonate buffer pH=10.5. [∑(RNH2)] (µM) -Ion Exchange Chromatography [RNH2] (µM] Microplate assay HIGHLIGHTS  An improved spectrofluorimetric method for the simultaneous and direct determination of ammonium and primary amine compounds is presented.  Reagents ratio has been optimized in order to suppress known cross-interferences.  Optimization of reagents formulation led to high reagents stability for routine analysis.  The method was validated on real samples (wine samples, compost extracts or wastewater).

Figure captions

  Fig. 1 displays the evolution of fluorescence intensity of OPA-NAC-ammonium adduct at amino compounds wavelengths as a function of reaction time. The increase in OPA and NAC concentration can reduce ammonium interference during primary amines determination. For a concentration greater than 8 mM of OPA and NAC, a reaction time of 600 seconds allows to fully eliminate the cross-interference of ammonium over amino compounds determination.

Fig. 1 : 5 .Fig. 2 :Fig. 3 :

 1523 Fig. 1: Fluorescence intensity of OPA-NAC-ammonium adduct at λ ex =335 nm / λ em =455 nm as a function of reaction time and OPA/NAC concentration. [NH 4 + ]: 50 µM; borate buffer pH=10.5.

Fig. 4 :

 4 Fig. 4: Evolution of fluorescence intensity (λ ex =415 nm / λ em =485 nm) of an ammonium standard adduct (100 μM) over a period of 70 days as a function of TCEP concentration.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Evolution of the slope of calibration curves over time depending on conservation mode of reagents. A: OPA and NAC mixed reagent; B: OPA and NAC separated liquid reagents; C: solid NAC and liquid OPA. Confidence intervals (CI) are represented in dotted lines. [OPA]: 8 mM; [NAC]: 8 mM; [TCEP]: 1 mM; carbonate buffer pH=10.5.Fig. 6: Screening of biogenic amines and primary amino acids (25 µM). [OPA]: 8 mM; [NAC]: 8 mM; [TCEP]: 1 mM; carbonate buffer pH=10.5.

Fig. 7 :

 7 Fig. 7 : Regression line for comparison of analytical results between Microplate Assay and Ion Chromatography for ammonium determination.

Fig. 8 :

 8 Fig. 8 : Regression line for comparison of analytical results between Microplate Assay and Ionic Exchange Chromatography for primary amines determination.

Acknowledgment

This work was financially supported by the French Research Agency (ANR) through the programme "EMERGENCE" [ANR-10-EMMA-038] and by the French Environment and Energy Management Agency (ADEME) through the programme "DOSTE" [1506C0034].


F.-D Desgorces
email: francois.desgorces@univ-paris5.fr

G Berthelot

A Charmantiert

M T Afflet

K Schaal

P Jarnet

J.-F Toussaint

Franc ¸ois-Denis Desgorces

Similar slow down in running speed progression in species under human pressure

Keywords: phenotype, physical performance, running

Running speed in animals depends on both genetic and environmental conditions. Maximal speeds were here analysed in horses, dogs and humans using data sets on the 10 best performers covering more than a century of races. This includes a variety of distances in humans (200-1500 m). Speed has been progressing fast in the three species, and this has been followed by a plateau. Based on a Gompertz model, the current best performances reach 97.4% of maximal velocity in greyhounds to 100.3 in humans. Further analysis based on a subset of individuals and using an 'animal model' shows that running speed is heritable in horses (h 2 = 0.438, P = 0.01) and almost so in dogs (h 2 = 0.183, P = 0.08), suggesting the involvement of genetic factors. Speed progression in humans is more likely due to an enlarged population of runners, associated with improved training practices. The analysis of a data subset (40 last years in 800 and 1500 m) further showed that East Africans have strikingly improved their speed, now reaching the upper part of the human distribution, whereas that of Nordic runners stagnated in the 800 m and even declined in the 1500 m. Although speed progression in dogs and horses on one side and humans on the other has not been affected by the same genetic ⁄ environmental balance of forces, it is likely that further progress will be extremely limited.

Introduction

Locomotor performance is a key trait in mobile species that is closely associated with fitness [START_REF] Irschick | Do lizards avoid habitats in which performance is submaximal? The relationship between sprinting capabilities and structural habitat use in Caribbean anoles[END_REF]. In particular, improving running speed might allow for reaching prey or avoiding predator more efficiently [START_REF] Husak | Does survival depend on how fast you can run or how fast you do run?[END_REF]. It is therefore of importance to better evaluate those factors, whether genetic or environmental, affecting maximum speed. However, experimentally evaluating how far maximum speed can improve is difficult, because assessing it over meaningful time periods is not always feasible. We propose a way to alleviate this issue by using race records in species in which fastest speeds have been monitored over a long time span. Such data are available in horses, dogs (greyhounds) and humans.

Speed progression, that is, the increase in maximal speed over time, in these three species results from both genetic and environmental factors, although to various extents according to species [START_REF] Nevill | Are there limits to running world records?[END_REF][START_REF] Niemi | Mitochondrial DNA and ACTN3 genotypes in Finnish elite endurance and sprint athletes[END_REF][START_REF] Davids | Genes, environment and sport performance. Why the nature-nurture dualism is no longer relevant[END_REF]. Moreover, some variables acting on speed progression depend on training (relating to physiology, psychology, biomechanics, technology or tactics improvement), whereas others are outside the athletes' control (genetics, anthropometric characteristics, climatic conditions; [START_REF] Smith | A framework for understanding the training process leading to elite performance[END_REF][START_REF] Brutsaert | What makes a champion? Explaining variation in human athletic performance[END_REF]. In domesticated animals, sustained selection by breeders has long been known to cause large and accelerated phenotypic changes contributing to short-term evolutionary processes [START_REF] Darwin | Animals and Plants Under Domestication[END_REF][START_REF] Falconer | Introduction to Quantitative Genetics[END_REF]. Racing horses have indeed been selected from the 16th century, based on closed populations and a very small number of founders [START_REF] Willett | An Introduction to the Thoroughbred[END_REF]. Beginning later, similar selection processes have been imposed on greyhounds for dog racing. This means that phenotypic expression (such as running speed) relies on a narrow genetic basis in comparison with the variation available in these species. However, genetic variance for performance has recently been detected in thoroughbred horses [START_REF] Gu | A genome scan for positive selection in thoroughbred horses[END_REF][START_REF] Hill | A sequence polymorphism in MSTN predicts sprinting ability and racing stamina in thoroughbred horses[END_REF].

The improvement in fast-running performances in humans does not (of course) rely on selective breeding, but on the detection of fast-running athletes generally during adolescence or later through national systems that were optimized after World War II [START_REF] Guillaume | Success in developing regions: world records evolution through a geopolitical prism[END_REF]. Importantly, the athlete population has increased in size proportionally to the development of modern sport throughout the last century. For example, 241 athletes from 14 national Olympic committees participated in the first modern Olympic games (Athens, 1896), whereas 10 942 athletes coming from 204 nations attended the 29th games in Beijing (2008). Thus, the best human runners are now selected from a much larger number of countries [START_REF] Guillaume | Success in developing regions: world records evolution through a geopolitical prism[END_REF], presumably over a larger genetic basis for performance [START_REF] Yang | ACTN3 genotype is associated with human elite athletic performance[END_REF][START_REF] Williams | Similarity of polygenic profiles limits the potential for elite human physical performance[END_REF]. This is to be opposed to the limited variation for running capacity observed in dogs and horses [START_REF] Denny | Limits to running speed in dogs, horses and humans[END_REF]. A striking tendency in humans is also related to geographical origins of runners, with, for example, the massive rise of African runners among best performers (BPs) in middle to long distance over the recent decades [START_REF] Onywera | Demographic characteristics of elite Kenyan endurance runners[END_REF].

Other factors relating to runner physiology (e.g. training, running style, nutrition and, sometimes, doping activities) or to environment sensu lato (e.g. climatic conditions, riding style, rules, betting activity, reward) have also played a significant role in improving running performance [START_REF] Norton | Morphological evolution of athletes over the 20th century: causes and consequences[END_REF][START_REF] Noakes | Tainted Glory. Doping and athletic performance[END_REF][START_REF] Pfau | Modern riding style improves horse racing times[END_REF][START_REF] Toutain | Veterinary medicines and competition animals: the question of medication versus doping control. comparative veterinary and pharmacology[END_REF]. The respective influence of genetic and nongenetic factors may therefore largely differ in domesticated animals and in humans [START_REF] Brutsaert | What makes a champion? Explaining variation in human athletic performance[END_REF]. Whatsoever, recent studies have demonstrated that the maximal running speed may soon reach its limits in dogs, horses and humans [START_REF] Berthelot | The citius end: world records progression announces the completion of a brief ultra-physiological quest[END_REF][START_REF] Berthelot | Athlete atypicity on the edge of human achievement: performances stagnate after the last peak[END_REF][START_REF] Denny | Limits to running speed in dogs, horses and humans[END_REF].

Best running performances in humans have been under scrutiny [START_REF] Nevill | Are there limits to running world records?[END_REF][START_REF] Berthelot | The citius end: world records progression announces the completion of a brief ultra-physiological quest[END_REF], but a full analysis of speed progression in greyhounds and horses is not available. The comparison of speed progression in animals (horses and dogs) with that in humans requires long-term data over comparable periods and distances.

We collected data built up over more than a century (up to 118 years) for the 10 BPs in races (450-500 m in dogs, 2200-2800 m in horses and 200-1500 m in humans)the larger range in humans allowing direct comparison with the two other species over similar running times. We also tested the heritability of BPs using pedigrees of dogs and horses, whereas in humans, performance analysis from different geographical regions allowed us to test the progression of maximum running speed according to the geographical origin of runners. Our objectives here are (i) to compare the progression of speed performances in humans, horses and dogs and (ii) to evaluate the potential influence of genetic factors in horses and dogs, based on a so-called animal model approach [START_REF] Kruuk | Estimating genetic parameters in wild populations using the 'animal model[END_REF], and of geographical origin in humans. Our approach is comparative (not experimental) in essence as it is based on observational data over the long term in three species, although it allows to dissect the respective influences of genetic and environmental factors on patterns of speed progression based on fairly large data sets.

Materials and methods

The performance progression of the 10 BPs was recorded yearly throughout the world in flat, thoroughbred horse races (years: 1898-2009; distances: 2200-2800 m; effort duration from 130 to 170 s) and greyhound races (years: 1929-2009; distances: 450-500 m; effort duration from 24 to 28 s). Men's track and field races (years: 1891-2009; distances: 200, 400, 800 and 1500 m; effort duration from 20 to 230 s) were used to express human 10 BPs. The means of 10 BPs from sprint (200 and 400 m) and short to middle distances (800 and 1500 m) were considered separately for a best correspondence to thoroughbred and greyhounds' BP times, respectively. For each species, only the best yearly performance of a single athlete or animal was kept, so that any given athlete appears only once per year in the data sets. The yearly BP records were obtained in thoroughbreds from 30 events at the highest competitive level over the world ('Group 1 and 2' in Europe, Oceania and Asia and 'Stakes' for North America). In greyhounds, we collected the yearly 10 best performances recorded in short race's rings (25 events in Great Britain, Ireland, Spain, United States, Australia and New Zealand). In humans, track and field outdoor best performances were collected. Speed data were collected with similar methodology as recently reported [START_REF] Denny | Limits to running speed in dogs, horses and humans[END_REF][START_REF] Desgorces | From Oxford to Hawaii ecophysiological barriers limit human progression in ten sport monuments[END_REF] from various sources in humans (Associations of Track and Field Statisticians;[START_REF] Rabinovich | Track and Field Statistics[END_REF], horses (Galop course, 2011;Galopp sieger, 2011) and greyhounds (Greyhounds-data, 2011). A total of 6620 performances were gathered (4720 in humans, 1120 in horses and 810 in dogs). The BPs in dogs and humans were male only, whereas the horse data set included some females as well. However, as the fraction of female BPs was limited, we did not account for a sex effect when analysing the data. Speed data were expressed in m s -1

Progression pattern of maximal running speeds

Previous studies reported that best performances' progression over the last century was best described by logistics and ⁄ or multiexponential curves [START_REF] Nevill | Are there limits to running world records?[END_REF][START_REF] Berthelot | The citius end: world records progression announces the completion of a brief ultra-physiological quest[END_REF][START_REF] Denny | Limits to running speed in dogs, horses and humans[END_REF]. [START_REF] Blest | Lower bounds for athletic performance[END_REF], analysing a set of world records in athletics, showed that Gompertz models provided lower standard errors of estimates compared with other models (i.e. antisymmetric exponential and logistic models). They also described well best performances in humans [START_REF] Berthelot | Athlete atypicity on the edge of human achievement: performances stagnate after the last peak[END_REF]. We therefore opted for such a model using the following function:

V P = V A + V R ,
where V A is the additive genetic variance and V R is the residual variance, consisting of environmental effects, nonadditive genetic effects and error variance. A single speed record was available in 10 years in dog races and 20 years in horses; hence, a year could not be entered as a random effect in the model. The full model outlined above was compared with a simpler model where V A was removed using a chi-squared test, to determine whether speed displayed significant additive genetic variance.

Geographical origin of human best runners

The full human data set (200-1500 m) was split accord-Y(t) = a.e be c.t +d ing to the geographical origin (Africa, America, Asia, Europe and Oceania) of runners. Africa, Asia and where a gives the upper asymptote of y, b sets the value of t displacement, c is the curve steepness and d accounts for the fact that the minimum y value is not 0. a and d takes here positive values, whereas b and c are negative. The model parameters were estimated using a nonlinear least-squares method on the uniformized [(0, 1) range] vector of recorded values. The physiological limit for each species was given by computing the year corresponding to 99.95% (1 ⁄ 2000th) of the estimated asymptotic value.

Oceania are poorly represented in the 10 BPs over the period considered (1891-2009; Fig. S1). The analysis was further refined for short to middle distance (800-1500 m; year range: 1970-2009) by comparing the five BPs from North European countries (Nordic: Denmark, Norway, Sweden, Finland) and from East Africa (EAf; Djibouti, Eritrea, Ethiopia, Somalia, Tanzania, Kenya, Uganda, Burundi), for which large data sets are available, with runners from rest of world (ROW). An analysis of Curve fitting was performed using M M A A T T L L A A B B (version variance was used to determine the regional (Nordic, 7.11.0.584, MathWorks, Natick, MA, USA).

The yearly progression of human speed was compared with that of greyhounds (200-400 m in humans) and thoroughbreds (800-1500 m in humans) and expressed as the percentage of a human-animal ratio. The annual speed variation was also observed in each species through coefficient of variation (CV) changes.

Speed heritability in dogs and horses

For the recent period, genealogical data were available in both dogs and horses, allowing for a quantitative genetics approach. The speeds of current 10 BPs (2007)(2008)(2009) were collected and compared with those of their ancestors (individual best performance; Galop course 2011, Galopp sieger 2011, Greyhounds-data 2011). These ancestor data sets bear on 67 dogs and 64 horses including six females in the current 10 BPs (2007)(2008)(2009). All dogs and horses are part of a pedigree (seven generations in dogs and six in horses) with only male links known.

To decompose the phenotypic variance expressed in speed of greyhounds and horses lineages and to estimate the heritability (h 2 ) of this character, we used two methods: (i) a classic father-midsons regression and (ii) a restricted estimate maximum likelihood procedure to run a mixed model with the software ASReml [START_REF] Gilmour | ASReml User Guide Release 2.0[END_REF]. An 'animal model' [START_REF] Kruuk | Estimating genetic parameters in wild populations using the 'animal model[END_REF] was used in which the year was considered as a fixed effect and the total phenotypic variance (V P ) was broken into two components of variance as follows: EAf, ROW) and time (data arranged per decade; 1970-1979; 1980-1989; 1990-1999; 2000-2009) influence on speed progression. When speed differences were detected, Tukey's post hoc tests were used to identify significant differences according to region and decade.

The software package S S T T A A T T I I S S T T I I C C

A A (version 6.1; Statsoft, Maisons-Alfort, France) was used for statistical analyses. The level of significance for all analyses was set at P < 0.05. Data are expressed as mean ± SD.

Results

The Gompertz model fits speed progression with good accuracy in animals (horses: R 2 = 0.56, MSE = 0.169; greyhounds: R 2 = 0.81, MSE = 0.55; Fig. 1a,b) and in humans (800-1500 m 10 BPs: R 2 = 0.97, MSE = 0.006, Fig. 1c; 200-400 m 10 BPs: R 2 = 0.94, MSE = 0.008, Fig. 1d). The asymptotic limit in horses and dogs was 16.59 and 17.76 m s )1 , respectively, that is, 99.0% and 97.4% of the respective Gompertz asymptotes. In humans, the speeds of sprint and middle distances have already reached their estimated maximum based on the Gompertz curves (sprint: 9.54 m s )1 in 1996, 100.3% of asymptotic speed; middle distance: 7.45 m s )1 in 2001, 100.1% of asymptotic speed). Speed progression was evaluated by comparing the first 10 BPs recorded with the 10 BPs ever observed, and it appears similar in the three species (11.1% of initial value in horses, 9.4% in greyhounds, 11.1% in 200-400 m and 14.2% in 800-1500 m in humans; Fig. 1). Even less difference in speed progression was observed in the two animal species when using the asymptotic speed limit of the Gompertz curves rather than the 10 BPs ever observed (12.4% in horses, 11.9% in greyhounds, and 11.1% and 14.2% in humans).

Although the overall progression was similar, the curves differed in shape among species (b and c coefficients). The b ⁄ c ratios revealed a monoexponential shape (b ⁄ c > 3) in both horses and greyhounds, whereas performances of humans follow an S-shaped development (b ⁄ c < 0.1; Fig. 1). The CVs of dog and human speed were of the order of 0.02 (or less) over the period considered (Fig. 2). In horses, the CV was also 0.02 for the 1940-2009 period, but the 1898-1939 period had larger variance with CV up to 0.05. Humans have increased their mean speed compared with dogs over a comparable distance with a current human-dog ratio downward plateauing towards 53.2% (Fig. 3). The comparison with horses shows a current human-horse ratio of 45.2%. Both ratios have been stable for 18 years (dogs) and 42 years (horses).

Heritability estimates based on father-midsons comparisons were significant neither in greyhounds (30 pairs; h 2 = 0.042, SE = 0.34, P = 0.90) nor in horses (34 pairs; h 2 = 0.272, SE = 0.23, P = 0.25). The 'animal model' confirmed this trend in greyhounds (N = 67 data points): the additive variance was low (0.028, SE = 0.039), and model comparison (with and without V A ) showed that the heritability (h 2 = 0.183, SE = 0.240) did not differ from 0 (chi-square = 3.08, P = 0.080). In horses, though (N = 64 data points), more additive variance was detected (0.085, SE = 0.059), and the heritability differed from 0 (h 2 = 0.438, SE = 0.267; chi-square = 6.14, P = 0.013). We note here that our approach, based on BPs, underestimates the available phenotypic variance in both greyhounds (V P = 0.156, SE = 0.003) and horses (V P = 0.193, SE = 0.037).

Human speeds achieved in the 800-and 1500-m races by the five BPs over the 1970-2009 period differ according to performance years and geographical origin of runners (800-m races, F 1,39 = 5.89, P < 0.001 and 1500-m races F 1,39 = 6.66; Fig. 4). EAf and ROW runners clearly increased their speed in both distances, compared with Nordic runners. The Nordic-versus-EAf difference was not significant over the 1970-1989 decade, and both groups performed less well than the ROW group (all P < 0.001). Pairwise comparisons also showed a Nordic ⁄ EAf ⁄ ROW increasing hierarchy for 800-m races. In the most recent decade (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009), speeds on the 800-and 1500-m races are lower in Nordic than in EAf runners (both P < 0.001), but there was no difference 1969 1974 1979 1984 1989 1994 1999 2004 2009 7 1969 1974 1979 1984 1989 1994 1999 2004 2009 42 40 1890 1905 1920 1935 1950 1965 1980 1995 2010

Discussion

Our study shows that the maximum running speed over short to middle distances increased over the last century in dogs, horses and humans, but is currently reaching its asymptotic value. This is a striking result because of the difference in genetic and environmental conditions leading to speed improvement in the three species. The fitted Gompertz curves do not exhibit the same shape (see values of b ⁄ c for the three curves in Results section)the initial plateau in humans is not detected in horses and greyhoundsbut this might simply be due to the larger variance in dogs and horses in the first decades of records or the facts that data were collected earlier in the speed progression in humans than in dogs and horses. Human speed has indeed already reached its asymptote, whereas horses and greyhounds speeds are 1.0% and 2.6% down from their respective values. These results are in agreement with recent studies hypothesizing that current speeds are reaching the species' locomotory limits and explain their conclusions [START_REF] Berthelot | The citius end: world records progression announces the completion of a brief ultra-physiological quest[END_REF][START_REF] Denny | Limits to running speed in dogs, horses and humans[END_REF]. However, the similarities do not appear only in the progression patterns over the last century, but also in the progression ranges that were very close, especially when using the asymptotic speed limits to estimate the maximal speed progression per species. Over the last decades, we also noted that the speed gap between species pairs remained remarkably stable (Fig. 3). The speed CVs among the ten BPs are low as well (Fig. 2) and very similar across species. The large CV recorded in the earlier decades for horses and dogs might be accounted for by the fact that rank, rather than speed, was often recorded in races at the end of the 19th century and beginning of the 20th century. It is also likely that the homogenization in training methods and the selection of similar genetic backgrounds also lead to reduced CVs.

The similarity in speed patterns (progression, asymptotes, CV) across species is somewhat unexpected because the balance between genetic and environmental forces acting on this pattern is different. Dogs for about 20 generations and horses for 25 generations have been submitted to intense artificial selection over the period considered (artificial selection was indeed initiated much earlier in both species; [START_REF] Willett | An Introduction to the Thoroughbred[END_REF]. Quite clearly, artificial selection has reached a phenotypic limit with regard to the maximal speed and minimal variance across the 10 BPs, at least under the environmental conditions imposed by humans on dog and horse champions. Interestingly, the quantitative genetic analysis indicated some genetic variance and heritability in horses. These genetic effects are larger than those reported recently for lifetime earnings in a larger thoroughbred population [START_REF] Wilson | Breeding racehorses: what price good genes?[END_REF]. This marked genetic influence on speed appears surprising when considering the reduced speed progression over the last 40 years. However, the animal model was run on a much more reduced data set than that used for getting the general trend, and the ancestors of the current 10 BPs did not belong to the 10 BPs in their generation. It might also be that training and raising environments for best horse racing should have been homogenized over time, enhancing in return h 2 estimates. The heritability in dogs was on the verge of statistical significance (P = 0.08). Previous studies reported that selective breeding may have led to high homogeneity of predispositions for running [START_REF] Gu | A genome scan for positive selection in thoroughbred horses[END_REF][START_REF] Hill | A sequence polymorphism in MSTN predicts sprinting ability and racing stamina in thoroughbred horses[END_REF], suggesting reduced chance for the occurrence of genetically gifted individuals. Our results highlight that genetic predispositions for running fast in these particular populations are still good indicators of individual speed.

The optimization of running speed in humans probably essentially relies on training and national detection systems, but these might also allow identifying favourable polygenic profiles for elite runners [START_REF] Yang | ACTN3 genotype is associated with human elite athletic performance[END_REF][START_REF] Williams | Similarity of polygenic profiles limits the potential for elite human physical performance[END_REF][START_REF] Bejan | The evolution of speed in athletics: why the fastest runners are black and swimmers white[END_REF]. It remains therefore possible that part of speed progression in humans is due to genetic (evolutionary) processes because there might be some selection to run fast under some conditions. However, this effect might only be minor given the very short time period considered. Our data also suggest that estimated speed limits of the 10 BPs have already been achieved in 200-400 and 800-1500 m, although exceptional athletes may sometimes set atypical performances [START_REF] Berthelot | Athlete atypicity on the edge of human achievement: performances stagnate after the last peak[END_REF]. Over the century, the number of individuals engaged in athletic competitions evolved with societies' development and their emphasis on sport [START_REF] Guillaume | Success in developing regions: world records evolution through a geopolitical prism[END_REF]. America and Europe largely contributed to the 10 BPs with differences according to distance, whereas Asia and Oceania did not. The contribution of Africa to the 10 BPs in middle distance over the most recent decades is noticeable. Initially less engaged, East Africans achieved speed records comparable to those of Nordic athletes on the 1500 m in the 1970s. The striking speed improvement over the last 40 years now placed them in the first ranks, comparable to the other world regions. It is no less striking that running speeds of natives from Nordic countries stagnated over the same period in 800m races and even declined in 1500-m race. Trainers and scientists from Northern Europe were indeed largely involved in the development of modern training methods and scientific results [START_REF] Astrand | Influence of Scandinavian scientists in exercise physiology[END_REF], questioning their real impact on current best performances. On the other hand, Nordic athletes are still successful in other sports (i.e. jumps and throws in athletics, speed skating, cross-country skiing, rowing), suggesting that their genetic potential may be more favoured under the environmental constraints of other sports.

Over the last decades, the maximal human speed has progressed with the involvement of runners from new geographical origins, leading to optimized phenotypes [START_REF] Guillaume | Success in developing regions: world records evolution through a geopolitical prism[END_REF]. The enlargement of the runner population in humans certainly enlarged the genetic pools upon which elite athletes were detected [START_REF] Williams | Similarity of polygenic profiles limits the potential for elite human physical performance[END_REF]. Furthermore, some studies suggested that successful runners from East Africa originated from distinct ethnic and environmental backgrounds compared with the general population of these countries [START_REF] Onywera | Demographic characteristics of elite Kenyan endurance runners[END_REF][START_REF] Scott | Mitochondrial haplogroups associated with elite Kenyan athlete status[END_REF]. Quite clearly, improving speed through artificial selection in dogs and horses or detecting better athletes through an increasing population can only be actually efficient under appropriate environmental conditions, including training and competing conditions [START_REF] Davids | Genes, environment and sport performance. Why the nature-nurture dualism is no longer relevant[END_REF][START_REF] Desgorces | From Oxford to Hawaii ecophysiological barriers limit human progression in ten sport monuments[END_REF]. The decrease in the 10 BPs during the two World Wars [START_REF] Guillaume | Success in developing regions: world records evolution through a geopolitical prism[END_REF] is an indication of the role of environmental conditions. Speed increase requires prosperous societies with a flourishing economy as described for improved health and body size over the 19th and 20th centuries [START_REF] Fogel | The Escape from Premature Death and Hunger[END_REF].

Our analysis is based on patterns exhibited in longterm data sets collected in arguably artificial environments. It would certainly be interesting to use more experimental approaches to test whether other species are not far away from their limit and whether this limit can be experimentally manipulated and increased. Speed increase has indeed been described in nature when environmental conditions allow for the improvement in maximal capacities [START_REF] Miles | The race goes to the swift: fitness consequences of variation in sprint performance in juvenile lizards[END_REF][START_REF] Husak | Does survival depend on how fast you can run or how fast you do run?[END_REF] and recently suggested as describing phenotypic expansion in humans [START_REF] Berthelot | A double exponential dependence toward developmental growth and time degradation explains performance evolution in individual athletes and human species[END_REF]. For example, dietary and thermal conditions experienced both during embryogenesis and early in life may favour the expression of genetic predisposition for running [START_REF] Elphick | Long term effects of incubation temperatures on the morphology and locomotor performance of hatchling lizards (Bassiana duperreyi, Scincidae)[END_REF][START_REF] Galliard | Physical performance and darwinian fitness in lizards[END_REF]. Trade-offs are of course expected between running performances and appropriate behaviour or the ability to migrate towards more favourable environmental conditions [START_REF] Irschick | Do lizards avoid habitats in which performance is submaximal? The relationship between sprinting capabilities and structural habitat use in Caribbean anoles[END_REF][START_REF] Husak | Field use of maximal sprint speed by collared lizards (Crotaphytus collaris): compensation and sexual selection[END_REF]. In natural conditions, such adaptations in animals have been associated with survivorship and reproductive success [START_REF] Miles | The race goes to the swift: fitness consequences of variation in sprint performance in juvenile lizards[END_REF]. It is ironical that behaviour training and migration to more favourable environments also occur in competitive sports.

Conclusion

The parallel progression of maximal running speeds in these three species over the last decades suggests that performances will no longer progress despite genetic selection in animals and best population detection in humans. Regardless of differences between species (biological, environmental and competition history), human pressure, which has accelerated the biological adaptations allowing to run faster, is a process with limited potential and reduced benefits in the near future.

Fig. 1

 1 Fig. 1 Models fitting for speed progression (m s -1 ) between 1891 and 2009, in (a) 10 best thoroughbred performers (R 2 = 0.56); (b) 10 best greyhound performers on short ring races (R 2 = 0.81); (c) Mean speed of the 10 best human performers on 800-to 1500-m track races (R 2 = 0.97); (d) Mean speed of the 10 best human performers on 200-to 400-m track races (R 2 = 0.94). The calculated a, b, c, d parameters of the Gompertz function were for thoroughbred(respectively, 77.8, 3.77, 0.46, 16.59), greyhound (respectively, 14.99, 1.99, 0.60, 17.7), 800-to 1500-m human races (respectively, 1.45, 0.26, 3.06, 7.44) and for 200-to 400-m human races(respectively, 1.29, 0.20, 3.31, 9.52).

Fig. 2

 2 Fig. 2 Coefficient of variations of 10 best performers in thoroughbred (1899-2009; grey squares), greyhounds (1929-2009; black squares), human 200-to 400-m races (1891-2009; grey open circles) and humans 800-to 1500-m races (1891-2009; black open circles).

Fig. 4

 4 Fig. 4 Five best human performances in 800-m (a) and 1500-m (b) races in runners from Nordic countries (open circles), East African countries (grey circles) and rest of World (black circles).

Fig. 3

 3 Fig. 3 Ratios of human vs. greyhound (black squares, comparison with human 200-400 m mean speed) and human vs. thoroughbred (grey circles, comparison with human 800-1500 m mean speed). Dashed lines for mean speed gap between humans and animals when stabilized.

Acknowledgments

We thank the INSEP teams for full support.

Supporting information

Additional Supporting Information may be found in the online version of this article: Figure S1 Humans 10 best performances in sprint, up figures: 200 m (grey circles), 400 m (black circles); and middle distance, down figures: 800 m (grey circles) and 1500 m (black circles) according to the geographic origin of runners.

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be reorganized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.


Gustavo H Lopes

Nelson Ibaseta

Pierrette Guichardon
email: pierrette.guichardon@centrale-marseille.fr

Pierre Haldenwang

Effects of solute permeability on permeation and solute rejection in membrane filtration

Keywords: permeate flux, concentration polarization, solute permeability, Reverse Osmosis, solute rejection Permeate flux, solute rejection, concentration polarization, solute permeability, reverse osmosis Wiley-VCH

come

Effects of solute permeability on permeation and solute rejection in membrane filtration

Introduction

Reverse osmosis (RO) and nanofiltration (NF) are mainly applied for seawater desalination, wastewater treatment and water reclamation, for ultrapure water production and in process industry niches [START_REF] Fane | Treatise on Water Science[END_REF][START_REF] Schaefer | Nanofiltration Principles and Applications[END_REF]. These processes use membrane separation to achieve high purification and relatively high solvent permeation rates [START_REF] Fane | Treatise on Water Science[END_REF]. The development and optimization of these separation techniques typically rely on abundant, laborious, often costly pilot experiments while the prediction of their performances remains underexplored. In this context, the use of predictive models and the application of the subsequent fundamental knowledge would be valuable.

The performance of pressure-driven membrane filtration processes is determined by an intimate interaction between the transport properties of the membranes and the hydrodynamics and mass transfer taking place inside a membrane-bound channel. It is well known that this interaction gives rise to a reversible accumulation of solute in a mass boundary layer on the filtrating surface of the membrane, the so-called concentration polarization layer [START_REF] Strathmann | Ullmann's Encyclopedia of Industrial Chemistry[END_REF][START_REF] Sablani | [END_REF][5][6]. Combined with osmosis, concentration polarization hinders solvent permeation and increases solute passage into the filtrate (permeate) in addition to playing a part in scaling and fouling [START_REF] Strathmann | Ullmann's Encyclopedia of Industrial Chemistry[END_REF][START_REF] Sablani | [END_REF].

New membranes are under development with the aim of maximizing the permeation rate by enhancing the membrane permeability to the solvent while ensuring highest selectivity, so as to keep the solute concentration in the permeate as low as possible. Unfortunately, the effort is partly wasted, as increased permeation inherently causes enhanced concentration polarization. Reducing this concentration polarization can nonetheless be achieved by disturbing the concentration layers with eddy-promoting spacers put into the flow channel [7]. Notwithstanding, the question may be raised as to whether tailoring the selectivity of the membrane can induce intensified permeation, irrespective of the polarization conditions. The role played by the membrane solute permeability here has not been discussed enough. This is the point we herein investigate.

This work follows the publication by Lopes et al. [8], which demonstrated the adequacy of the numerical model developed by the authors for predicting permeate fluxes and solute rejection obtained experimentally in RO and tight NF in flat and spiral-wound geometries. The current article begins with a summary of the model and a description of the simulations. It then presents the results, discussions and conclusions about the impact of solute permeability at different operating conditions upon the fundamental behavior of an ideal separation process, as well as on its two main outputs: permeate flux and solute rejection. The study considers numerous orders of magnitude of solute permeability from 0 m s -1 to 10 -6 m s -1 and a solvent permeability in the range of RO (10 -12 m Pa -1 s -1 ).

Model description

As the model we used is described extensively in [6,8,9], only its main elements will be given here. The model considers a liquid solution of one solvent and one solute in laminar, steady, incompressible crossflow filtration (tangential filtration) along a two-dimensional planar symmetric channel of axial and transverse coordinates ܼ and ܺ, respectively, the channel walls being permeable to both solvent and solute. Axial velocity (ܹ), transverse velocity (ܷ), permeate flux (ܷ ୵ ), solute concentration (or concentration polarization) ,)ܥ( gauge pressure (ܲ) and permeate concentration ܥ( ୮ ) are considered as functions of ܼ and ܺ. The input parameters are all easily accessible experimentally: two properties of the membrane (permeability to the solvent, ܫ ିଵ , and permeability to the solute, ,)ܤ two properties of the membrane filtration module (channel length, ,ܮ and channel half-height, ݀), two operating conditions (feed pressure, ܲ ୧୬ , and axial feed velocity, ܹ ୧୬ ) and four properties of the solution (solute feed concentration, ܥ ୧୬ , solution mass density, ߩ, solution viscosity, ߤ, and solute diffusivity in the solvent, .)ܦ A schematic is sketched in Fig. 1. Note that subscripts "w", "p" and "in" refer to the membrane surface on the retentate side (wall), the membrane surface on the permeate side, and the inlet (or feed) conditions, respectively. Fouling is not considered while osmotic counter-effects are taken into account. ߩ, ߤ and ܦ are equal to their values in the feed. The solution-diffusion model [START_REF] Fane | Treatise on Water Science[END_REF]10] describes locally the transmembrane solvent and solute fluxes, as in Eq. ( 1) and Eq. ( 2), respectively:

ܷ ୵ ሺܼሻ = ܫ ିଵ ሾܲሺܼሻ -Δߎሺܼሻሿ (1)
ܥ ୮ ሺܼሻܷ ୵ ሺܼሻ = ܥൣܤ ୵ ሺܼሻ -ܥ ୮ ሺܼሻ൧ (2)
where

ܷ ௪ ሺܼሻ = ܷሺ݀, ܼሻ (3)
ܥ ௪ ሺܼሻ = ܥሺ݀, ܼሻ (4) and Δߎ is the osmotic pressure difference between the retentate and permeate sides of the membrane,

Δߎሺܼሻ = ߎሾܥ ୵ ሺܼሻሿ -ߎൣܥ ୮ ሺܼሻ൧ (5)
calculated based on the van't Hoff's osmotic pressure law, ߎ = ܥܴܶ݅ (6) where ݅ is the van't Hoff's factor, ܴ is the ideal gas constant and ܶ is the solution temperature.

The numerical solutions are calculated at each grid point in half of the channel via a secondorder finite difference scheme which solves the continuity equation, the two-dimensional Navier-Stokes equations and the solute conservation equation simultaneously [6]. The system is handled in dimensionless form under Prandtl's hypotheses [6,8,9] whereby diffusion of momentum and mass in the longitudinal (axial) flow direction is negligible compared with that in the transverse direction. These equations are solved in the filtration channel only (flow domain), whereas membrane transport takes the form of boundary conditions (Eqs. ( 1) and ( 2)). As will be seen, the flow in the whole domain will depend on the membrane transport properties.

The simulations consider the desalination of aqueous sodium chloride solutions at 25°C by membranes of solvent permeability ܫ ିଵ = 5×10 -12 m Pa -1 s -1 (typical for RO) and solute permeability, ,ܤ tuned from 0 m s -1 (membrane impermeable to the solute, i.e., perfectly permselective) through 10 -8 m s -1 and 10 -7 m s -1 (typical for RO) up to 10 -6 m s -1 . The flow channel reproduces the length of an industrial membrane module with six identical membranes arranged in series, thus ܮ = 6 m and ݀ = 5×10 -4 m. As presented in Tab. concentrations ranging from that of low-concentration brackish water up to that of seawater are simulated. P in varies from 1.5×10 5 Pa to 60×10 5 Pa. W in is 0.1 m s -1 . Empirical laws are used to estimate ρ, µ and ܦ [11]. The computational domain is discretized into 1000 transverse and 8000 axial grid points.

(Tab. 1)

Results

Permeate fluxes

Let us first consider the behavior of the averaged permeate flux measured by experimentalists, ܷ ୟ୴ , equivalent to the local permeate flux averaged along the membrane length [8]. The classic influence of the inlet pressure on it is depicted in Fig. 2 for three feed concentrations using the nondimensional "three-Péclet-numbers" representation introduced by Haldenwang et al. [12].

(Fig. 2)

Accordingly, ܲ݁ ୟ୴ is the averaged (subscript av) permeation Péclet number (dimensionless permeate flux), ܲ݁ ୧୬ is the inlet pure-solvent Péclet number (nondimensional inlet pressure), and ܲ݁ ୧୬ ୭ୱ୫ is the inlet osmotic (superscript osm) Péclet number (dimensionless inlet solute concentration):

ܲ݁ ୟ୴ = ܷ ୟ୴ ݀ ܦ (7)
ܲ݁ ୧୬ = ܲ ୧୬ ܫ ିଵ ݀ ܦ (8)
ܲ݁ ୧୬ ୭ୱ୫ = Π ୧୬ ܫ ିଵ ݀ ܦ (9)
This representation is convenient because the three Péclet numbers are of the same order of magnitude. Hence, for low solute concentrations, i.e., low values of ܲ݁ ୧୬ ୭ୱ୫ , ܲ݁ ୟ୴ is close to but always lower than ܲ݁ ୧୬ . As concentration polarization increases, so does the gap between ܲ݁ ୟ୴ and ܲ݁ ୧୬ . Finally, if the membrane is fully impermeable to the solute, ܲ݁ ୟ୴ will be positive only if ܲ݁ ୧୬ is higher than ܲ݁ ୧୬ ୭ୱ୫ .

Tab. 2 exemplifies the values of ܲ ୧୬ and ܲ݁ ୧୬ . As expected, Fig. 2 shows that the averaged permeate flux increases with the inlet (or applied) pressure. For the lowest solute concentration (ܲ݁ ୧୬ ୭ୱ୫ = 0.13), concentration polarization remains weak as long as the inlet pressure is low; for ܲ݁ ୧୬ ≤ 1 in particular, ܲ݁ ୟ୴ ≈ ܲ݁ ୧୬ . However, as ܲ݁ ୧୬ rises, concentration polarization becomes significant; the increase in effective operating pressure tends to vanish (term in brackets in Eq. ( 1)) and so does the permeation. Two observations can be made regarding higher feed concentrations. First, whenever the membrane is fully selective, and for because ܲ݁ ୧୬ must exceed ܲ݁ ୧୬ ୭ୱ୫ , as concluded from Eq. ( 1). Second, it is reasonable to expect ܲ݁ ୟ୴ to grow linearly with ܲ݁ ୧୬ -ܲ݁ ୧୬ ୭ୱ୫ provided that concentration polarization is negligible, and to infer that the coupling of polarization and osmotic pressure is significant whenever the growth of ܲ݁ ୟ୴ with ܲ݁ ୧୬ -ܲ݁ ୧୬ ୭ୱ୫ tends to deviates from linearity even for low pressures. However, the slopes of the linear segments are very different depending on ܲ݁ ୧୬ ୭ୱ୫ :

higher feed concentrations intensify polarization and osmosis, ergo reducing permeation.

(Tab. 2)

It is also noteworthy to analyze the dependence of the permeate flux on the solute permeability value. The units of ܤ allow us to envisage it as the diffusion velocity of the solute across the membrane and thus to express the permeability values in nondimensional form by dividing them by the solute diffusion velocity in the feed channel, ܦ ݀ ⁄ . This gives rise to the dimensionless membrane solute permeability, ߜ, whose correspondence with the values of ܤ in this study is presented in Tab. 3:

ߜ = ܤ ݀ ܦ (10) (Tab. 3)
Fig. 2 evaluates three orders of magnitude of ߜ and reveals that the more solute-permeable (or the less permselective) the membrane, the higher the permeate fluxes for a given solvent permeability. This tendency is even greater when the inlet concentration rises and at lower feed pressures. In the cases where this tendency is clearest, ܲ݁ ୟ୴ for a membrane of ߜ ~ 10 -1 is almost 4 times higher than for a membrane of ߜ ~ 0 when ܲ݁ ୧୬ ୭ୱ୫ is 1.46 and ܲ݁ ୧୬ is 1.7. Also, ܲ݁ ୟ୴ for ߜ ~ 10 -1 is more than 3 times higher than for ߜ ~ 0 when ܲ݁ ୧୬ ୭ୱ୫ is 5.12 and ܲ݁ ୧୬ is 6.

In fact, as will be demonstrated in the following subsection, an intricate mechanism accounts for the reduction of the osmotic pressure difference between both sides of the membrane. This happens when the membrane becomes more permeable to the solute, leading to higher permeation rates. Under our simulation conditions, the effects of the solute permeability upon this mechanism with respect to ܲ݁ ୟ୴ cannot be neglected unless the order of magnitude of ߜ is below the threshold of 10 -2 (in which case there is overlap with ߜ = 0 [6]). In accordance with this rationale, it is worth noticing that the results simulated here for mild polarization conditions (low ܲ݁ ୧୬ ) for the two membranes of lowest solute permeability are comparable to those calculated with equation numbered (41) in Haldenwang et al [12].

Axial and transverse profiles

Dimensionless concentrations, fluid velocities, fluxes and transverse coordinate are henceforth represented by the same symbols as their homonyms but in the small letter version. Fig. 3 and Fig. 4

ܿ ୵ = ܥ ୵ ܥ ୧୬ (11)
ܿ ୮ = ܥ ୮ ܥ ୧୬ (12)
ݏܱ = ߎ ୧୬ ܲ ୧୬ (13)
ݑ ୵ = ܷ ୵ ܲ ୧୬ ܫ ିଵ (14) (Fig. 3a, Fig. 3b, Fig. 3c) (Fig. 4a, Fig. 4b) In Eq. ( 13), ݏܱ is the osmotic number [8]. Profiles in Fig. 3 and4 are represented as functions of the dimensionless axial coordinate, ߞ:

ߞ = ܼ ܮ (15)
We first focus on the case of membranes totally impermeable to the solute (ߜ = 0): ܿ ୮ is null and therefore an osmotic pressure develops only in the retentate. As a consequence of the solvent passage into the permeate, the concentration of the retentate grows as it flows forward in the membrane channel, and so does the membrane surface concentration (ܿ ୵ ). Figs. 3a-3c show the increase in ܿ ୵ along ߞ and Figs. 4a-4b the consequent increase in osmotic pressure difference and the reduction in permeate flux. The magnitude of these effects is however dependent on the feed concentration. In fact, depending on the conditions, ܿ ୵ may become from a little more than 1 up to 9 times higher than the feed concentration along the flow channel. Figs. 3a-3c and Figs. 4a-4b reveal that the dimensionless permeate flux becomes weaker at higher ܲ݁ ୧୬ ୭ୱ୫ , just as the nondimensional magnitude of concentration polarization.

As a result, the rise in osmotic pressure and the consequent reduction in permeate flux are attenuated. Note that, in nondimensional form (as in Fig. 3b and according to Eq. 11), concentration polarization (and thus the value of ܿ ୵ ) can be proportionally lower for higher feed concentrations than for lower feed concentrations because of a lower nondimensional permeation rate at higher polarization.

The rationale changes considerably if the membrane is permeable to the solute: the transmembrane solute flux has to be taken into account in the calculations. The solute concentration in the permeate is no longer zero. An osmotic pressure develops in the permeate, and not only in the retentate. This alone would tend to increase the permeation rate. Somewhat surprisingly however, Figs. 3a-3c reveal that ܿ ୵ is higher for a membrane of high solute permeability (ߜ ~ 10 -1 ) than when ߜ = 0. This itself would cause ݑ ୵ to decrease. The final result of these opposing tendencies upon ݑ ୵ is observed in Figs. 4a-4b. The rise in ܿ ୮ counterbalances that in ܿ ୵ , i.e., ܿ ୵ -ܿ ୮ diminishes and so does the local osmotic pressure difference, resulting in higher permeate fluxes. This contributes, in turn, to the rise in ܿ ୵ , as previously observed.

A crossflow is not one-dimensional by definition. While the previous paragraphs insisted on the role of ܷ on the establishment of the polarization layer by advection of solute onto the membrane surface, the influence of the axial shearing generated upon this layer by ܹ should not be neglected [6,8]. Consider:

ܿ = ܥ ܥ ୧୬ (16) ݓ = ܹ ܹ ୧୬ (17)
ݔ = ܺ ݀ (18)
Fig. 5a reveals that, for higher ߜ, the axial velocity, ,ݓ is lower at all transverse positions )ݔ( as a consequence of the strong increase in solvent permeation seen in Fig. 5b as an increased transverse velocity, ݑ (crossflow velocity, whose maximum value is ݑ ୵ , as illustrated in Fig. 1). Hence, for higher ߜ, less solute is swept downstream by the flow, intensifying the concentration polarization layer, as shown in Fig. 5c. It is interesting to note that there is a certain compensation between ݓ and ,ݑ which is reflected by the inverted positions that straight and dashed lines have in Fig. 5a and Fig. 5b.

(Fig. 5a, Fig. 5b, Fig. 5c) Fig. 5a also allows us to conclude that the retentate flow is increasingly decelerated along the membrane channel. The comparison of Fig. 5b and Fig. 5c furthermore shows that the increase in polarization in the axial direction is accompanied by a sharp reduction in the transverse velocity as the fluid flows along the filtration channel. Moreover, for the same reasons as in Fig. 2, the local values of the crossflow velocity are somewhat larger for higher ߜ. More details on the transverse profiles of the crossflow velocity are presented in [6].

The model is also capable of calculating the magnitude of concentration polarization at different cross-sections of the flow domain. Fig. 5c depicts the axial evolution of the transverse concentration gradient along the membrane filtration channel. It is evident from Fig. 5c that actually not only ܿ ୵ but also the whole bulk solution becomes more concentrated along the flow channel. This corroborates the usual experimental finding according to which the retentate stream is more concentrated than the feed solution. In other words, the transverse concentration profiles hypothesized by the film model, according to which the concentration boundary layer is found on the membrane surface only, [START_REF] Fane | Treatise on Water Science[END_REF][START_REF] Sablani | [END_REF]6] are only found at the beginning of the flow channel. This remark underlines the limitations of the one-dimensional film model for describing a crossflow in long filtration channels [6,9]. For a membrane of given solute permeability (ߜ), the difference between the nondimensional values of ܿ at positions ݔ = 0 (center of the filtration channel) and ݔ = 1 (membrane surface) in Fig. 5c is the extent of concentration polarization at each cross-section (ߞ). According to Eq. 6, this value also represents the local enhancement of osmotic pressure on the retentate side caused by the buildup of the polarization layer. This enhancement is strongly related to the reduction in solvent permeation and the increase in the solute passage into the permeate, as indicated by Eq. 1 and Eq. 2, respectively. From Fig. 5c, an enhancement of approximately 2 to 3 times occurs depending on the membrane properties and the axial coordinate. The figure also confirms that the osmotic pressure on the retentate side increases with ߞ (this can also be concluded from Fig. 4).

The axial pressure profiles had been analyzed beforehand according to Eq. ( 1) since the permeate velocity, ݑ ୵ , is proportional to ሺߞሻ -ܱݏൣܿ ୵ ሺߞሻ -ܿ ୮ ሺߞሻ൧ where ሺߞሻ = ܲሺܼሻ ܲ ୧୬ ⁄

is the local pressure. These profiles are presented in reference [6]. The pressure drop was low in all cases: less than 5% at lowest feed pressure and negligible otherwise. It is interesting to realize how the influence of membrane selectivity upon the hydrodynamics of the problem extends to the pressure values. Indeed, enhanced permeation at higher values of ܤ is accompanied by a deceleration of the axial flow and so by a lower pressure drop (or increased filtration pressure). This has a retroactive effect on the solvent permeation, intensifying it [6,13,14]. However, the effect was minor under our simulation conditions.

Solute rejection

Together with the averaged permeate flux, the averaged solute rejection [8], ܴܶ ୟ୴ , is of prime importance for experimentalists:

ܴܶ ୟ୴ = 1 -ܿ ୮ ౬ (19)
where ܿ ୮ ౬ is the mean bulk concentration of the permeate solution reduced by ܥ ୧୬ [7].

Fig. 6a represents ܴܶ ୟ୴ as a function of ܲ݁ ୧୬ for several values of ߜ and ܲ݁ ୧୬ ୭ୱ୫ . The solute rejection obviously diminishes when the solute permeability increases. Total rejection can only be admitted for ߜ < 10 -3 (or ܤ < 10 -8 m s -1 ). This can be more clearly distinguished in Fig. 6b where all curves correspond to orders of magnitude of ܿ ୮ ౬ above 10 -2 . The remarkable finding in Fig. 6 is that the solute rejection exhibits a non-monotonical dependence on the applied pressure. On the one hand, for low pressures leading to relatively low permeate fluxes, any pressure rise will result in a higher permeate flux, which dilutes the solute in the permeate and results in a higher solute rejection. By contrast, for high pressures causing high permeate fluxes, the higher the pressure, the more severe the concentration polarization, which increases the solute transfer across the membrane and reduces the solute rejection. In other words, there is a maximum value for the operating pressure which will lead to a maximum solute rejection (possibly regarded as optimal).

(Fig. 6a, Fig. 6b)

F o r P e e r R e v i e w 9
The example in Fig. 7 helps clarify the effect of ߜ seen in Fig. 6. From Fig. 7, the increase in ݑ ୵ (due to higher solute permeability) is not sufficient for the soaring transmembrane solute flux (due to higher concentration polarization at higher ݑ ୵ ), ܿ ୮ × ݑ ୵ , to be diluted. Indeed, as opposed to ܿ ୮ × ݑ ୵ , ݑ ୵ depends indirectly on ߜ [6, 8] and its sensitivity is not too high.

(Fig. 7) Fig. 6 also demonstrates that the maximum value of the solute rejection that can be attained is practically independent of the inlet concentration. It however shows that the corresponding pressure increases with ܲ݁ ୧୬ ୭ୱ୫ .

Concentration polarization affects simultaneously, in opposite directions and to different extents, the driving forces for both solvent and solute transmembrane transport. It modifies their magnitudes and determines their axial evolutions. As such, it influences the whole process behavior and outputs. At the same time, these driving forces are also functions of the membrane transport properties (among which the solute permeability), the operating conditions and the characteristics of the filtration module. That is to say, concentration polarization is "cause and effect" of deeply convoluted aspects. Unless simulations or experiments are carried out for each set of input conditions, it is not possible to quantify concentration polarization and its effects upon solute rejection. The only statements that can be made in advance are the behaviors highlighted in the previous paragraphs leading to the non-asymptotic dependence of the solute rejection on the applied pressure.

Conclusions

This study has pointed out the effects of membrane selectivity on the overall hydrodynamics and bulk mass transfer in the flow channel. The membrane transport properties regarding the solute may modify concentration polarization to such significant extent as to define not only the values of solute rejection but also those of permeate flux. The reason behind this modification is an intertwined coupling between membrane transport properties, hydrodynamics, concentration polarization, osmotic pressures on the feed and permeate sides of the membrane, and pressure drop. As long as the membrane solute permeability is high, the consideration of the transmembrane solute flux, and thus of an integrated treatment coupling permeate flux and permeate concentration, should not be circumvented. This calls for an accurate estimation of the membrane transport parameters [15].

One main finding of this study is the increase in permeate flux with increasing solute permeability. This owes to the coupling between the osmotic pressures on the two sides of the membrane and the concentration polarization. This effect is significant for relatively high values of membrane solute permeability not necessarily in the range of reverse-osmosis membrane permeability values. It is useful to understand that a less selective membrane of higher solute permeability might be a good choice whenever the target of the separation process is to concentrate the retentate instead of obtaining a high-purity permeate.

The second main finding is the existence of an optimal applied pressure leading to maximum solute rejection (or lowest permeate concentration) for a given feed concentration. This is the result of the combination of two regimes: the dilutive regime, where rising pressures will increase the permeate flux and result in higher solute rejection, and the concentrative regime, where even higher pressures will result in lower and even negative solute rejections. The maximum solute rejection depends on the solute permeability but is rather independent of the inlet concentration. Some considerations apply. The effect of higher solute permeability upon the permeate flux would be lessened in modules where concentration polarization is weakened, as for example in spiral-wound modules with feed spacers. Conversely, if the osmotic pressure happens to be higher than that predicted by Eq. ( 6), the effect would be intensified; this is the case for some solutes whose osmotic pressure obeys a polynomial law or power law with exponents higher than one. Finally, higher solute permeability leads to higher concentrations on the membrane surface. This could be a problem in systems prone to fouling, but could be interesting for specific applications.

Acknowledgement

Gustavo H.

Short text for the table of contents section

The coupling of concentration polarization, transmembrane solute and solvent fluxes and osmotic pressures was studied by solving the continuity, Navier-Stokes and solute transfer equations. Solvent permeation was found to rise with the value of membrane solute permeability. Moreover, there is an optimal value of inlet pressure which leads to maximum solute rejection at a given feed concentration.

Graphical abstract

(submitted online)

  pass into the permeate, the value of the abscissa-intercept increases with ܲ݁ ୧୬ ୭ୱ୫

Fig. 1 :

 1 Fig.1: Two-dimensional flow channel bound symmetrically by two equally permeable membranes. A crossflow occurs in the channel whereby the feed solution splits into the retentate stream and the solute-containing permeate. Process variables are described locally and vary axially and/or transversally. Sketch out of scale ܮ( ≫ ݀).

14 Fig. 2 :

 142 Fig. 2: Three-Péclet-number diagram representing the dimensionless averaged permeate flux (ܲ݁ ୟ୴ ) as a function of the nondimensional applied pressure (ܲ݁ ୧୬ ) for three values of dimensionless solute concentration (ܲ݁ ୧୬ ୭ୱ୫ ). Results are represented for three values of dimensionless solute permeability (ߜ).

Fig. 3 :Fig. 4 :

 34 Fig. 3: Axial profiles of the nondimensional membrane and permeate concentrations, ܿ ୵ and ܿ ୮ , respectively, for two values of nondimensional solute permeability (ߜ). a) ܯ ୧୬ = 3.5 %; ܲ ୧୬ = 60×10 5 Pa. b) ܯ ୧୬ = 1.0 %; ܲ ୧୬ = 60×10 5 Pa. c) ܯ ୧୬ = 0.1 %; ܲ ୧୬ = 1.5×10 5 Pa.

Fig. 5 :

 5 Fig. 5: Transverse profiles in the channel half-height at different axial positions along the flow channel during the desalination of a solution of ܯ ୧୬ = 1.0 % at ܲ ୧୬ = 30×10 5 Pa for two values of solute permeability (ߜ). a) Axial velocity, .ݓ b) Transverse velocity, .ݑ c) Solute concentration, ܿ.

Fig. 6 :

 6 Fig. 6: Influence of the dimensionless applied pressure (ܲ݁ ୧୬ ) on the overall purification for three feed concentrations (ܲ݁ ୧୬ ୭ୱ୫ ) and using membranes of different solute permeabilities (ߜ). a) Averaged rejection, ܴܶ ୟ୴ . b) Logarithm of ܿ ୮ ౬ , the averaged solute concentration.

Fig. 7 :

 7 Fig. 7: Axial evolution of the local solute and solvent fluxes, ݑ ୵ ܿ ୮ and ݑ ௪ , respectively, in the case of a solution of ܯ ୧୬ = 1.0 % desalinated at ܲ ୧୬ = 60×10 5 Pa for four values of dimensionless solute permeability (ߜ).

Fig. 1 297x209mm

 1 Fig. 1 297x209mm (300 x 300 DPI)

Fig. 2 147x101mm

 2 Fig. 2 147x101mm (300 x 300 DPI)

  Fig. 3a 147x101mm (300 x 300 DPI)

  Fig. 3b 145x101mm (300 x 300 DPI)

  Fig. 3c 153x109mm (300 x 300 DPI)

  Fig. 4a 144x95mm (300 x 300 DPI)

  Fig. 4b 145x96mm (300 x 300 DPI)

  Fig. 5a 150x102mm (300 x 300 DPI)

  Fig. 5b 149x102mm (300 x 300 DPI)

  Fig. 5c 146x100mm (300 x 300 DPI)

  Fig. 6a 149x102mm (300 x 300 DPI)

  Fig. 6b 142x99mm (300 x 300 DPI)

Fig. 7 144x94mm

 7 Fig. 7 144x94mm (300 x 300 DPI)

  represent the nondimensional axial profiles of the concentration on the membrane ܿ ୵ , permeate concentration, ܿ ୮ , osmotic pressure difference, ܱݏ൫ܿ ୵ -ܿ ୮ ൯, and local permeate flux, ݑ ୵ :

	surface,
	F o r
	P e
	e r
	R e
	v
	i e
	w
	6

  Lopes thanks the Conseil Régional de Provence-Alpes-Côte d'Azur and the École Centrale de Marseille for financing this work. Dimensional feed pressure values (ܲ ୧୬ ) and their nondimensional counterparts (ܲ݁ ୧୬ ). The variation with ܲ݁ ୧୬ ୭ୱ୫ is due to the concentration-dependence of the salt diffusivity[11] in the feed solution.

	ܷ ݑ ܹ ݓ ܺ Tab. 2: ܲ ୧୬ (10 5 Pa) [m s -1 ] [-] [m s -1 ] [-] [m] ݔ [-] ܼ [m] 0	transverse velocity dimensionless transverse velocity axial velocity dimensionless axial velocity ܲ݁ ୧୬ ୭ୱ୫ ܲ݁ ୧୬ transverse coordinate 0.13 0 reduced transverse coordinate 1.46 0 axial coordinate 5.12 0
			0.13	2.36
	Greek symbols 15	1.46	2.59
			5.12	2.59
	Δ ߜ ߞ ߤ ߎ ߩ	[-] [-] 30 [-] [Pa s] [Pa] [kg m -3 ] 45 60	F o r difference between the feed and permeate membrane sides, respectively 0.13 4.72 1.46 5.17 dimensionless membrane solute permeability 5.12 5.17 dimensionless axial coordinate 0.13 7.09 feed solution viscosity osmotic pressure feed solution density F o r 1.46 7.76 F 5.12 7.76 0.13 9.45 o r 1.46 10.34
	P e e r R e averaged inlet (feed, applied) conditions osmotic P e e r 5.12 10.34 P Tab. 3: Dimensional solute permeability values )ܤ( studied in the current work and their Sub-/superscripts av in osm e nondimensional counterparts (ߜ). The variation with ܲ݁ ୧୬ ୭ୱ୫ is due to the concentration-e dependence of the salt diffusivity [11] in the feed solution. r p permeate w wall (membrane surface) R e ܤ (m s -1 ) ܲ݁ ୧୬ ୭ୱ୫ ߜ R 0.13 0 e 0 1.46 0 Symbols used ܤ [m s -1 ] membrane solute permeability ܥ [mol m -3 ] solute concentration ܿ [-] dimensionless solute concentration ܦ [m 2 s -1 ] v i e w v i e w 5.12 0 v 0.13 3.15×10 -3 i 10 -8 1.46 3.45×10 -3 e 5.12 3.45×10 -3 0.13 3.15×10 -2 w 10 -7 1.46 3.45×10 -2 solute diffusion coefficient in the feed solution ݀ [m] 5.12 3.45×10 -2 flow channel half-height ܫ [m -1 Pa s] membrane resistance to transmembrane solvent flow ܫ ିଵ 0.13 3.15×10 -1 Tables with headings 10 -6 1.46 3.45×10 -1 [m Pa -1 s -1 ] membrane solvent permeability ݅ [-] van't Hoff's factor ܮ [m] flow channel length respective inlet osmotic Péclet numbers (ܲ݁ ୧୬ ୭ୱ୫ ). Tab. 1: Mass percentages ܯ( ୧୬ ) and molar concentration ܥ( ୧୬ ) of sodium chloride and their 5.12 3.45×10 -1
	ܯ ݏܱ ܯ ୧୬ (%) [%] [-] ܲ [Pa] 0.1 1.0 ܲ݁ [-] 3.5	solute mass percentage ୭ୱ୫ ܥ ୧୬ (mol m -3 ) ܲ݁ ୧୬ osmotic number 17.1 0.13 hydrodynamic pressure 171.1 1.46 Péclet number 598.9 5.12
	ܴ	[J K -1 mol -1 ] ideal gas constant
	ܶ	[K]	solution temperature
	ܴܶ	[-]	solute rejection
				11 13

Wiley-VCH Chemical Engineering & Technology

Abbreviations

NF nanofiltration RO reverse osmosis