William E Douglas
email: douglas@univ-montp2.fr

Francesco Baldini

Jiri Homola

Kassem Amro

Sébastien Clément

Robert Lieberman

Kyriacos Kalli

Philippe Dejardin

Philippe Gerbier

Jean-Marc Janot

Philippe Déjardin

Thierry Thami

Novel optical sensors for detection of nitroaromatics based on supported thin flexible poly(methylhydrosiloxane) permeable films functionalised with silole groups

Keywords: sensor, silole, polymethylhydrosiloxane, film, nitroaromatic, explosive, hydrosilylation

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

INTRODUCTION

Chemical sensors for detection of traces of explosives, in particular nitroaromatic compounds, are of great current interest for purposes of public security and environmental protection. [START_REF] Mcquade | Conjugated polymer-based chemical sensors[END_REF][START_REF] Krausa | Vapor and Trace Detection of Explosives for Anti-terrorism Purposes[END_REF][START_REF] Thomas | Chemical sensors based on amplifying fluorescent conjugated polymers[END_REF] A variety of conjugated polymers have been used as sensors for nitroaromatics explosives detection [START_REF] Toal | Polymer sensors for nitroaromatic explosives detection[END_REF] including metallole-containing polymers. [START_REF] Sohn | Detection of nitroaromatic explosives based on photoluminescent polymers containing metalloles[END_REF][START_REF] Toal | Visual detection of trace nitroaromatic explosive residue using photoluminescent metallole-containing polymers[END_REF] The first metallole to be used was a polysilole, 7 polymers [START_REF] Sanchez | Efficient blue-emitting silafluorene-fluorene-conjugated copolymers: selective turn-off/turn-on detection of explosives[END_REF][START_REF] Sanchez | Catalytic hydrosilylation routes to divinylbenzene bridged silole and silafluorene polymers. Applications to surface imaging of explosive particulates[END_REF] and nanoparticles [START_REF] Toal | Luminescent oligo(tetraphenyl)silole nanoparticles as chemical sensors for aqueous TNT[END_REF] containing silole groups being of particular interest. Silole molecules and polymers exhibit aggregation-induced emission (AIE) caused by the restricted intramolecular rotations of the peripheral aromatic rings about the axes of the single bonds linked to the central silole cores. [START_REF] Liu | Aggregation-induced emission of silole molecules and polymers: fundamental and applications[END_REF][START_REF] Chen | Synthesis, light emission, nanoaggregation, and restricted intramolecular rotation of 1,1-substituted 2,3,4,5tetraphenylsiloles[END_REF] The emission is quenched by nitroaromatic compounds, the effect being enhanced by Lewis acid-base interactions between the silacycle and the nitroaromatic compound. [START_REF] Sanchez | Lewis acid-base interactions enhance explosives sensing in silacycle polymers[END_REF] However, polymer-based sensors made from linear uncrosslinked polymers usually suffer from the drawback of polymer leakage into the medium and ensuing shortened lifetime and inefficient analyses. We report here the development of a new family of fluorescent film sensors for which these disadvantages have been overcome, made from thin films of crosslinked resin covalently bonded to the substrate and containing a very low concentration of silole groups. They exhibit the AIE effect owing to restricted intramolecular rotation, [START_REF] Chen | Synthesis, light emission, nanoaggregation, and restricted intramolecular rotation of 1,1-substituted 2,3,4,5tetraphenylsiloles[END_REF] and show enhanced sensitivity to nitroaromatic analytes because of the very low concentration of silole groups. Thus, a new silole bearing an allyl group at silicon has been incorporated into previously-reported novel reactive polysiloxane coatings made from polymethylhydrosiloxane (PMHS) polymers crosslinked by the sol-gel process allowing subsequent functionalization by hydrosilylation of the SiH reactive groups. [START_REF] Thami | Functionalization of surface-grafted polymethylhydrosiloxane thin films with alkyl side chains[END_REF][START_REF] Nasr | Functionalization of polymethylhydrosiloxane gels with an allyl ureido benzocrown ether derivative: complexation properties[END_REF][START_REF] Thami | Tailoring of elastomeric grafted coating via sol-gel chemistry of crosslinked polymethylhydrosiloxane[END_REF][START_REF] Amro | Supported thin flexible polymethylhydrosiloxane permeable films functionalised with silole groups: new approach for detection of nitroaromatics[END_REF] The films can be used to test for nitroaromatics present not only in the vapour phase but also in many types of solvent because of the robust nature of the crosslinked network and covalent bonding to the substrate. They can be made in thicknesses ranging from 20 nm up to 1 μm. The silole groups are readily accessible, and the sensors can be regenerated by washing with solvents such as chloroform. The new pale yellow fluorophore 1-allyl-1-methyl-2,3,4,5-tetraphenylsilole (1) was synthesized in 55% yield by using Curtis's method [START_REF] Curtis | Synthesis and reactions of some functionally substituted sila-and germacyclopentadienes[END_REF] in two steps; (a) lithiation of tolane, followed by (b) reaction of the intermediate dilithiotetraphenylbutadiene with allylmethyldichorosilane (Scheme 1).

Scheme 1. Synthesis of 1-allyl-1-methyl-2,3,4,5-tetraphenylsilole (1). Reagents and conditions: i, Li shavings, THF, 12 h, room temp.; ii, allylmethyldichlorosilane, THF, 2 h at room temp., 5 h under reflux.

Preparation of crosslinked polymethylhydrosiloxane (PMHS) thin films

Crosslinked polymethylhydrosiloxane (PMHS) thin films of 5% crosslinking density were prepared by room temperature sol-gel polymerization of methyldiethoxysilane/triethoxysilane 95:5 (mol %) sol mixtures deposited by spin-coating on silicon wafer Si(100) or microscope glass slide substrates freshly activated with "piranha" solution. The substrates bearing PMHS thin films were then cured at 100 °C in an oven for 10 min. The thickness of the virgin PMHS films was found to be ca. 1 μm as measured by infrared spectroscopy from the absorbance of the Si-H peak at ca. 2167 cm -1 and the calibrated absorption coefficient.

Hydrosilylation of 1 by PMHS thin films and characterization of resulting silole-containing films

The hydrosilylation reaction between the allyl group of 1 and the PMHS Si-H function was performed in air by placing the virgin PMHS thin film/substrate samples in a toluene solution of 1 in the presence of Karstedt's catalyst for 18 h at 60°C with stirring. The samples were then removed from the reaction mixture, rinsed with toluene and chloroform to remove any physisorbed material, and dried in a stream of dinitrogen. Dioxygen acts as a co-catalyst in hydrosilylation reactions catalyzed by Karstedt's catalyst. [START_REF] Lewis | On the mechanism of metal colloid catalyzed hydrosilylation: proposed explanations for electronic effects and oxygen cocatalysis[END_REF] Hydrosilylation of 1 with triethoxysilane showed that the reaction is regiospecific at the allyl group.

Previous studies on hydrosilylation by PMHS have shown that the reaction goes essentially to completion. [START_REF] Thami | Functionalization of surface-grafted polymethylhydrosiloxane thin films with alkyl side chains[END_REF][START_REF] Nasr | Functionalization of polymethylhydrosiloxane gels with an allyl ureido benzocrown ether derivative: complexation properties[END_REF] Indeed, in this case too, no IR spectral evidence for any remaining unreacted silole allyl groups present in the thin films was observed. The degree of silole incorporation into the thin films was found to be 7-8% from the normalized IR absorbance ratio of the methylene group ν as (CH 2 ) antisymmetric stretch at ca. 2922 cm -1 (Fig. 1) and the ν(SiH) band at ca. 2167 cm -1 for the unreacted sample (virgin PMHS), all the methylene groups originating from the silole allyl groups. As expected, the total intensity of the methylene absorbance corresponded to three methylene groups per silole following complete hydrosilylation of 1 and covalent bonding into the PMHS network. The residual SiH function was determined to be ca. 15-17% from the IR spectra by measuring the total integrated absorbances of the ν(SiH) bands in the 2100-2300 cm -1 region for the reacted and unreacted samples (Fig. 1).

[Si]H To summarize, 15-17% of the SiH groups remained unreacted, 7-8% underwent hydrosilylation, and the remainder (ca. 75%) underwent reaction with water (present from air moisture) catalyzed by Karstedt's catalyst [START_REF] Lewis | On the mechanism of metal colloid catalyzed hydrosilylation: proposed explanations for electronic effects and oxygen cocatalysis[END_REF] (Scheme 2) as confirmed by the increase in the IR Si-O-Si stretch band at ca. 1100 cm -1 and the Si-OH band at ca. 3500 cm -1 observed after hydrosilylation of 1 with the PMHS films. The formation of additional Si-O-Si crosslinks serves to strengthen the film resistance.

Nitroaromatic sensor properties of silole 1 in chloroform solution

The ability of the new silole to act as a nitroaromatic sensor was first studied in solution. Fluorimetric analysis of a solution of 1 in chloroform (10 -5 M) containing increasing amounts of m-dinitrobenzene (Fig. 3

Nitroaromatic sensor properties in solution of PMHS thin films containing silole 1

Similar results were observed for a thin film of PMHS containing 1. The sample was immersed in a chloroform solution and increasing amounts of m-dinitrobenzene (Fig. 4) and picric acid (Fig. 5) were added. The emission spectra show that the quenching effect increases with the concentration of m-dinitrobenzene (Fig. 4) or picric acid (Fig. 5).

No corrections for inner filter effects or analyte absorption in the emission spectra were made since, firstly, re-absorption of emitted photons in the ultra-thin PMHS films can be neglected and, secondly, a front-face setup with an optical path of ca. 1 cm and extremely low analyte concentrations were used. In the case of the m-dinitrobenzene solution, the emission spectra did not change with time of immersion. However, after the sample had been immersed for 1 h in the picric acid solution, the emission intensity decreased markedly (cf. Fig. 5(a), the two measurements in the presence of 0.025 mM picric acid) consistent with some secondary reaction occurring between the silole groups and picric acid. This is reflected in the break exhibited by the Stern-Volmer plot (Fig. 5(b)). In the case of the m-dinitrobenzene analyte the quenching effect is found to be reversible. Simple washing of the detector film with chloroform regenerates the initial fluorescence peak with the same intensity and form (Fig. 6 (B)) as for the pristine film (Fig. 6 (A)). The same procedure of washing with chloroform the sensor film treated with picric acid gives rise to an emission spectrum of lower intensity and showing two peaks at 408 and 455 nm (Fig. 6 (C)). This behaviour is consistent with the formation of a new fluorescent product by reaction of the silole groups and picric acid. Indeed, with picric acid the quenching effect has been found previously to be partly irreversible in some cases. [START_REF] Sohn | Detection of TNT and picric acid on surfaces and in seawater by using photoluminescent polysiloles[END_REF][START_REF] He | A novel picric acid film sensor via combination of the surface enrichment effect of chitosan films and the aggregation-induced emission effect of siloles[END_REF] Figure 6. Emission spectra (λ excit. = 375 nm) of sample of PMHS containing 1: (A) pristine film, (B) after immersion in chloroform solution containing m-dinitrobenzene followed by rinsing with chloroform, and (C) after immersion in chloroform solution containing picric acid followed by rinsing with chloroform.

Nitroaromatic sensor properties in the vapour phase of PMHS thin films containing silole 1

The sample of the PMHS thin film containing silole 1 was placed in a closed container and the emission spectrum was measured (Fig. 7 (A)). Crystals of m-dinitrobenzene were then added and the container re-closed. The emission spectrum was measured after 1 min (Fig. 7 (B)). Almost instantaneous visible quenching was observed, the effect being reversible after ca. 1 h in ambient air.

EXPERIMENTAL

Preparation of PMHS thin films

Both precursors methyldiethoxysilane HSi(CH 3 )(OCH 2 CH 3 ) 2 (DH) and triethoxysilane HSi(OCH 2 CH 3 ) 3 (TH) were purchased from ABCR (Karlsruhe, Germany) and used as received. Water used for cleaning the substrates was obtained from a Milli-Q water purification apparatus (Millipore). Absolute ethanol for sol-gel synthesis was of synthesis grade purity. The catalyst trifluoromethanesulfonic acid CF 3 SO 3 H (Aldrich) was dissolved in absolute ethanol (1 M). Toluene used for thin film hydrosilylation was distilled before use. The platinum-divinyltetramethyldisiloxane complex in xylene (PC072) (platinum concentration ca. 0.1 M assuming 2.4% Pt in xylene), also known as Karstedt's catalyst, was purchased from ABCR.

Silicon wafers Si(100) or microscope glass slides cut into rectangular square strips of 2 × 2 cm 2 were used as substrates.

To bond covalently the PMHS thin films to native oxide silica wafers (thickness ∼2 nm), or to silica glass slides, the substrates were first cleaned and activated using the previously described procedure. [START_REF] Thami | Tailoring of elastomeric grafted coating via sol-gel chemistry of crosslinked polymethylhydrosiloxane[END_REF] The substrates were placed for 30 min in a hot (90°C) H 2 SO 4 /H 2 O 2 (70/30 v/v) solution ("piranha" solution) and then allowed to cool to room temperature. Caution! Piranha solution should be handled with extreme care. The clean substrates were then rinsed thoroughly with high-purity water, dried in a stream of dinitrogen and heated at 110°C in an oven for 20 min.

PMHS thin films of 5% crosslinking density were prepared by room temperature sol-gel polymerization of DH/TH 95:5 (mol %) sol mixtures deposited by spin-coating on freshly activated substrates using the previously described procedure [START_REF] Thami | Functionalization of surface-grafted polymethylhydrosiloxane thin films with alkyl side chains[END_REF][START_REF] Nasr | Functionalization of polymethylhydrosiloxane gels with an allyl ureido benzocrown ether derivative: complexation properties[END_REF] which is summarized as follows. Trifluoromethanesulfonic acid CF 3 SO 3 H (1M in absolute ethanol) was used as sol-gel catalyst (0.5 mmol/mol of monomers). The mixture of monomers DH/TH was polymerized at ca. 4 M concentration in EtOH (molar ratio [EtOH]/[Si] = 1), with 0.5 equiv. water (hydrolysis ratio

h = [H 2 O]/[SiOEt] = 0.5).
The resulting clear sol was allowed to age for 30 minutes with magnetic stirring before deposition by spin-coating. Subsequently, a fully crosslinked film was obtained by spin-coating the mixture under dinitrogen at 4000 rpm (spin acceleration 2000 rpm/s) the time of rotation being 30 s. The substrates with PMHS thin films were then cured at 100 °C in an oven for 10 min. The thickness of the PMHS film was about 1 μm as measured by infrared spectroscopy (see 3.4). 14

Synthesis of 1-allyl-1-methyl-2,3,4,5-tetraphenylsilole (1)

All the reagents were purchased from Acros. Tetrahydrofuran (THF) was distilled from sodium/benzophenone immediately before use. The 1 H, [START_REF] Sanchez | Lewis acid-base interactions enhance explosives sensing in silacycle polymers[END_REF] C and 29 Si NMR spectra were obtained on a Bruker Advance 200 DPX spectrometer, the FT-IR spectra on a Thermo Nicolet Avatar 320 spectrometer, the UV-visible absorption spectra on a Secomam Anthelie spectrometer and the mass spectra were determined on a Waters Q-tof instrument. Elemental analyses were determined with a Thermofinigane Flash EA 1112 apparatus. Photoluminescence (PL) studies were made with a SPEX Fluorolog 1681 0.22 m spectrometer.

Under dry argon, freshly cut lithium (177 mg, 25.3 mmol) shavings were added to a solution of diphenylacetylene (5 g, 28.0 mmol) in THF (25 cm 3 ). The mixture was stirred for 12 h at room temperature and the resulting THF solution of 1,4-dilithio-1,2,3,4-tetraphenylbutadiene was added dropwise to a solution of allylmethyldichlorosilane (1.55 cm 3 , 10.7 mmol) in THF (120 cm 3 ). The mixture was stirred for 2 h at room temperature and refluxed for 5 h. After being allowed to cool to room temperature, the mixture was filtered and the crude product was purified on a silica gel column using pentane/dichloromethane (8:2 by volume) as eluent. Product 1 (2.6 g) was isolated in 55% yield (based on allylmethyltrichlorosilane) as a yellow-white solid: mp 120-121

Incorporation of silole 1 into PMHS thin films by hydrosilylation

In a typical preparation, two samples grafted with a PMHS thin film (∼1 μm) were placed in the presence of air in a 10 mM solution of the silole 1 (24 mg; 0.055 mmol) and Karstedt's catalyst (4 μL) in toluene (25 cm 3 ). After the reaction mixture had been stirred for 18h at 60°C, the samples were removed, rinsed with toluene (twice) and chloroform (once) to remove any physisorbed material, and dried under a stream of dinitrogen.

Characterization of PMHS thin films

Infrared spectra of the PMHS layer were recorded on a Nexus FTIR spectrometer with the use of unmodified silicon wafer substrates as the background in the 400-4000 cm -1 range. The thickness (e) of the virgin PMHS thin films deposited on the glass or wafer substrate by spin-coating was measured by infrared spectroscopy from the absorbance of the Si-H peaks at ca. 2167 cm -1 : A 2167 = α SiH e where α SiH (0.27 μm -1 ) is the calibrated absorption coefficient. 14 A mean thickness of 1.23 ± 0.05 μm was found for four spin-coated samples.

To quantify the SiH conversion after hydrosilylation of the PMHS thin films, the disappearance of the strong Si-H stretching bands ν(SiH) of both DH and TH subunits was studied by measuring the total integrated absorbances in the 2100-2300 cm -1 region of the reacted and unreacted samples. The SiH residual percentage (% SiH) of ca. 15-17 % is calculated by dividing the integrated absorbance of the reacted samples with that measured before reaction (same sample).

Following PMHS hydrosilylation with the silole compound 1, the percentage of PMHS functionalization (% SiC) of ca.

7-8 % can be measured with good sensitivity from the strong absorption of the methylene group, ν as (CH 2 ) antisymmetric stretching, in the 2935-2915 cm -1 region for alkanes. [START_REF] Lin-Vien | The Handbook of Infrared and Raman Characteristic Frequencies of Organic Molecules[END_REF] For this calculation, the ν as (CH 2 ) absorption was previously calibrated for alkyl-functionalized PMHS thin films (∼1 μm) prepared by hydrosilylation with 1-akenes CH 2 =CH(CH 2 ) n- 2 CH 3 of various lengths (n = 5 to 17). [START_REF] Thami | Functionalization of surface-grafted polymethylhydrosiloxane thin films with alkyl side chains[END_REF][START_REF] Nasr | Functionalization of polymethylhydrosiloxane gels with an allyl ureido benzocrown ether derivative: complexation properties[END_REF] Following reaction of the SiH groups, the normalized absorbance ratio A CH 2 /A SiH increases with the number of methylene groups (n) in the hydrocarbon chain Si(CH 2 ) n CH 3 as follows:

SiC n A A SiH CH 2 × = 284
. 0

where SiC = 100% for complete addition of the alkene molecules to the SiH bonds as well as for the functionalization of the PMHS network with short alkyl sides chains.

In the case of the silole fonctionnalized PMHS, the above equations were applied assuming the number of methylene groups is n = 3 ; A CH 2 of the reacted silole samples was measured from the peak at ca. 2922 cm -1 ; A SiH was measured before the hydrosilylation reaction at ca. 2167 in the corresponding unreacted samples (virgin PMHS).

CONCLUSIONS

A new family of fluorescent highly sensitive crosslinked film sensors has been developed which does not suffer from commonly observed polymer leakage into the medium with ensuing shortened lifetime and inefficient analyses. The thin film sensors made from crosslinked PMHS polymers covalently bonded to the glass substrate contain a very low concentration of covalently bonded silole groups. They exhibit the AIE effect owing to restricted intramolecular rotation, and show enhanced sensitivity to nitroaromatic analytes because of the very low concentration of silole groups. The films can be used to test for nitroaromatics present not only in the vapour phase but also in many types of solvent because of the robust nature of the crosslinked network and covalent bonding to the substrate. They can be made in thicknesses ranging from 20 nm up to 1 m. The silole groups are readily accessible, and the sensors can be regenerated by washing with solvents such as chloroform.

Figure 1 .

 1 Figure 1. IR absorption spectra: PMHS film on glass slide (A) after (magnified x 10), and (B) before incorporation of 1 by hydrosilylation; (C) 1 in KBr.

Scheme 2 .

 2 Scheme 2. Reactions of PMHS (represented by [Si]-H) in the presence of Karstedt's catalyst and air: hydrosilylation of 1 and reaction with H 2 O.The UV/visible absorption and emission spectra of the thin films confirm the presence of silole groups showing a characteristic absorption band at ca. 370 nm assigned to the silole π-π* transition (Fig.2(a)) and an intense emission band at 485 nm (Fig.2(b)). The spectra remain unchanged after repeated washing of the samples with chloroform, thus confirming the covalent bonding of the silole groups to the PMHS matrix and ruling out physisorption. The silolecontaining PMHS films retain their fluorescent properties for at least 3 months in air, and the Si-H groups in PMHS gels are stable.[START_REF] Thami | Tailoring of elastomeric grafted coating via sol-gel chemistry of crosslinked polymethylhydrosiloxane[END_REF]

Figure 2 .

 2 Figure 2. (a) UV/visible absorption, and (b) emission spectra (λ excit. = 375 nm) of PMHS film containing 1.

  (a)) and picric acid (Fig.3(b)) showed the expected fluorescence quenching attributed to Lewis acid-base interactions between the silole silicon centres and the lone pairs of the nitro groups of the nitroaromatic analyte, providing a bridging bond through which electron transfer occurs from the excited state of the silole to the analyte.[START_REF] Sanchez | Lewis acid-base interactions enhance explosives sensing in silacycle polymers[END_REF]

Figure 3 .

 3 Figure 3. Decrease in emission intensity (λ excit. = 375 nm) of chloroform solution of 1 (10 -5 M) with increasing concentration of (a) m-dinitrobenzene, and (b) picric acid.

Figure 4 .

 4 Figure 4. (a) Emission spectra (λ excit. = 375 nm) and (b) Stern-Volmer plot for sample of PMHS containing 1 immersed in chloroform solution with increasing concentration of m-dinitrobenzene.

Figure 5 .

 5 Figure 5. (a) Emission spectra (λ excit. = 375 nm) and (b) Stern-Volmer plot for sample of PMHS containing 1 immersed in chloroform solution with increasing concentration of picric acid (a period of 1 h passed between the two measurements in the presence of 0.025 mM picric acid).

Figure 7 .

 7 Figure 7. Emission spectra (λ excit. = 375 nm) of sample of PMHS containing 1: (A) pristine film, (B) 1 min after immersion in m-dinitrobenzene vapour at ambient temperature.

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ACKNOWLEDGEMENTS

Financial support was received from the Agence Nationale de la Recherche and the CNRS. μ


Matei Razvan Georgescu
email: matei.georgescu@univ-rennes1.fr

Pache Protopopescu

Amina Meslem
email: amina.meslem@univ-rennes1.fr

Ilinca Nastase
email: ilinca.nastase@utcb.ro

Accumulation and spatial distribution of CO 2 in the astronaut's crew quarters on the International Space Station

Keywords: ISS ventilation, CO 2 accumulation in microgravity, Human breathing simulation, Breathing zone definition

In poorly ventilated confined spaces, assessing the accumulation of CO 2 in the breathing zone (BZ) is important evaluating human safety. The current study presents an experimental and numerical investigation of the CO 2 generation rate and spatial distribution in the crew quarters (CQ) of the International Space Station. In microgravity, density-difference based airflow is nonexistent, and CO 2 accumulates around the astronaut's head if the BZ is poorly or not at all ventilated. The aim is to study the breath's influence on CO 2 spatial distribution in order to circumscribe the region that needs to be ventilated in the CQ. An experimental setup was used to measure the CO 2 generation rate of several test subjects on Earth in a non-ventilated full-scale model of the CQ. The experimental CO 2 results were used to validate CFD simulations of the CQ with gravity, with a human model inside featuring a full respiratory cycle. The validated CFD model was then used without gravity for a CO 2 accumulation study. The respiratory cycle was analyzed in order to propose a rigorous definition of the BZ based on a frequency analysis of the breath. Results show that CO 2 concentrations in the identified BZ are greater in the absence of gravity compared to a similar situation with gravity. It is believed that the ventilation system presently in place in the CQ does not effectively ventilate this strategic area, therefore a personalized ventilation type solution should be studied in the future.

Introduction

The present study is part of a larger investigation concerning the evaluation of the internal environment on the International Space Station (ISS) crew quarters (CQ), where the astronauts sleep. The ISS internal environment has no supply of fresh air. The existing air is reconditioned, CO 2 is scrubbed and oxygen is regenerated by the Environmental Control and Life Support System [START_REF] Nastase | National Aeronautics and Space Administration HUMAN INTEGRATION DESIGN HANDBOOK[END_REF][START_REF] Bagdigian | International Space Station Environmental Control and Life Support System Mass and Crewtime Utilization In Comparison to a Long Duration Human Space Exploration Mission[END_REF]. In microgravity, without ventilation, exhaled CO 2 forms pockets due to the lack of natural convective flows. This problem is aggravated when the astronauts spend long periods of time in confined spaces, like the CQ. Despite the removal of CO 2 from the atmosphere, there have been reports of astronauts suffering from carbon dioxide intoxication after sleeping in the CQ [START_REF] Matty | Overview of Carbon Dioxide Control Issues During International Space Station/Space Shuttle Joint Docked Operations[END_REF][START_REF] Shiming | Influence of IMV on Space Station[END_REF][START_REF] Fairburn | Sleeping With the Stars' -The Design of a Personal Crew Quarter for the International Space Station[END_REF][START_REF] James | The headache of carbon dioxide exposures[END_REF][START_REF] Schlesinger | International Space Station Crew Quarters On-Orbit Performance and Sustaining Activities[END_REF]. This suggests that CO 2 accumulates in the CQ at a faster rate than the CO 2 scrubber is able to handle. The CO 2 accumulation and its spatial distribution in a confined space are the primary subjects of this paper, tailored to the CQ aboard the ISS but with potential applications for air quality control in other environments.

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

Standards for the built environment [START_REF] Standardization | [END_REF] specify that the CO 2 concentration should be between 400 and 1000 ppm over the outdoor level. For reference, at sea level the CO 2 concentration is around 400 ppm. Aboard the ISS, minimum ambient CO 2 concentrations are approximately 3000 ppm, but can reach values greater than 6500 ppm [START_REF] James | Crew Health and Performance Improvements with Reduced Carbon Dioxide Levels and the Resource Impact to Accomplish Those Reductions[END_REF]. The mean concentration is not reduced below 3000 ppm because the energy supply is limited. Studies to determine an acceptable upper limit which prevents CO 2 intoxication [START_REF] James | Crew Health and Performance Improvements with Reduced Carbon Dioxide Levels and the Resource Impact to Accomplish Those Reductions[END_REF][START_REF] Law | In-Flight Carbon Dioxide Exposures and Related Symptoms: Associations, Susceptibility and Operational Implications[END_REF] found that variable levels of tolerance to high CO 2 concentrations were developed by the astronauts. Recommendations were to keep the upper limit as low as possible for safety concerns. Identifying and ventilating the above-mentioned CO 2 pockets would be a good compromise.

Studies [START_REF] Son | Cfd Modeling of International Space Station and Visiting Spacecraft Ventilation : Evaluation of Design Solutions for Complex on-Orbit Operations[END_REF][START_REF] Son | Investigation of Airflow and Accumulation of Carbon Dioxide in the Service Module Crew Quarters[END_REF][START_REF] Son | Integrated Ventilation Modeling for Crew Quarter Airflow[END_REF][START_REF] Son | CFD analysis of node 1 ventilation and carbon dioxide transport for the maximum stowage configuration[END_REF][START_REF] Son | Computational Fluid Dynamics Ventilation Study for the Human Powered Centrifuge at the International Space Station[END_REF][START_REF] Smirnov | CFD modelling of cabin air ventilation in the international space station: A comparison of RANS and LES data with test measurements for the Columbus module[END_REF] show the importance of on-board ventilation and CO 2 control in the CQ. Extensive use of CFD was made for studying the ventilation in the ISS corridor adjacent to the CQ [START_REF] Son | Investigation of Airflow and Accumulation of Carbon Dioxide in the Service Module Crew Quarters[END_REF][START_REF] Son | Integrated Ventilation Modeling for Crew Quarter Airflow[END_REF][START_REF] Son | CFD analysis of node 1 ventilation and carbon dioxide transport for the maximum stowage configuration[END_REF][START_REF] Son | Computational Fluid Dynamics Ventilation Study for the Human Powered Centrifuge at the International Space Station[END_REF][START_REF] Smirnov | CFD modelling of cabin air ventilation in the international space station: A comparison of RANS and LES data with test measurements for the Columbus module[END_REF] in microgravity. Numerical investigations of the CO 2 accumulation in an older model of the CQ, during fan-failure were performed [START_REF] Standardization | [END_REF]. A human model generated CO 2 in the virtual CQ, exhaling a constant flow through the nose, calibrated after an astronaut's daily CO 2 generation rate. Important accumulations were found near the chest and mouth of the human model. The constant flow approach is correct in regards to the global mass balance of CO 2 in the CQ, but it does not consider the dynamics of the breathing process which might, influence the local distribution of CO 2 in the vicinity of the astronaut's head where the air is immediately inhaled by the astronaut, causing self-contamination. For ventilation strategies aimed at reducing CO 2 concentrations, information is required regarding CO 2 accumulation in the case of a realistic breathing cycle. To the author's best knowledge, no measurements exist of CO 2 accumulation in the CQ on the ISS.

Mazumdar and Chen [START_REF] Mazumdar | Influence of cabin conditions on placement and response of contaminant detection sensors in a commercial aircraft[END_REF] and Zhang and Chen [START_REF] Zhang | Identification of contaminant sources in enclosed spaces by a single sensor[END_REF], highlight the importance of pollutant accumulation in confined spaces and of evaluating air quality close to the pollutant source. When the breath is the pollutant source, the zone that characterizes it is designated BZ, for "Breathing Zone". The exposure of a subject, could be evaluated by measuring pollutant concentration in the BZ (either self-generated, as in our case, or from a different source).

The geometric extents of the BZ are a matter of debate. Haselton et al. [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] performed breathing visualizations through the nose using an artificial lung connected to a model of the human face. They concluded that the zone of inhalation can be represented as a hemisphere of radius 6.2 cm around the nose (~500 cm 3 in volume), while the exhalation can be represented by a 23° cone extending approximately 20 cm away from the nose (~350 cm 3 in volume). In studies concerning air quality in close proximity to humans, Brohus [START_REF] Brohus | Measurement of Personal Exposure Using a Breathing Thermal Manikin[END_REF] reports that the BZ is habitually considered as a hemisphere of radius 30 cm (a volume of 56550 cm 3 ) centered on the human nose, drawing attention to the fact that the pollutant concentration is not constant in this sphere contrary to previous beliefs. This definition was adopted by the American Industrial Hygiene Association [START_REF] Dinardi | The Occupational Environment: Its Evaluation and Control and Management[END_REF], the European Committee for Standardization (EN 15251 [START_REF]EN 15251 CEN/TC 156 Indoor environmental input parameters for design and assessment of energy performance of buildings-addressing indoor air quality, thermal environment, lighting and acoustics[END_REF]), the U.S Dept. of Energy Guidelines [START_REF][END_REF] and recently EN ISO 18158 [24]. Melikov [START_REF] Melikov | Personalized ventilation: Evaluation of different air terminal devices[END_REF] recalls that this definition is inaccurate. Liden et al. [START_REF] Lidén | A headset-mounted mini sampler for measuring exposure to welding aerosol in the breathing zone[END_REF] states that the 30 cm hemisphere is a technical definition based on the unlikely assumption of uniformity of concentration within this volume. Pantelic et al. [START_REF] Pantelic | Personal CO2 cloud: laboratory measurements of metabolic CO2 inhalation zone concentration and dispersion in a typical office desk setting[END_REF] performed breathing measurements with human subjects in a zone of 30x60x50 cm (LxWxH), equivalent to a volume of 90000 cm 3 . Air sampled in front of the nose led to the conclusion that there is significant variance in pollutant concentration between different points even for a single subject. Melikov [START_REF] Melikov | Personalized Ventilation[END_REF], citing Haselton et al. [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] states that there is little difference between inhaling through the nose or through the mouth and subsequently states that while velocities can be high (without specifying a value) at the nose/mouth, they fall off rapidly after 2-3 cm. He further states that the majority of the inspired air comes from the convective boundary layer surrounding the body. The question remains open in the absence of gravity, where the convective boundary layer is absent.

Rim et al. [START_REF] Rim | The influence of chemical interactions at the human surface on breathing zone levels of reactants and products[END_REF] considered the BZ a volume of 500 cm 3 of unspecified geometry (likely parallelepipedal), with one of its corners centered on the nose tip. Rim et al. [START_REF] Rim | The influence of chemical interactions at the human surface on breathing zone levels of reactants and products[END_REF] state, as Melikov [START_REF] Melikov | Personalized Ventilation[END_REF] previously did, that inhaled air mostly comes from the thermal boundary layer of the human body. Marr et al. [START_REF] Marr | Anisotropy in the breathing zone of a thermal manikin[END_REF] performed stereo PIV measurements in the breathing flow from the mouth, covering a rectangular region of 30x20 cm (HxL) in the median plane in front of the nose, tangential to the tip of the nose. Chen [START_REF] Chen | Differentiating between direct and indirect exposure to exhaled particles in indoor environments with mechanical ventilation systems[END_REF], states that the breathing zone is considered to be a cube with a 30 cm length (27000 cm 3 ) positioned with its corner centered on the nose. Recently Hweij et al. [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF] and Assaad et al. [START_REF] Assaad | Mixing ventilation coupled with personalized sinusoidal ventilation: Optimal frequency and flow rate for acceptable air quality[END_REF][START_REF] Assaad | Effectiveness of intermittent personalized ventilation in protecting occupant from indoor particles[END_REF][START_REF] Katramiz | The effect of human breathing on the effectiveness of intermittent personalized ventilation coupled with mixing ventilation[END_REF] define the BZ as a sphere with a 2 cm diameter (a volume of 4.2 cm 3 ) situated 2.5 cm away from the nose, considering it the source of inhaled air.

Certain aspects are consistent throughout most of the studies: (1) the concentration is not uniform in the zone commonly designated by BZ when considering a large volume [START_REF] Brohus | Measurement of Personal Exposure Using a Breathing Thermal Manikin[END_REF][START_REF]EN 15251 CEN/TC 156 Indoor environmental input parameters for design and assessment of energy performance of buildings-addressing indoor air quality, thermal environment, lighting and acoustics[END_REF][START_REF][END_REF][24][START_REF] Pantelic | Personal CO2 cloud: laboratory measurements of metabolic CO2 inhalation zone concentration and dispersion in a typical office desk setting[END_REF][START_REF] Chen | Differentiating between direct and indirect exposure to exhaled particles in indoor environments with mechanical ventilation systems[END_REF]; (2) the inhalation zone from which the air is drawn, considered as being more relevant for a definition of the BZ following the concept of uniformity of concentration, is of small dimensions with a volume in the 4.2 cm 3 [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF] to 500 cm 3 [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF][START_REF] Rim | The influence of chemical interactions at the human surface on breathing zone levels of reactants and products[END_REF] range, potentially varying between individuals. All the definitions of BZ or of "Inhalation zone", which are given in the literature deal with on Earth contamination problems.

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

Concerning our primary goal, the identification of the spatial distribution of exhaled CO 2 in the CQ, more precisely in the breathing zone, in connection with the breath's dynamics, we have the opportunity to define the breathing zone based on the dynamics of human respiratory cycles. The study was performed in a confined space in the absence of ventilation. The CO 2 accumulation was measured experimentally on Earth in a full-scale mockup of the CQ, and the resulting data were used to validate a numerical model. The validated numerical model was used to study the same phenomena in microgravity. The objective is (1) to understand the spatial distribution of CO 2 in the ISS CQ and (2) to investigate the geometric extents of the BZ with and without gravity. The BZ obtained with gravity will be compared to the numerous available definitions. The BZ without gravity will aid in reaching a clearer understanding of the possible deficiencies of the current ventilation system in the CQ, and to circumscribe the area that needs to be ventilated for the improvement of air quality in the astronaut's CQ.

Experimental Setup and Procedure

Experimental setup

A replica of the CQ was built for this study (Figure 1 a). The dimensions of the CQ and its ventilation system were extracted from its design documents [START_REF] Fairburn | Sleeping With the Stars' -The Design of a Personal Crew Quarter for the International Space Station[END_REF][START_REF] Broyan | International Space Station USOS Crew Quarters Development[END_REF][START_REF] Broyan | International Space Station Crew Quarters Ventilation and Acoustic Design Implementation[END_REF], and the dimensions of the standard racks on the ISS [START_REF] Mazumdar | Influence of cabin conditions on placement and response of contaminant detection sensors in a commercial aircraft[END_REF]. The plywood walls were covered with layers of the same materials used as on the ISS for acoustic and radiation isolation purposes (NOMEX and Kevlar [START_REF] Zhang | Identification of contaminant sources in enclosed spaces by a single sensor[END_REF]).

Three NDIR CO 2 sensors (C1-C3), with a measurement range of 0-10000 ppm and a precision of ±50 ppm ±3% of reading with signal noise levels below 10 ppm, were installed inside the CQ model at different heights (Figure 1 b-e). The interior volume of the CQ is equal to 2.4 m 3 . Each sensor was affected to one third of the total volume. Sensor (C1) is situated in the middle area of the model (Figure 1 b,c) at a height around the torso of the test subject, sensor (C2) was placed in the upper region of the model (Figure 1 b,d) and sensor (C3) was placed in the lower region (Figure 1 b, e). A fourth CO 2 sensor (C4) was installed outside adjacent to the CQ (Figure 2 a) to monitor exterior CO 2 levels.

Eight thermocouples were installed operating between -20 ÷ 60°C with an accuracy of ± 0.4°C between -20 ÷ 0°C and ± 0.1°C between 0÷60°C meant to verify the stability of the environment. Four thermocouples measured air temperatures (AT1-AT4) at the same positions as the CO 2 sensors (Figure 1 b-d). Another four measured interior wall temperatures (WT1-WT4) (Figure 2 b). One relative humidity sensor (RH1), with a range of 5÷98% RH with an accuracy of ±2% RH, was also placed at the same position as C1 (Figure 1 b andc), the closest position to the human head The CQ replica was installed in a laboratory room where the air temperature, relative humidity and the CO 2 level were monitored. The average air temperature in the room was stable, at a value of 27°C with a standard deviation of ±1°C for all measurements. The relative humidity was 65% and the CO 2 level was found to be about 900 ppm. The indoor environment of the CQ model was at thermal equilibrium prior to testing. At the beginning of each test, conditions inside the CQ were the same as outside the CQ.

Experimental Procedure

A sample of 13 subjects was selected with ages in the 22-50 years interval, heights in the 1.65-1.89 m interval and weights in the 65-110 kg interval, 10 of them were males and 3 of them were females. This meets the recommendations of standard ISO 61010 [START_REF][END_REF], whereby a minimum of 8 subjects is needed for any sort of statistical evaluation of human-dependent phenomena.

Measurement time was limited to 15 minutes for health and safety concerns, with the subject inside the CQ model, the ventilation system deactivated and all openings sealed. Subjects were seated in a resting position, facing the wall featuring sensor WT4, on a modified chair, simulating the neutral posture of the body in microgravity. The subjects' feet did not touch the ground, similar to that of the human body, floating in microgravity. Subjects were instructed to count their number of breaths over a minute, 3 times during the test and to behave as they would normally while sitting at rest.

Prior to the tests, the subjects did not engage in significant physical activity and were kept for a period of about 10-20 minutes in the room where the CQ was placed, to ensure thermal acclimatization. Once the experimental procedure started, the CO 2 concentrations were recorded with a frequency of 0.5 Hz, while the temperature and relative humidity were logged with a frequency of 0.066 Hz. Over each of the 13 tests, exterior CO 2 levels measured by sensor C4 (adjacent to the CQ) remained constant, while interior CO 2 levels increased, indicating that no significant amount of CO 2 leaked from the CQ model. At the start of the tests, average wall and air temperatures were around 27°C, and the relative humidity was around 65%. At the end of the 15-minute testing period, both wall and air temperature sensors showed, on average, increases of about 1°C, and RH had risen to 70%.

Since the volume of the CQ is small (2.4 m 3 ) and the general ventilation system (Figure 2 b) is stopped during the experimental tests, the concentration measured in the sub-volume affected to each CO 2 sensor (C1, C2, C3) should reasonably approximate the average over that volume. The concentrations measured will be used to validate the average concentration levels in the numerical model, in the three respective sub-volumes. The method is A c c e p t e d M a n u s c r i p t considered acceptable since the sensors measure CO 2 dispersion by natural convective mixing and diffusion while not directly influenced by the breath. The sensors were placed outside the area located in front of the test subject's head, to avoid the breath's influence.

Numerical Model and Boundary Conditions

The numerical model of the CQ (Figure 2) has a human model inside, resting in the neutral position of the body in microgravity, placed at the same height as the test subjects were seated during the experiments. Most of the subjects had heights around 1.80 m and the average value of all subjects' height was 1.79 m. The human model -if placed in straight position -has a height of 1.80 m. Its head features two nostrils, the inlets through which the realistic breathing process will occur.

The numerical grid has approximately 6 million tetrahedral elements with an average skewness of 0.22 and a wall y + ≈ 1 for compatibility with a wide range of RANS turbulence models [START_REF] Bode | Flow and wall shear rate analysis for a cruciform jet impacting on a plate at short distance[END_REF]. Five layers were created near the walls as shown in Figure 3. The darker regions represent a denser mesh around walls, areas with fine details such as the hands and around the nostril inlets (Figure 3 b,c).

Figure 3 Mesh in the median plane of the human model (a), and details of the human head (b) and the nostrils (c).

The nostril's dimensions and their spacing were kept to realistic values, but because of the model design, their orientation is closer to parallel than previous literature reports [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF][START_REF] Gupta | Characterizing exhaled airflow from breathing and talking[END_REF].

The human breath is generally characterized by the volume of air that enters or exits the lungs with each breath termed Tidal Volume (V t ) [START_REF] John | Guyton and Hall Textbook of Medical Physiology[END_REF], and the number of breaths over a minute (b f ). In emergency situations [START_REF] O'brien | Inaccuracies in calculating predicted body weight and its impact on safe ventilator settings[END_REF] V t can be estimated by the individual's body weight and sex. The Pulmonary Ventilation Rate or Minute Volume (MV) [l/min] which represents the volume of air exhaled over one minute [START_REF] Adams | Measurement of Breathing Rate and Volume in Routinely Performed Daily Activities[END_REF], is calculated as the product of V t and b f .

In our study, the breathing frequency is 14.7 breaths/minute (0.245 Hz), averaged over the 13 subjects, with an estimated [START_REF] O'brien | Inaccuracies in calculating predicted body weight and its impact on safe ventilator settings[END_REF] average tidal volume of 582 ml. MV (equivalent to exhalation/inhalation flow rates) can be computed as 𝑀𝑀𝑀𝑀 = 𝑄𝑄 𝐸𝐸𝑥𝑥ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑄𝑄 𝐼𝐼𝐼𝐼ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑀𝑀 𝑡𝑡 * 𝑓𝑓 [𝑚𝑚 3 /𝑠𝑠] and used in determining the CO 2 generation rate, by subtracting the volumetric concentration of CO 2 in the inhaled flow (0.04%) from the concentration of the exhaled flow (4%) as follows:

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

𝐶𝐶𝐶𝐶 2 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 = (𝑄𝑄 𝐸𝐸𝑥𝑥ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 • 0.04 -𝑄𝑄 𝐼𝐼𝐼𝐼ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 • 0.0004) �𝑚𝑚 𝐶𝐶𝐶𝐶 2 3 /𝑠𝑠� (1)
The result of Equation ( 1) multiplied by the test duration (15 min) falls within 5% of the overall CO 2 accumulation in the CQ after the experimental period giving confidence in the estimated value of V t .

V t, b f , MV and Exhalation/Inhalation velocities were extracted from several studies of the human breath [START_REF] Bjørn | Dispersal of exhaled air and personal exposure in displacement ventilated rooms[END_REF][START_REF] Qian | Dispersion of exhaled droplet nuclei in a two-bed hospital ward with three different ventilation systems[END_REF][START_REF] Yoo | Assessment of transient inhalation exposure using in silico human model integrated with PBPK-CFD hybrid analysis[END_REF][START_REF] Awbi | Ventilation of Buildings[END_REF][START_REF] Yao | Experimental study on flow behavior of breathing activity produced by a thermal manikin[END_REF] and of the cross-infection risk in the built environment [START_REF] Olmedo | Distribution of exhaled contaminants and personal exposure in a room using three different air distribution strategies[END_REF][START_REF] Olmedo | The risk of airborne cross-infection in a room with vertical low-velocity ventilation[END_REF][START_REF] Cao | Protected zone ventilation and reduced A c c e p t e d M a n u s c r i p t personal exposure to airborne cross-infection[END_REF][START_REF] Liu | Short-range airborne transmission of expiratory droplets between two people[END_REF][START_REF] Berlanga | Influence of the geometry of the airways on the characterization of exhalation flows. Comparison between two different airway complexity levels performing two different breathing functions[END_REF][START_REF] Cheng | Experimental study of the interaction between thermal plumes and human breathing in an undisturbed indoor environment[END_REF][START_REF] Xu | Measuring the exhaled breath of a manikin and human subjects[END_REF][START_REF] Zhang | Quantify impacted scope of human expired air under different head postures and varying exhalation rates[END_REF][START_REF]ASHRAE Handbook -Fundamentals[END_REF], for comparison with the present study in Table 1. The peak velocity at the breathing orifice is also given. In our study MV is approximately 8.5 l/min, and the peak exhalation/inhalation velocity is calculated at approximately 5.5 m/s (Table 1). V t is almost equal to the average of the above studies, while the b f , MV and velocity values fall in the ranges of the literature while slightly surpassing the average values.

In our CFD model, a breathing function was implemented, describing the breath through a sine function [START_REF] Xu | Measuring the exhaled breath of a manikin and human subjects[END_REF] as defined in Equation ( 2). This equation was determined based on 𝑀𝑀 𝑡𝑡 = 582 𝑚𝑚𝑚𝑚, 𝑓𝑓 = 0.245 𝐻𝐻𝐻𝐻 and the surface of the nostrils in our model

𝑆𝑆 = 0.8 [𝑐𝑐𝑚𝑚 2 ]. 𝑢𝑢 = 𝑢𝑢 𝑚𝑚𝑎𝑎𝑥𝑥 • 𝑠𝑠𝑔𝑔𝑔𝑔(2𝜋𝜋𝑓𝑓𝑔𝑔) = 5.49 • sin(2𝜋𝜋 • 0.245 • 𝑔𝑔) [𝑚𝑚/𝑠𝑠] (2)
In Equation ( 2) 𝑢𝑢 [m/s] is the inlet velocity, 𝑢𝑢 𝑚𝑚𝑎𝑎𝑥𝑥 [m/s] is the maximum velocity when sin =1, 𝑓𝑓 [Hz] is the breathing frequency and 𝑔𝑔 [s] is the time. The sine function ensures both positive (exhaled) and negative (inhaled) airflow at the nostrils.

Our study requires a turbulence model (the nose's inlet Reynolds number is Re=3600 based on the peak exhalation velocity and the equivalent diameter of the two nostrils), a species transport model and an energy model for the heat transfer. After testing several turbulence models, the realizable k-ε model was chosen. In previous comparisons of turbulence models for the ventilation of the ISS Node 2 corridor, Smirnov et al. [START_REF] Smirnov | CFD modelling of cabin air ventilation in the international space station: A comparison of RANS and LES data with test measurements for the Columbus module[END_REF] found that the standard k-ε model offered acceptable results when compared to LES models, being adequate for studying the ISS environment. Enhanced wall functions were used for our study to ensure compatibility wall y + values close to 1 [START_REF] Bode | Flow and wall shear rate analysis for a cruciform jet impacting on a plate at short distance[END_REF],

addressing the limitations caused by the logarithmic functions describing the viscous sublayer in k-ε models. Although the sine-driven flow regime changes with the variable velocity, going from turbulent through transient and eventually to A c c e p t e d M a n u s c r i p t laminar domains as it passes from the positive part of the sine function to the negative, previous studies of transient breathing functions [START_REF] Katramiz | The effect of human breathing on the effectiveness of intermittent personalized ventilation coupled with mixing ventilation[END_REF] have obtained acceptable results using k-ε turbulence models.

A transient simulation was performed for a period of 60 s, with a time step of t=0.05 s, recording data at 0.1 s intervals. Each full breathing cycle lasts around 4 s (80 time-steps per cycle). The boundary conditions are presented in Table 2 and Table 3.

Table 2 shows the temperature and composition of the air inside the CQ and of the breath. Air was defined as a mixture of N 2 , O 2 , CO 2 and H 2 O (vapors) volume fractions [m 3 component /m 3 mixture ]. O 2 and CO 2 volume fractions in the ambient air are equal to the normal air composition on Earth -21% O 2 and 0.04% CO 2 (equivalent to 400 ppm CO 2 ). H 2 O volume fraction was chosen so that the RH at the start of the simulation would be equal to 65% as measured in the experimental study. The N 2 volume fraction is automatically computed so the sum of all volume fractions equals unity. Ambient air temperature was set at 27°C (the initial value of the experimental study). The CO 2 concentration of 400 ppm is not equal to that of the experimental measurements, because of the assumptions made in Equation ( 1). This will not be a problem, since the objective is the study of accumulation and both experimental and numerical CO 2 curves will have their initial value subtracted so that they start from 0.

During exhalation O 2 and CO 2 volume fractions were set to their habitual values in the exhaled air [START_REF] John | Guyton and Hall Textbook of Medical Physiology[END_REF], 15% O 2 and 4% CO 2 (Table 2). The H 2 O volume fraction was chosen so that RH would reach 100% as stated in the medical literature [START_REF] John | Guyton and Hall Textbook of Medical Physiology[END_REF] and supported by other studies concerning the simulation of the breath [START_REF] Bjørn | Dispersal of exhaled air and personal exposure in displacement ventilated rooms[END_REF], [START_REF] Zhang | Quantify impacted scope of human expired air under different head postures and varying exhalation rates[END_REF], [START_REF] Liu | Short-range airborne transmission of expiratory droplets between two people[END_REF]. Air temperature was set to 36°C, the same temperature as the human head. Nostril velocity is governed by Equation ( 2). During the simulation, ambient parameters change, and air is inhaled at ambient temperature and gas concentrations. This differs from the assumptions of Equation ( 1), but its effect on exhaled CO 2 concentration is not felt over short periods of time [START_REF] John | Guyton and Hall Textbook of Medical Physiology[END_REF].

The wall temperature of the CQ is 27°C (Table 3) as at the start of the experimental study, the temperatures on the different human body parts have been selected from ASHRAE's recommendations [START_REF]ASHRAE Handbook -Fundamentals[END_REF] for the skin temperatures of an average human. It was not possible to measure the skin temperature of the test subjects for fear of inducing stress and potentially altering the CO 2 generation rate. The Coupled pressure-velocity algorithm was used, with a second-degree discretization scheme. Convergence criteria were set to reach the order of e-6 for all equations. Satisfactory convergence was reached upon the plateauing of the residuals after 50 iterations. Convergence was monitored by the mass flow rate on the inlet nostrils, the CO 2 volume fraction variation on the nostrils and in the CQ overall.

Two numerical simulations were performed, one reproducing the experimental conditions (𝑔𝑔 = 9.81 𝑚𝑚/𝑠𝑠 2 ) and another identical one with 𝑔𝑔 = 0 𝑚𝑚/𝑠𝑠 2 to reproduce microgravity conditions. The simulation without gravity was not meant to evaluate the CO 2 concentration at the end of an astronauts' sleeping period in the CQ, but to highlight the regions of CO 2 accumulation due to their breath.

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

Results and Discussion

Analysis of the numerical carbon dioxide accumulation in the CQ with and without gravity

CO 2 accumulation inside the CQ during experimental observation for all test subjects is given in Figure 4 a 1 -c 1 . A zoom is given for the first minute of observation in Figure 4 a 2 -c 2 .The initial CO 2 concentration [mg/m 3 ] was extracted from each measured concentration so that all curves start from 0. This result was multiplied by the volume affected to each sensor in order to obtain the quantity of CO 2 [mg] at the initial time 𝑔𝑔 0 , named 𝐶𝐶𝐶𝐶 2 (𝑔𝑔 0 ) [mg].

The difference between the quantity of CO 2 [mg] at time t and the same quantity at the initial time (𝑔𝑔 0 ) was termed 𝐶𝐶𝐶𝐶 2 𝑔𝑔𝑐𝑐𝑐𝑐𝑢𝑢𝑚𝑚𝑢𝑢𝑚𝑚𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 (Equation 3).

𝐶𝐶𝐶𝐶 2 𝑔𝑔𝑐𝑐𝑐𝑐𝑢𝑢𝑚𝑚𝑢𝑢𝑚𝑚𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 (𝑔𝑔) = 𝐶𝐶𝐶𝐶 2 (𝑔𝑔) -𝐶𝐶𝐶𝐶 2 (𝑔𝑔 0 ) [𝑚𝑚𝑔𝑔] (3)
The continuous black line on the graph (Figure 4 a 1,2 -c 1,2 ), corresponds to the best fit of 𝐶𝐶𝐶𝐶 2 𝑔𝑔𝑐𝑐𝑐𝑐𝑢𝑢𝑚𝑚𝑢𝑢𝑚𝑚𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 over all the points measured by each sensor for the 13 subjects, during the 15-minute duration of the test. The good regression coefficients attest to the linearity of the CO 2 accumulation phenomenon, as expected in the case of breathing inside a room without ventilation [START_REF] Awbi | Ventilation of Buildings[END_REF].

The human in our numerical model is static unlike the test subjects making punctual comparisons difficult. Consequently, for the numerical validation it was decided to affect the three sensors to three roughly equal fractions of the total CQ volume: one corresponding to the top region for C1, one to the middle for C2, and one to the bottom for C3. Hence, C1, C2 and C3 will represent either sensors or their corresponding volumes. For the three volumes, numerical CO 2 accumulation with gravity is in agreement with the experimental data (Figure 4 d-f). The CO 2 has a sharper slope at sensor C1 because the sensor's affected volume is below head level in the direction of the exhaled CO 2 . The undulations visible on the numerical curves relative to volumes C1 and C2 are imprints of the breathing cycle upon the CO 2 accumulation curves. The low time resolution of the CO 2 sensors used in the experiments does not capture such undulations. The curve relative to volume C3, the furthest from the breathing zone, does not show any undulation. The influence of the breathing cycle in Figure 4 d has a slight phase delay from what is seen in Figure 4 e, because the nose is situated in the volume fraction attributed to sensor C2 where the influence of the breath is sensed immediately.

Numerical results without gravity have a similar ascending tendency (Figure 4 d-f). Without gravity, C1 presents no significant difference relative to the case with gravity (Figure 4 d). Without gravity, C2 (Figure 4 e) presents a 40% deficit of CO 2 at t=60 s compared to the case with gravity (caused by the absence of natural convective flows). The exhaled CO 2 is driven solely by the momentum of the breath, directing it towards the bottom of the CQ. At C3 (Figure 4 f), the case without gravity presents a surplus of CO 2 accumulation. The ≈100 mg surplus found at t=60 s in C3 is quantitatively identical to the deficit present around C2.

The numerical CO 2 accumulation in the total volume of the CQ is almost identical with and without gravity (0.1% difference). The difference between numerical and experimental CO 2 accumulation is around 6% in favor of the experiment, considered acceptable. 4 presents average temperatures over the C1-C3 volumes for the numerical simulation compared to experimental sensors AT1-AT3 at t 0 and t=60 s. Over this interval, temperatures for AT1 rose with 0.1°C in both the experimental and the numerical cases, while for AT2 they increased by 0.3°C in the experimental case and 0.7°C in the numerical simulation. AT3 shows no change in both experimental and numerical cases. Average wall temperatures experimentally recorded by sensors WT1-WT4 were 27°C showing changes ≤0.1°C over 60 s. This is within their accuracy range (±0.1°C between 0°C and 60°C) and were thus considered constant in the timeframe of the CFD simulation.

RH values in the experimental measurements increased on average by 0.7% for the 13 subjects over 60 seconds. This value is lower than the accuracy of the sensor (±2%), thus for the 60-second time interval used in this study it is considered to remain constant. The numerical model shows a low increase of 0.1% in RH after 60 seconds. Given the agreement between the numerical and the experimental results with gravity, the numerical model was considered to be validated, giving confidence in the numerical results obtained without gravity aimed at studying microgravitational effects on the spatial distribution of CO 2 in the CQ.

Velocity fields at the exhalation's peak in the breathing cycle are given in Figure 5 a1, a2 for cases with and without gravity. When gravitational acceleration is present (Figure 5 a1), the thermal plume of the human body can be observed. In the convective boundary layer around a simulated human at 5 cm in front of the neck, chest, and upper legs, Cheng et al. [START_REF] Cheng | Experimental study of the interaction between thermal plumes and human breathing in an undisturbed indoor environment[END_REF] found values in the range of 0.05 m/s-0.12 m/s, which compare well with our results. In Figure 5 a1 the plume is seen interacting with the breathing jet in its low velocity top region, producing a recirculation in the top of the CQ. Without gravitational acceleration (Figure 5 a2), the breathing jet behaves similarly to an inclined impacting jet, reaching the opposite wall unimpeded and dispersing upon impact. The spatial distribution of CO 2 is closely related to the velocity fields (Figure 5 b1, b2). CO 2 preferentially accumulates in the upper regions of the CQ in the case with gravity (Figure 5

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

A direct comparison of the cases with and without gravity is given by the difference ΔCO 2 (Figure 6) between the 𝐶𝐶𝐶𝐶 2 𝑐𝑐𝑔𝑔𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [ppm] distributions with and without gravity respectively. The resulting fields are plotted at four key instants of the breathing cycle. Positive values of ΔCO 2 indicate higher concentrations without gravity than with gravity, and the corresponding regions are correlated to the trajectory of the breathing jet. The negative zones could be roughly associated with zones of low velocity where buoyancy plays a role in the airflow, as per the case with gravity. Absolute ΔCO 2 levels in the breathing flow are variable during the breathing cycle, high values are recorded during the exhalation phase (Figure 6,a,b) and low values during the inhalation phase (Figure 6,c,d). Regions far away from the nose do not show significant changes of ΔCO 2 during the breathing cycle. The authors' investigation of the general ventilation system of the CQ (not detailed for brevity) indicates that CO 2 accumulates in poorly ventilated regions where air stagnates. This will be detailed in future research. Currently the focus is on a precise definition of the BZ to be targeted by future ventilation solutions.

Dynamic analysis of the breathing flow

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

The numerical breathing flow, obtained with gravity, is compared to the experimental data of Yao et al. [START_REF] Yao | Experimental study on flow behavior of breathing activity produced by a thermal manikin[END_REF], where a manikin breathed through a circular orifice (the mouth), 12 mm in diameter, generating a single round jet. To our knowledge, there is no similar experimental data in the literature for breathing through the nostrils. In our case, each elliptic nostril has an equivalent diameter d e =7 mm. The equivalent diameter of the two nostrils is D e =11 mm (close to study [START_REF] Yao | Experimental study on flow behavior of breathing activity produced by a thermal manikin[END_REF]). While d e would be relevant for analyzing the interaction of the near field of nostril jets, D e is relevant for the analysis of the far field, where the flow behaves as a round jet coming from a single round orifice of diameter D e . It is possible to compare our numerical breathing flow to that of [START_REF] Yao | Experimental study on flow behavior of breathing activity produced by a thermal manikin[END_REF] The velocity fall-off (3 cm from the nostrils) considered by Melikov [START_REF] Melikov | Personalized Ventilation[END_REF] is represented by a vertical dashed line in Figure 8 a,b. It is situated immediately after the position where W B c begins to decrease on the peak exhalation velocity curve. The peak inhalation velocity drops to near 0 after the 3 cm limit.

The BZ as defined by Hweij et al. [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF] (a 1 cm radius sphere, 2.5 cm in front of the nose) is represented in Figure 8 a, b by a pink line. The exhalation zone (a 23° angle cone extending up to 20 cm, represented with a red line) and the inhalation zone (a 6.2 cm radius hemisphere represented with a blue line) of Haselton et al. [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] were A c c e p t e d M a n u s c r i p t superposed as well. The intersection between the exhalation cone and the inhalation hemisphere of Haselton et al. [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] (the hatched zone in Figure 8 a,b), corresponding to the zone where the exhaled air is rebreathed, compares well with the BZ of Hweij et al. [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF]. The 30 cm hemisphere representing the BZ according to Brohus (represented with a black dotted line) [START_REF] Brohus | Measurement of Personal Exposure Using a Breathing Thermal Manikin[END_REF] With the many different definitions of the BZ identified above we wanted to check if the entire sine dynamics of breathing (as opposed to instants in time) could be used to obtain a rigorous definition of the BZ, with and without gravity.

Our approach studies the Fast Fourier Transforms (FFTs) of the main velocity component of the breathing flow W B in the amplitude-frequency domain. Taking the FFTs of the corresponding velocity in a spatial point over time, if a peak is found at the breathing frequency (𝑓𝑓 0 = 0.245 𝐻𝐻𝐻𝐻) or at a multiple of this frequency, that point is considered sensitive to the breathing jet.

Two fixed planes were considered for this analysis: plane BP already defined in Figure 7 a and the vertical median plane MP passing through the middle of the head (Figure 9 The dotted black zone, contiguous to the yellow one, influenced by the half breathing cycle, considered as the BZ, takes a diamond-like shape, extending up to 10 cm in front of the nose with a width between 2 cm and 2.5 cm (~50 cm 3 in volume). In plane BP (Figure 12 a) differences along the X B axis between the cases with and without gravity, are less than 0.1 mm. In MP (Figure 12 b) along Y B axis there is a small difference (around 3 mm) between the delimitation of the zone with and without gravity. The zones thus delimited could be considered identical with and without gravity. Despite the thermal plume's influence on the breathing flow in the presence of gravity being evidenced in Chapter 4.1, it appears the FFT analysis is less sensitive to this effect. In Figure 12 a, b the BZ corresponds to higher velocity regions (>0.3 m/s) than caused by the human body thermal plume (0.25 m/s maximum), explaining why the BZ is the same with and without gravity. In Figure 12 c, the BZ is visible along with the axial changes of W B max , considering: one averaged cycle, the peak exhalation, and the peak inhalation fields. The averaged cycle's profile confirms that the mean velocity contour of 0.3 m/s, coincides with the border of the BZ (Figure 12 a andb) where W B max is 1 m/s at peak exhalation and 0 m/s at peak inhalation. In Figure 12 d, the BZ obtained by the FFT study is compared to the definitions proposed by Haselton [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] and Hweij [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF]. The 1 cm radius sphere of Hweij [START_REF] Hweij | Optimized performance of displacement ventilation aided with chair fans for comfort and indoor air quality[END_REF] is entirely contained within our BZ. The region of air that is rebreathed, according to Haselton [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF], is also circumscribed in our BZ. The inhalation hemisphere designated by Haselton [START_REF] Haselton | Convective exchange between the nose and the atmosphere[END_REF] (radius 6.2 cm) is visible in Figure 12 d and is probably relevant at peak inhalation, but does not include all the states of breathing flow over the entire inhalation half-cycle as the authors do in this study.

To directly link the identified BZ to the accumulation of CO 2 , we have superposed in Figure 12 e, f the BZ and the ΔCO 2 distributions, comparing the peak exhalation (Figure 12 e) with the peak inhalation (Figure 12 f). At peak exhalation, the BZ is located in the region where ΔCO 2 is equal to 0 indicating no difference in CO 2 concentration between the two cases. At peak inhalation, the BZ is located in a region of positive ΔCO 2 . To the extent that the BZ obtained is relevant, this means that the air inhaled by the astronaut is charged with more CO 2 in comparison to a similar situation on Earth.

Conclusions

The spatial distribution of breath CO 2 in the CQ of the ISS has been evaluated numerically, in order to circumscribe the region needing ventilation to prevent the astronaut's intoxication during sleep. This result required a multi-step approach.

Lacking CO 2 accumulation data inside the CQ in microgravity, a coupled experimental and numerical simulation of the accumulation problem was necessary on Earth, in order to obtain a valid model.

Experimental measurements performed with human subjects in the confined environment of a full-scale CQ mock-up, provided the CO 2 accumulation at different locations. A numerical model reproducing the experimental setup with a human model placed inside, aimed to replicate the CO 2 accumulation observed experimentally, using a realistic breathing function with gravity. The numerical results are in general accord with the experimental results.

The same numerical model was run again without gravity and compared to the one with gravity, directly investigating the difference ΔCO 2 between the distribution of CO 2 concentration with and without gravity. Positive values of ΔCO 2 were correlated to the trajectory of the breath's flow (high velocities). Negative values were associated with low velocity zones, where buoyancy plays a role in the airflow, when gravitational acceleration is present. High accumulations of CO 2 were found in the region in front of the astronaut's face.

The respiratory flow was analyzed in terms of overall behavior, comparable to twin jets at peak exhalation, and in dynamically looking for a rigorous definition of the BZ. The far field twin jets expansion was found to be close to previously reported values in the case of mouth breathing flow. For a more rigorous delimitation of the BZ, the zone influenced by the breath was spatially delimited by applying FFTs to the breath flow velocity variation over time along multiple lines in front of the human head. This FFT analysis delineated a small region influenced by the full breathing cycle, followed by a larger region presenting the influence of a half breathing cycle. The latter coincides with the high velocity region of the mean breathing velocity field (> 0.3 m/s). The BZ remained unchanged with or without gravity following this method. The resulting BZ encompassed two other BZ definitions, whose spatial limitation is not explained in the literature.

Finally, a direct link was made between the BZ and ΔCO 2 distribution. Without gravity, the air inhaled by the astronaut is charged with more CO 2 in comparison to a similar situation on Earth. A personalized ventilation system can be introduced in addition to the general one, targeted on the resulting BZ, to supply air less concentrated in CO 2 where it is needed. Future research will build upon the current results and investigate the viability of integrating a personalized ventilation system for the astronaut's CQ.

Figure 1 Figure 2

 12 Figure 1 Laboratory mock-up representing the ISS CQ at 1:1 scale, Position of CO 2 , Air Temperature and Relative Humidity sensors with planar coordinates: (b) 3D vision, (c, d, e) planes passing by sensors A c c e p t e d

Figure 4

 4 Figure 4 𝐶𝐶𝐶𝐶 2 𝑔𝑔𝑐𝑐𝑐𝑐𝑢𝑢𝑚𝑚𝑢𝑢𝑚𝑚𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 in the experimental model over 15 minutes for sensors C1 (a 1 ), C2 (b 1 ) and C3 (c 1 ) as well as over 60 s (a 2 , b 2 , c 2 ); numerical and experimental CO 2 accumulation data at sensors C1 (d), C2 (e), C3 (f)breathing velocity function superposed for investigating imprints on CO 2 accumulation. The experimental best fit curves (Figure 4 a 2 -c 2 ) are reported on Figure 4 d-f where the comparison with the numerical model covers the last 20 seconds (∼5 full breathing cycles) of the simulated duration of 60 seconds. This choice was made to allow the exhaled CO 2 to disperse inside the numerical model for the first 40 seconds of the simulation. In Figure 4 d-f, the numerical CO 2 accumulation curves with and without gravity are plotted on the same graphs as the nostril breathing velocity, to highlight possible correlations between them.

Figure 5

 5 Figure 5 Velocity magnitude contours (a 1 , a 2 ) and spatial distribution contours of 𝐶𝐶𝐶𝐶 2 𝑐𝑐𝑔𝑔𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 [𝑝𝑝𝑝𝑝𝑚𝑚] (b 1 , b 2 ) for the cases with and without gravity.

  b1), while without gravity (Figure 5 b 2 ) the CO 2 contours follow the velocity distribution of the impinging jet very closely. These observations are in agreement with the global results given in Figure 4 d-f. Without gravity, there is less mixing of CO 2 in the CQ and regions with CO 2 𝑐𝑐𝑔𝑔𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 < 400 𝑝𝑝𝑝𝑝𝑚𝑚, almost inexistent in the case with gravity, occupy almost a third of the CQ volume when 𝑔𝑔 = 0 𝑚𝑚/𝑠𝑠 2 (Figure 5 b 1 , b 2 ).

Figure 6

 6 Figure 6 Difference between the 𝐶𝐶𝐶𝐶 2 𝑐𝑐𝑔𝑔𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑠𝑠 of the no-gravity case and the 𝐶𝐶𝐶𝐶 2 𝑐𝑐𝑔𝑔𝑔𝑔𝑐𝑐𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑠𝑠 of the case with gravity, at different instants of breathing cycle.

  in the far field, by normalizing distances by D e , as the authors have, and by the normalized streamwise velocity W streamwise velocity at the nostril opening. Fields were extracted at the same instants observed in[START_REF] Yao | Experimental study on flow behavior of breathing activity produced by a thermal manikin[END_REF] (Figure7 b-f).For comparison, we retain instant t 2 = 54.1 s (Figure7d) corresponding to the developed exhalation, for which the far field exists. In the near field, the twin nostril jets are clearly visible. The velocity profile presents two maximums (W B max ) on either side of a central minimum (W B C ). This double hump profile disappears after a few diameters D e , and from this distance, the flow resembles a round jet coming from an orifice of diameter D e . Yao et al. [57] present the field for a maximum distance of 8 D e , where the normalized velocity of 0.25 compares well with our result at 8 D e . The dynamic expansion, based on a normalized velocity W .1, at a value of ± 1 D e and a normalized distance of 8 D e , is similar to the literature results [57].

Figure 7

 7 Figure 7 The breathing plane -BP (a), a breathing cycle (b), nostril twin-jet velocity fields at different instants of the breathing cycle (c-f) in plane BP with gravitational acceleration Streamwise centerline velocity W B c and streamwise maximum velocity W B max are plotted in Figure 8 a,b, at peak exhalation (t 2 =54.1 s), and peak inhalation (t 4 =56.1 s).

Figure 8

 8 Figure 8 Streamwise central (a) and maximum (b) velocities in the breathing flow, superposed to the breathing zone definitions.

  using a mobile frontal plane FP i perpendicular to BP. When FP i intersects BP (Figure 9 a), a line L BP i is generated and when FP i intersects MP a line L MP i is generated (Figure 9 b). 31 L BP i and 31 L MP i lines were generated as shown in Figure9 c. For i=1…4, the distances to the nostrils are given. For i>4, the distance increases in increments of 2.5 cm up to a distance of 70 cm.

  Figure 9 Lines L BP i (a) and L MP i (b) for BZ investigation. (c) the generated lines and their positions relative to the nostrils. FFTs of W B along the L BP i lines will delimit the zone influenced by the breath along the X B axis, while FFTs of W B along the L MP i lines will delimit the zone along the Y B axis. The zone's depth along the Z B axis will be determined by the maximum amplitude of the FFTs at f 0 from L BP 1-31 or L MP 1-31 . Theoretical limits of FFT amplitude (both superior and inferior) must be determined, to evaluate how closely the signal follows the breathing function.Three limits were determined in Figure10 d-f, 𝑚𝑚 (1) the theoretical upper limit (Figure10 d), indicating perfect synchronization with the sinewave in Equation (2) (Figure10 a), 𝑚𝑚 (2) an intermediate limit (Figure10 e) obtained by taking the FFT of the positive half of the-sine wave (Figure10b, considering the negative half leads to an identical result); 𝑚𝑚 (2) corresponds to a weaker influence of the breathing cycle or to solely the exhalation or inhalation part of the cycle. 𝑚𝑚 (3) is the lower limit (Figure10 f) below which the breathing cycle is not felt, computed as the average maximum amplitude of several white noise signals (Figure10 c).

Figure 10 Figure 11 FFT

 1011 Figure 10 Normalized FFT limits for the full breathing cycle (a, d), the breathing half-cycle (b, e) and random white noise signals (c, f). The FFT of Equation (2), at a frequency of 10 Hz (the 0.1 s time step of the simulation), results in a peak at 𝑓𝑓 = 0.234 𝐻𝐻𝐻𝐻 ≅ 𝑓𝑓 0 . For comparison, the results FFT(W B ) are normalized by the maximum amplitude of the velocity function given by Equation (2), which is W B 0 (t 2 ) = 5.49 m/s. In the following FFT(W B )/W B 0 (t 2 ) will be designated by FFT N , leading to an upper limit 𝑚𝑚 (1) = 0.76, an intermediate limit 𝑚𝑚 (2) = 0.38 and a lower limit 𝑚𝑚 (3) = 0.06 of FFT N (Figure 10 d-f). The FFT analysis was performed from L BP 1 to L BP 31 and L MP 1 to L MP 31 for both numerical cases. Beyond L BP 7

Figure 12

 12 Figure 12 Zones influenced by the breathing cycle in planes MP (a) and BP (b). BZ determined by the FFT analysis superposed on W B max plots (c) with other BZ definitions (d); ∆CO 2 contours superposed on the BZ at instants t 2 (e) and t 4 (f).

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

Table 1

 1 Summary of the breathing parameters found in the literature.

		Type of study	V t [ml]	b f [min	-1 ]	MV [l/min]	Peak Exhalation/Inhalation
							Velocity [m/s]
	Guyton and Hall [41]	Medical Manual	500	12		6	N/A
	Adams [43]	Experimental	373	19.5		7.3	N/A
	Bjorn, Nielsen [44]	Experimental and Numerical	600	10		6	N/A
	Qian et al. [45]	Experimental	600	10		6	N/A
	Olmedo et al. [46]	Experimental	570 / 660	19 / 15	10.8 / 9.9	4.74
	Olmedo et al. [47]	Experimental	750 / 660	14.6 / 10	10.9 / 6.6	5.74
	Cao et al. [48]	Experimental	550	16		8.8	3.4 ±0.3
	Liu et al. [49]	Experimental and Numerical	~700	15		~10.5	No
	Yoo, Ito [50]	Numerical	~555	14.8		~8.2	~ 2 -4
	Berlanga et al. [51]	Experimental	~570	~15.6	~8.9	~ 1 -4
	Cheng et al. [52]	Experimental	492	17.5		8.61	3.7
	Average values	N/A	577	13 -14	7.5 -8	3.5 -5
	Present study	Experimental and Numerical	582	14.7		~8.5	5.49

Table 2

 2 CQ ambient air parameters and nostril inlet boundary conditions

		Boundary condition	T [°C]	O 2 volume fraction [-]	CO 2 volume fraction [-]	H 2 O volume fraction [-]	Velocity [m/s]
	Ambient air	-	27	0.21 (21%)	0.0004 (0.04%)	0.0244 (2.44%)	-
	Nostrils during exhalation	Velocity inlet	36	0.15 (15%)	0.04 (4%)	0.0615 (6.15%)	𝑢𝑢 = 5.49 • sin(2𝜋𝜋 • 0.245 • 𝑔𝑔)
	Nostrils
	during	Velocity inlet		Ambient values		𝑢𝑢 = 5.49 • sin(2𝜋𝜋 • 0.245 • 𝑔𝑔)
	inhalation

Table 3

 3 Wall and human body surface boundary conditions[START_REF]ASHRAE Handbook -Fundamentals[END_REF]

	Region Walls Head	Torso	Arms	Forearms Hands Lower abdomen and thighs	Shins	Feet
	T [°C]	27	36	34.5	33	32	30	32.5	30	27

Table 4

 4 Experimental-numerical comparison of air temperatures (AT sensors) and their variation over 60 s

			M a n u s c r i p t
	Time t = 0 s A c c e p t e d AT1 27.4	Temperature [°C] AT2 27.6	AT3 27.5
	Experimental
		t = 60 s	27.5	27.9	27.5
	Numerical	t = 0 s	27.7	27.7	27.7

Acknowledgements

This work was supported by a "Presidency" scholarship from the University of Rennes 1, for which the authors are grateful. This work was also supported by the grant of the Romanian Space Agency ROSA STAR-CDI-C3-2016-577.