Antoine Giovanni
email: antoine.giovanni@ap-hm.fr

Thomas Radulesco

Gilles Bouchet

Alexia Mattei

Joana Révis

Estelle Bogdanski

Justin Michel

Transmission of droplet-conveyed infectious agents such as SARS-CoV-2 by speech and vocal exercises during speech therapy: preliminary experiment concerning airflow velocity

Keywords: COVID-19, voice, pulmonary ventilation, speech therapy Left: 0.98", Right: 0.98", Top: 0.98", Bottom: 0.98", Header distance from edge: 0.49", Footer distance from edge: 0.49

Introduction

Airborne infectious agents such as SARS-CoV-2, responsible for COVID-19 disease, are transmitted by droplets of different sizes expelled in the exhaled air, especially during violent events such as cough, but also during speech and singing [START_REF]Modes of transmission of virus causing COVID-19: implications for IPC precaution recommendations[END_REF][START_REF] Wölfel | Virological assessment of hospitalized patients with COVID-2019[END_REF]. Health workers, e.g. Otolaryngologist, phoniatricians and speech therapists are therefore at high risk of viral exposure during vocal exercises [START_REF] Schutte | Recommendation by the Union of European Phoniatricians (UEP): standardizing voice area measurement/phonetography[END_REF]. Associated with ventilated room and physical distancing, masks have shown to reduce the risk of contamination for the wearer [START_REF] Leung | Respiratory virus shedding in exhaled breath and efficacy of face masks [published correction appears in[END_REF][START_REF] Thamboo | Clinical evidence based review and recommendations of aerosol generating medical procedures in otolaryngology -head and neck surgery during the COVID-19 pandemic[END_REF]. Few data concerning loud voicing, singing and/or vocal exercises are available in literature; moreover, these activities do not always allow the patient to wear a mask. A security issue in the field of vocal speech therapy, singing lessons or in choirs arose during the outbreak.

There is a lack of knowledge allowing to resume normal activities.

State of the literature

The risk of contamination during vocal exercises was highlighted in March 2020 within a choir in North America [START_REF] Read | A choir decided to go ahead with rehearsal. Now dozens of members have COVID-19 and two are dead[END_REF].

Current data from the literature establish that the risk of contamination mainly depends on three factors related to the emitted droplets: (i) the intrinsic contagiousness of droplets, (ii) the type of vocal exercise, (iii) the spatial dissemination of droplets.

The intrinsic contagiousness of droplets

The droplets emitted by an individual contain all the mucus elements and, potentially, a positive viral load if the emitter is infected. The contagiousness of biological fluids is proportional to their viral load [START_REF] Wölfel | Virological assessment of hospitalized patients with COVID-2019[END_REF]: large droplets contain more viruses and therefore have a higher contagiousness than small droplets [START_REF] Wölfel | Virological assessment of hospitalized patients with COVID-2019[END_REF]. The probabilities that 50-, 10-and 1-micron droplets express (after dehydration) at least one copy of the virus are respectively 37%, 0.37% and <0.01% [START_REF] Stadnytskyi | The airborne lifetime of small speech droplets and their potential importance in SARS-CoV-2 transmission[END_REF]. Very small droplets would therefore be less contaminating. However, being able to remain suspended in the air, they were shown to be responsible for SARS-Cov-2 titrations in ambient air for 3 hours [START_REF] Van Doremalen | Aerosol and Surface Stability of SARS -CoV-2 as Compared with SARS-CoV-1[END_REF].

Therefore, the time spent with an infected individual could be another key factor. Otherwise, the great number of small droplets expelled probably lead to significant risk of contamination [START_REF] Morawska | Size distribution and site of origin of droplets expelled from the human respiratory tract during expiratory activities[END_REF].

The type of vocal exercise

It is proven that more bioaerosols are generated during speech than during calm breathing [START_REF] Gupta | Characterizing exhaled airflow from breathing and talking[END_REF][START_REF] Xie | Exhaled droplets due to talking and coughing[END_REF]. The number of droplets larger than 50-100 microns expelled during speech is estimated between 1 and 50 particles per second while less than 2 particles per second for normal breathing [START_REF] Wells | On air born infection. Study II. Droplet and droplet nuclei[END_REF][START_REF] Duguid | The size and the duration of the air-carriage of respiratory droplets and droplet-nuclei[END_REF]. Consonants /p/, /t/, /s/ generate more droplets (1.8/cm 3 ) than vowels (1/cm 3 ) and normal breathing (0.1/cm 3 ) [START_REF] Asadi | Aerosol emission and superemission during human speech increase with voice loudness[END_REF][START_REF] Asadi S Wexler | Effect of voicing and articulation manner on aerosol particle emission during human speech[END_REF]. Asadi et al. have shown that droplets emission rates increase with the loudness of the voice, regardless of the language used [START_REF] Asadi | Aerosol emission and superemission during human speech increase with voice loudness[END_REF][START_REF] Asadi S Wexler | Effect of voicing and articulation manner on aerosol particle emission during human speech[END_REF]. Anfinrud et al. [START_REF] Anfinrud | Visualizing Speech-Generated Oral Fluid Droplets with Laser Light Scattering[END_REF] also demonstrated that droplets from 20 to 500 microns emitted in loud voices are twice as numerous as in normal voice. Droplets emitted during speech probably partly originate from the vocal folds' collision during phonation: they could derive from microscopic ruptures of vocal folds lubricating mucus [START_REF] Johnson | The mechanism of breath aerosol formation[END_REF]. Indeed, the size distribution of droplets differs between vocalization and whisper [START_REF] Morawska | Size distribution and site of origin of droplets expelled from the human respiratory tract during expiratory activities[END_REF]. One would think that vocal exercises and singing are considered as violent events leading to a greater number of large droplets than in normal voice, although not demonstrated by scientific evidences. Increased breathing amplitudes, articulatory work and the use of semi occluded vocal tract (SOVT) exercises are supposed to generate more droplets [START_REF] Schutte | Recommendation by the Union of European Phoniatricians (UEP): standardizing voice area measurement/phonetography[END_REF].

The spatial dissemination of droplets

The contamination of an individual depends on his physical exposure to the infectious agent and is therefore closely related to the spatial dissemination of droplets emitted by an infected individual.

The spatial distribution of droplets emitted depends on their sizes and initial velocities. When speaking, large (> 50-100 microns), intermediated-sized (10-50 microns) and small (<10 microns) droplets are emitted [START_REF] Lindsley | A Cough Aerosol Simulator for the Study of Disease Transmission by Human Cough-Generated Aerosols[END_REF]:

-Large droplets have ballistic trajectories, without significant evaporation, which directly depends on their initial velocities [START_REF] Dbouk | On coughing and airborne droplet transmission to humans[END_REF]. They are quickly slowed down by ambient air and fall to the ground in one to two seconds [START_REF] Wells | On air born infection. Study II. Droplet and droplet nuclei[END_REF].

They are propelled up to 6 meters during sneezing (v=50 m/s), 2 meters during cough (v = 10 m/s) and less than 1 meter during normal breathing (v=1 m/s) [START_REF] Wei | Airborne spread of infectious agents in the indoor environment[END_REF][START_REF] Bourouiba | Bush JWM Violent expiratory events: on coughing and sneezing[END_REF]. These distances may vary depending on the air distribution in rooms (ventilation systems, patient's own movement) [START_REF] Thamboo | Clinical evidence based review and recommendations of aerosol generating medical procedures in otolaryngology -head and neck surgery during the COVID-19 pandemic[END_REF][START_REF] Morawska | Airborne transmission of SARS-CoV-2: The world should face the reality[END_REF].

-Intermediate-sized droplets make the risk of contamination significant because they have trajectories more difficult to predict that strongly depends on their initial velocity but also turbulence and/or shears effects [START_REF] Bourouiba | Turbulent Gas Clouds and Respiratory Pathogen Emissions: Potential Implications for Reducing Transmission of COVID-19[END_REF].

Their speed of fall depends on their dehydration: a 50 microns droplet reduced to 10 microns by dehydration sees its speed of fall decrease from 6.8 cm/s to 0.35 cm/s [START_REF] Stadnytskyi | The airborne lifetime of small speech droplets and their potential importance in SARS-CoV-2 transmission[END_REF].

-Small droplets are impacted by air movements and have therefore an unpredictable trajectory after the first second. They could be residues of larger dehydrated droplets [START_REF] Thamboo | Clinical evidence based review and recommendations of aerosol generating medical procedures in otolaryngology -head and neck surgery during the COVID-19 pandemic[END_REF][START_REF] Bourouiba | Turbulent Gas Clouds and Respiratory Pathogen Emissions: Potential Implications for Reducing Transmission of COVID-19[END_REF]. But they can also correspond to smaller droplets produced at the free edge of the vocal folds because of aerosolization of secretions lubricating the vocal folds [START_REF] Morawska | Size distribution and site of origin of droplets expelled from the human respiratory tract during expiratory activities[END_REF][START_REF] Johnson | The mechanism of breath aerosol formation[END_REF].

To date, the velocity of expired air according to the type of vocal exercise performed during speech therapy is unknow. Specifying these velocities would allow to better predict emission distance of droplets during phonation.

The objective of this study was to determine the velocity of the expired air during vocal exercises, and to compare these data with a Ccomputational Ffluid Ddynamics (CFD) study.

Methods

Experimental study

Two subjects (TR, JR) gave their written consent to participate in this study which was carried out in accordance with the Declaration of Helsinki. It was an observational study that did not substantially change the behavior of subjects who are daily e-cigarette users.

A propylene glycol cloud produced by 2 e-cigarettes' users allowed visualization of the exhaled air emitted during vocal exercises (Eleaf® TC40W, 29W, 0 .58 ohms, 4.15V). The room was quiet and closed. The ventilation system Computational Fluid Dynamics (CFD) study.

(ceiling) lead to air movements inferior than 5 cm/s. Exhaled airflow velocities were measured on video records during the first 200 milliseconds during successive vocal exercises and during 3 seconds for two of them (long exhalation and sustained vowel /a/):

sustained vowel /a/ (comfortable intensity and loud intensity). We were not able to determine the absolute value of intensity.

-

voiceless

CFD study

We compared velocities measured experimentally with a two-dimensional CFD simulation. CFD was performed using Star-CCM + ® software (Siemens®). The boundary conditions were as follows: airflow= 200 mm 3 /s; initial velocity=1 m/s; humidity=25%; temperature=22 ° C; vertical ambient air displacement=5 cm/s.

Results

Expired air velocities varied according to vocal exercises and are reported in Table 1. Concerning the production of vowels, we found higher velocities in loud and whispered voice. The production of voiced consonants like /ʒ/ or /v/ generated higher velocities than vowels. For voiceless consonants, some, e.g. /t/, generated very fast airflows, close to normal breathing. SOVT exercises generated airflows faster than loud speech. Velocities decreased when voicing in the device.

The evolution of airflow velocities during the first 3 seconds of a long exhalation and a sustained /a/ are reported in Figure 1. Evolution of velocities experimentally measured had a profile similar to that of CFD data (Figure 2).

The evolution of the droplets cloud's length during the production of a sustained /a/ is reported in Figure 3 and4 and the corresponding video (Online Resource 1).

Discussion

The objective of this study was to evaluate the initial velocity of the exhaled air during speech and vocal exercises.

This study completes our knowledge concerning the dissemination of droplets during speech, which have been reported to be more numerous in loud voice [START_REF] Asadi | Aerosol emission and superemission during human speech increase with voice loudness[END_REF]. Our results showed great variability in the expired air velocities, and the corresponding video (Online Resource 1).

ranging from 0.28 to 1.8 m/s depending on the vocal exercise performed. However, these velocities remained lower than velocities reported for violent events such as coughing and sneezing. [START_REF] Wei | Airborne spread of infectious agents in the indoor environment[END_REF][START_REF] Bourouiba | Bush JWM Violent expiratory events: on coughing and sneezing[END_REF].

The use of propylene glycol for visualization of the exhaled air is a relevant method: e-cigarettes deliver 0.3 microns droplets whose permanence in the air is around 11 seconds, this allowing to calculate exhaled air velocities [START_REF] Bertholon | Comparaison de l'aérosol de la cigarette électronique à celui des cigarettes ordinaires et de la chicha[END_REF]. However, the future of this cloud after this deadline cannot be accurately evaluated. The deep inspiration required using e-cigarettes was comparable to the deep inspiration required in speech therapy (one of the two subjects is a speech therapist), especially before performing a loud voicing or SOVT exercises. This type of inspiration can also be compared to that used in singing.

The variability of measures reported in figure 1 is probably related to the uncertainties of measurements because velocities were calculated on a very short period (200ms). This is a preliminary study carried out during containment without full access to the technical resources (e.g. velocimeters or lasers) which would have allowed accurate analysis. However, our data agreed with the findings of Anfinrud et al. [START_REF] Anfinrud | Visualizing Speech-Generated Oral Fluid Droplets with Laser Light Scattering[END_REF].

In all vocal exercises, the initial velocity remained inferior to 1 m/sec for vowels and voiced consonants, even in loud voicing. These data perfectly match with literature: a pressure drop is found at glottic level during voicing and there is no proportionality between the airflow and the acoustic power of the emitted sound. [START_REF] Traunmüller | Acoustic effects of variation in vocal effort by men, women, and children[END_REF]. This velocity becomes close to 1 m/s or slightly higher in the production of voiceless consonants, whispered voicing or SOVT, i.e. in productions where airflow is close to normal expiratory airflow.

Our data suggest that the size of the exhaled cloud should remain limited, even in loud voice. As a result, the risk of spatial dissemination of the droplets is not significantly modified compared to long exhalations. Assuming the speaker is COVID-19 positive, high level personal protective equipment are still needed for healthcare workers.

However, we do not report an increased risk during loud voicing or vocal exercises compared to standard speech.

The usual rules of physical distance, or wearing a mask in cases where this distance cannot be respected or in a closed place, seem valid. More studies should be performed especially regarding choral singing.

Conclusion

The size and velocity of expelled droplets are key factors in transmission of infectious agents. Our study revealed that velocities of the expired air produced during vocal exercises are slower than in long exhalation, suggesting no increased risk compared to standard speech. More studies must be carried out to better understand the infectious risk associated with droplets in speech.

Figures

Fig.

1 Fig. 2 Fig. 3 Fig. 4 Figure

 1234 Fig. 1 Evolution of airflow velocities (in cm/s) during the first 3 seconds of two long exhalations for subject n ° 2 (A) and during the first 3 seconds of a sustained vowel /a/ for subject 1

The authors declare no funding source.

all data and materials support our published claims and comply with field standards.

Code availability: software applications support our published claims and comply with field standards.


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Degradation of wood by microorganisms: ultrastructural aspects


Thomas Radulesco
email: thomas.radulesco@ap-hm.fr

Lionel Meister

Gilles Bouchet

Arthur Varoquaux

Jérome Giordano

Julien Mancini

Patrick Dessi

Pierre Perrier

Justin Michel

Radulesco Thomas

Meister Lionel

Bouchet Gilles

Giordano Jérôme

Mancini Julien

Dessi Patrick

Perrier Pierre

Michel Justin

Correlations between computational fluid dynamics and clinical evaluation of nasal airway obstruction due to septal deviation: An observational study

Keywords: CFD, nasal airway obstruction, surgery, functional, septal deviation, nasal valve, inferior turbinate hypertrophy

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

INTRODUCTION

Nasal airway obstruction (NAO) is a common symptom leading many patients to seek a medical consultation and occasionally undergo surgical procedures (1) [START_REF] Teichgraeber | Surgical Management of Nasal Airway Obstruction[END_REF]. Septal deviation (SD) is one of the main causes of NAO [START_REF] Teixeira | Nasal Septal Deviations: A Systematic Review of Classification Systems[END_REF].

Clinical evaluation of NAO is usually carried out by patient interview, self-questionnaires and various physical tests designed to quantify NAO [START_REF] Rhee | A Systematic Review of Patient-Reported Nasal Obstruction Scores: Defining Normative and Symptomatic Ranges in Surgical Patients[END_REF]. Anterior active rhinomanometry is a physical test performed in clinical routine, in many centers, to calculate resistance to the airflow in the nasal cavity [START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF].

Computational Fluid Dynamics (CFD) is a recent tool for modeling the nasal cavity as well as for analyzing air conditioning and airflow [START_REF] Kim | Patient specific CFD models of nasal airflow: Overview of methods and challenges[END_REF]. Over the past 10 years, more and more authors have assessed the nasal airway using CFD [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF]. New measurements, such as Heat Flux (HF) and Wall Shear Stress (WSS), are computable by CFD in addition to usual data such as nasal resistances [START_REF] Leong | A review of the implications of computational fluid dynamic studies on nasal airflow and physiology[END_REF] [START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency: Mucosal Cooling and Nasal Patency[END_REF]. However, only a few publications have attempted to correlate CFD with clinical evaluation of NAO and these studies were usually based on a limited number of cases or on healthy subjects [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF] [START_REF] Lu | Accuracy evaluation of a numerical simulation model of nasal airflow[END_REF]. In our view, the correlation between CFD and clinical evaluation of NAO (patient perception and rhinomanometry) would permit validation and improved interpretation.

Regarding NAO, patients often complain of unilateral impairment. This is convenient for correlating CFD data as they can be easily calculated on each side: the more obstructed side (MOS) and the less obstructed side (LOS). However, the most frequently used selfquestionnaires are quality-of-life evaluation tools, which is why they do not investigate lateralization of the functional impairment, thus making it difficult to correlate them with CFDcalculated data [START_REF] Floyd | Systematic Review and Meta-analysis of Studies Evaluating Functional Rhinoplasty Outcomes with the NOSE Score[END_REF] [START_REF] Hsu | Evaluation of nasal patency by visual analogue scale/nasal obstruction symptom evaluation questionnaires and anterior active rhinomanometry after septoplasty: a retrospective one-year follow-up cohort study[END_REF].

The primary objective of this study was to determine how CFD could be correlated to clinical evaluation of NAO in a population of patients with symptomatic SD. To do so, we researched the correlations between CFD and patient perception on one hand, and CFD and rhinomanometric data on the other for each of the nasal cavities.

The secondary objective of the study was to determine whether CFD could define which side was the MOS and the LOS.

METHODS

Ethical standards

All patients gave written consent before participating in the study, which was conducted according to the Declaration of Helsinki. We obtained Ethical Committee Authorization (Assistance Publique des Hôpitaux de Marseille) to conduct this study (Authorization N° 2017-14-12-005).

Patient selection

All patients were referred for septal surgery at our center between January 2017 and September 2018. Age range was 19 to 58 years (mean 37 years). Preoperative CT scans were obtained using 2 CT scanners (Scanner Siemens Somatom definition, Siemens Healthcare, Germany and Scanner General Electric Light speed LS 16 Pro, GE) applying the following parameters: Kv: 120, mAs : 130, 0.3mm slice every 0.6 mm.

All patients with other causes of NAO such as rhinitis, sinusitis or tumoral / autoimmune processes (i.e., not due to anatomic obstruction) were excluded. We also excluded patients presenting symptoms alternating from one side to the other as this can create bias, especially regarding CFD-NR [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF].

Clinical evaluation of NAO

Patient perception scores

In all patients, assessment of NAO perception was performed separately for each nasal cavity. Thus, patients were assessed as follows for right and left nasal fossae: 0 = "no obstruction", 1 = "slight obstruction", 2 = "moderate obstruction", 3 = "severe obstruction" and 4 = "total obstruction". The more obstructed side was abbreviated to MOS. The less obstructed side was abbreviated to LOS. NAO perception could be scored 0/4, 1/4, 2/4, 3/4 or 4/4 on each side.

Clinical evaluation was performed one month before surgery, in the absence of any intercurrent infectious episode.

Rhinomanometry

Rhinomanometry (without vasoconstriction test) was performed before surgery. No procedures (e.g. Cottle or Bachman tests) were performed in order to avoid deforming the nasal anatomy. The same rhinomanometer was used for all patients (Otopront® Rhinon-sys © Happersberger Otopront GmbH 2008). The threshold value used to assess the presence of nasal obstruction was 0.30 sPa/mL, as defined by the manufacturer. Resistance between 0.30 and 0.49 sPa/mL denoted mild obstruction, resistance between 0.50 and 0.80 sPa/mL moderate obstruction and resistance greater than 0.80 sPa/mL severe obstruction. Right and left nasal resistances were calculated. Nasal resistances obtained using rhinomanometry are abbreviated to RMM-NR.

Creation of 3-Dimensional Models 3D reconstructions were obtained using ITK-Snap (3.6.0) [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability[END_REF]. The procedure was as follows:

(1) Importation of CT scan images (DICOM formats) into ITK-Snap, (2) segmentation process using ImageJ (software version 1.44o) to determine the boundaries of anatomical structures, and (3) paranasal sinus surface extraction [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Some manual corrections were performed when the threshold did not permit identification of thin anatomical structures. No smoothing algorithm was applied. The file containing the sinonasal 3D surface mesh was saved in STL format.

CFD protocol CFD was performed using Star-CCM+® software (CD-ADAPCO -www.cd-adpaco.com). The procedure for surface preparation was as follows: (1) definition of a new orthonormal XYZ (2), reduction of the computational domain from the nostril to the nasopharynx, (3) definition of the boundary conditions.

Volume meshing of the computational domain was performed using a polyhedral mesher with parameters defined after a convergence mesh study: 10 prismatic layers with elements of 0.25 mm. We defined the following computational hypothesis: airflow to standard conditions for temperature (19°) and atmospheric pressure (101 325 Pa). Air was considered to be a newtonian fluid, incompressible with constant density (ρ=1.225 kg/m3) and viscosity μ= 1.18x10-5 Pa.s. Nasal airflow at resting breathing rates has been described as predominantly laminar in healthy individuals; we considered the flow to be laminar. Steady computation was used, with a segregated solver and second order accuracy in space. Sinonasal surface was a non-slip wall. Wall temperature was 34°C [START_REF] Lindemann | Impact of menthol inhalation on nasal mucosal temperature and nasal patency[END_REF]. Nostrils were pressure outlets with an imposed atmospheric pressure (DP=0 Pa). Temperature of inspired air was 19°C. Nasopharynx was a pressure outlet with an imposed pressure. In case of reentry, the temperature of air in the nasopharynx was 37°C. The differential pressure imposed in the nasopharynx was -150 Pa. CFDcalculated nasal resistances were called CFD-NR. CFD-NR were calculated for the right and left side. Nasal resistances were expressed as R = #$ % , where DP is the pressure differential between the nostril and the rhinopharynx and V is the airflow rate, expressed in sPa/mL. A total of 30 CFD-calculated data were collected for each patient, 15 on each side (Figure 1): Total Pressure was measured in the ambient air (P1), before the nasal valve (P2), after SD on MOS (or symmetrically for LOS) (P3), at the posterior third of the nasal septum (P4) and at the choana (P5). Peak Heat flux (i.e. the rate of heat transfer across a surface per unit of time and area and measures of heat loss from the nasal mucosa to the inspired air) was measured in a surface area of 1 cm 2 at the entry of the nose (HF1), in the nasal valve area (HF2), after SD on MOS (and symmetrically for LOS) (HF3), and in the posterior third of the nasal septum (HF4). WSS was measured in the nasal valve area (WSS1) and at the maximum SD (WSS2). Maximum velocity was assessed for each nasal fossa (Vmax). Temperatures were recorded in ambient air (T1), in the middle meatus (after the SD for MOS, symmetrically for LOS) (T2), and at the choana (T3).

Statistical analyses

Results were analyzed using Microsoft Office Excel. Statistical calculations were performed using PAST software (Oyvind Hammer, Natural History Museum, University of Oslo, Norway).

To compare CFD-NR and RMM-NR, statistical differences were assessed using a paired t-test.

Comparisons between NAO and CFD values were made using the Spearman correlation test (rs). The correlation was considered perfect if rs = 1 or -1, very strong if rs > 0.8 or <-0.8, strong if 0.5> rs > 0.8 or -0.8 < rs <-0.5, moderate if 0.2> rs > 0.5 or -0.5 < rs <-0.2, low if rs <0.2 or> -0.2 and null if rs = 0. Comparisons between nasal cavity MOS and LOS were made using paired Wilcoxon test. p values <0.05 were considered to be statistically significant.

RESULTS

Population

We selected 22 patients complaining of NAO with SD. We were thus able to perform 44 analyses comparing each side with its CFD data. Regarding patient perception scores, we found for MOS a severe obstruction score (mean score ± SD = 3.13±0.79); For LOS, we found a low obstruction score (mean score ± SD = 0.95±0.78). The difference between MOS and LOS was statistically significant (p<0.05).

Correlation of CFD with clinical evaluation of NAO

Results are reported in Table 1.

Pressures, Heat Flux, Temperatures, Velocities, Wall Shear Stress

Regarding correlations with patient perception, we found a very strong correlation for Heat Flux values after SD (HF3). We also found a strong correlation with all other HF values, T2 and WSS2. Moderate correlations were found for P2, P3, P4, T3 and Vmax. Correlations were low for P5 and WSS1.

RMM-NR and CFD-NR

Both RMM-NR and CFD-NR had strong correlations with nasal impairment (rs=0.75, p<0.001 and rs=0.6, p<0.001, respectively).

Comparison between MOS and LOS

Results are reported in Table 2.

Pressures, Heat Fluxes, Temperatures, Velocities, Wall Shear Stress (Figures 2 and3)

Regarding Total Pressure, we found a big pressure drop after SD (P3) in MOS (Figure 4a, Video 1). The difference was statistically significant comparing MOS and LOS for P3 (p<0.001).

However, we found no statistically significant differences for P2, P4 and P5. There was also a HF drop after SD on MOS (HF3, Figure 4 b). The difference was statistically significant comparing MOS and LOS for HF1, HF2, HF3, and HF4 (p <0.001). At T2 (Figure 4c), mean temperatures were 28.06 ± 3.65 °C and 23.5 ± 2.87°C, respectively, for MOS and LOS. At T3, mean temperatures were 30.6 ± 1.97 °C and 29.08 ± 2.15°C, respectively, for MOS and LOS.

Differences were statistically significant at T2 and T3 between MOS and LOS (p<0.001 and p=0.007, respectively). We also found a strong correlation between HF and temperatures (rs=0.56, p<0.001). Maximum velocities were higher on MOS. The difference between MOS and LOS was statistically significant (p=0.039). Comparing WSS, they were statistically higher on MOS in WSS2 values but not in WSS1 (p=0.065) (Figure 4d).

RMM-NR and CFD-NR

RMM-NR were mean 1.8 ± 2.2 sPa/mL for MOS. RMM-NR were mean 0.6 ± 0.37 sPa/mL for LOS. The difference was statistically significant (p=0.01). CFD-NR were mean 0.8 ± 1.17 sPa/mL for MOS. CFD-NR were mean 0.23 ± 0.1 sPa/mL for LOS. The difference was statistically significant (p=0.03).

We also found a statistically significant difference between RMM-NR and CFD-NR (p=0.003).

DISCUSSION

Synopsis of new findings

The ability to analyze airflow and air conditioning within the nasal cavities offers new perspectives in rhinology. Over the past 10 years, many CFD studies have investigated the nose, first in healthy or cadaveric subjects, and then in patients (17)(18) [START_REF]Characterization of Postoperative Changes in Nasal Airflow Using a Cadaveric Computational Fluid Dynamics Model[END_REF]. The analysis and interpretation of CFD-calculated data must be correlated with the patient's clinical experience [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF]. To that end, CFD must be compared with already existing tests or examinations, especially relative to new data such as HF or WSS. [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF]. Despite being widely validated in the literature, these questionnaires do not lateralize MOS and LOS although, in most cases, patients with NAO complain more about one side than about the other. Furthermore, CFD analysis is predominantly performed unilaterally [START_REF] Kimbell | Computed nasal resistance compared with patient-reported symptoms in surgically treated nasal airway passages: a preliminary report[END_REF] [START_REF] Roithmann | Acoustic rhinometry, rhinomanometry, and the sensation of nasal patency: a correlative study[END_REF]. It is not logical, therefore, to compare a unilateral CFD analysis with a global clinical feeling. For this reason, we found it useful to make separate clinical evaluations of MOS and LOS so as to compare with their CFD data. Establishing the correlation between CFD data and patients' clinical perceptions appears fundamental in order to better interpret CFD.

Comparison with other studies

In most data in the literature, we found a significant pressure drop and a big change in airflow on MOS [START_REF] Do | Predicting postsurgery nasal physiology with computational modeling: current challenges and limitations[END_REF] [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF] after surgery (Video 1). Similarly for HF, which decreased after SD and was closely correlated with patient perception (Figure 2,4). Although there are different ways of measuring HF (Total HF, Peak HF, SAHF50), many authors have found a strong correspondence between HF and patient perception [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF] [START_REF] Sullivan | Perception of better nasal patency correlates with increased mucosal cooling after surgery for nasal obstruction[END_REF] [START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency[END_REF], whatever the method adopted. We also noted this strong correlation. This finding reinforces the idea that the mucosal cooling effect plays a large part in NAO perception, and that the latter is probably multifactorial and not dependent exclusively on nasal resistances as suggested for many years [START_REF] Lindemann | Impact of menthol inhalation on nasal mucosal temperature and nasal patency[END_REF]. Since HF is dependent on air and wall temperatures, it is scientifically logical to find a strong correlation between HF and temperatures (rs=0.56). It is also logical that temperature differences between MOS and LOS are lower at T3 than at T2 as temperature is measured at the choana and, in this region, thermal exchanges may occur between MOS and LOS.

Regarding WSS, there was a good correlation for the WSS2 measured on the maximum SD but not in the nasal valve area (WSS1). Kimbell et al. reported a correlation with patient perception measuring HF on the entire MOS [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF]. In our patient presented in Figure 2c, we did not observe higher WSS in the nasal valve area. From our study, it appears that WSS is very dependent on anatomic variation. Indeed, when no airflow is possible due to severe deviations, WSS corresponding to air friction is inevitably close to 0.

Regarding velocities, discordant results were found in our series which sometimes displayed higher velocities in LOS [START_REF] Liu | Effects of septal deviation on the airflow characteristics: using computational fluid dynamics models[END_REF]. Moreover, although the difference was statistically significant between MOS and LOS with higher mean velocities in MOS, Vmax was poorly correlated with patient perception. These discrepancies for WSS1 and Vmax can be explained by an "ON-OFF" effect in case of total NAO. Indeed, velocity and WSS are null in the presence of total NAO and are therefore lower in MOS than in LOS (Figure 3). It is therefore essential to be wary when interpreting statistical analyses of velocities and WSS, which cannot be significant in case of total NAO. Nasal resistance is one of the most used data for assessing NAO perception prior to surgery (septoplasty, inferior turbinate hypertrophy or functional rhinoplasty). Thanks to developments and technical progress in recent years, it is now possible to calculate CFD-NR. However, few studies have sought to compare RMM-NR and CFD-NR. Those studies that have been performed analyze only small cohorts or healthy subjects (9) (10) [START_REF] Zachow | Visual exploration of nasal airflow[END_REF]. Our study found a good correlation between patient perception and both RMM-NR and CFD-NR, thus validating the use of this datum on patients with SD. However, great care is needed when calculating CFD-NR, and different points must be checked to ensure the accuracy of the data obtained. Indeed, the presence of a strong nasal cycle could bias CFD-NR analysis. Although the inferior turbinates can be reduced by applying vasoconstrictors before rhinomanometry, this procedure is often difficult to perform before a CT scan. Whatever the case, the use of vasoconstrictors distorts reality. A better option is to choose patients who do not display a widely varying nasal cycle. To overcome this problem, Gaberino et al. proposed virtual surgery in order to correct the nasal cycle [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF]. The authors reported that after virtual correction of the nasal cycle, the correlation between CFD-NR and patient perception was greatly increased.

Limits

To date, CFD can only analyze static disorders related to nasal ventilation. However, it is well known that ventilatory disorders can be dynamic, especially regarding the nasal valve, [START_REF] Maalouf | A functional tool to differentiate nasal valve collapse from other causes of nasal obstruction: the FRIED test[END_REF].

These disorders appear only above an airflow threshold involving dynamic nasal valve collapse.

To date, CFD in the nasal airway does not assume deformable walls.

We used a steady flow simulating continuous inspiration. This model is quite different from clinical reality in which a nasal cycle follows a curve, as described by Vogt et al. [START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF]. CFD can calculate these inspiration/expiration cycles, even if the computing times are much longer.

Importantly, we analyzed inspiratory and not expiratory resistance. This choice was made because, in most cases, patients complain only of impairment due to inspiration.

CONCLUSION

This study aimed to enhance our ability to interpret CFD-calculated data in the nasal airway. It highlights and confirms that Heat Flux measures are very closely correlated to patient perception in cases of SD. It would be valuable to perform a similar study before and after surgery and compare CFD with changes in patient perception. Obstruction" (4/4). On the left side, he reported "No obstruction" (0/4). On the MOS, we observed a strong Pressure drop and decreased Heat Flux. WSS1 and 2 were null and lower, respectively, on the MOS.

  Clinical applicability of the study Clinical evaluation of NAO remains difficult. Many tools have been developed in recent years and Patient Reported Outcome has become more and more important in functional procedures. Evaluation can be performed subjectively, often by self-questionnaires. The NOSE, SNOT-22 and ENS6Q self-questionnaires and VAS are the most used in the literature (20)(21)

Figure 1 .

 1 Figure 1. Example of CT scan in axial and coronal view showing where CFD data were calculated

Figure 2 .

 2 Figure 2.Figure 2 shows a patient with a severe obstruction in the right nasal fossa according

Figure 3 .

 3 Figure 3. shows the same patient as in Figure 2 in section planes according to a) Temperatures

Figure 4 .

 4 Figure 4. shows the changes in Total Pressure and Heat Fluxes. A huge Pressure and Heat Flux

Figure 01 Figure 02

 0102 Figure 01

Figure 03

 03 Figure 03

Figure 04

 04 Figure 04

Table 1 .

 1 Correlations of CFD data with patient perception. HF3 had the best match with patient perception. * marks very strong and strong correlations.

		Clinical evaluation		Total Pressure			Heat Flux			Temperature Velocity Wall Shear Stress
			P2	P3	P4	P5	HF1	HF2	HF3	HF4	T2	T3	Vmax	WSS1	WSS2
	MOS	3.18	-34.62 -128.5 -114.91 -123.57 -1069.45 -731.5	-153.86 -276.68 28.47 30.88 13.03	5.68	7.21
	±SD	0.8	39,94	47.59 33.73	24.87	872.21	941.72	212.44 308.84 3.56	1.88	4.04	6.15	4.78
	LOS	0.95	-42,95 -75.41 -99.27	-123.82 -2192.86 -1952.41 -1290	-944	23.27 28.98 10.17	2.54	2.89
	±SD	0.79	31,85	42.03 38.46	24.62	867.57	864.34	947.68 709.33 2.78	2.3	4.02	1.99	2.23
	p	<0.001	0,52	0.003 0.11	0.775	<0.001	0.001	<0.001 <0.0001 <0.001 0.007 0.039	0.065	0.002

Table 2 .

 2 Comparisons between mean CFD values for more obstructed side and less obstructed side. MOS = More Obstructed Side; LOS = Less Obstructed Side. P2, P4 and P5 and WSS1 showed no statistical difference between MOS and LOS. Bold = statistically significant differences.

			Total pressure			Heat Flux		Temperature	Velocity Wall Shear Stress
		P2	P3	P4	P5	HF1*	HF2*	HF3*	HF4*	T2*	T3	Vmax	WSS1 WSS2*
	rs	0.31	-0.47	-0.33 -0.02 0.51	0.65	0.86	0.71	0.53	0.44	0.26	0.05 0.52
	p	0.041	0.001	0.002 0.89	<0.001 <0.001 <0.001	<0.001 <0.001	0.003	0.11	0.75 <0.001

Conflict of interest: none


Fatima-Ezahra Annanouch
email: fatima.annanouch@im2np.fr

Gilles Bouchet
email: gilles.bouchet@univ-amu.fr

Pierre Perrier
email: pierre.perrier@univ-amu.fr

Nicolas Morati
email: nicolas.morati@im2np.fr

Christelle Reynard-Carette
email: christelle.carette@univ-amu.fr

Khalifa Aguir
email: khalifa.aguir@im2np.fr

Virginie Martini-Laithier
email: virginie.laithier@im2np.fr

Marc Bendahan
email: marc.bendahan@im2np.fr

Hydrodynamic evaluation of gas testing chamber : Simulation, Experiment

Keywords: Gas sensor, Gas testing chamber, Metal oxides, Tin oxide, Mathematical modeling, gas flow simulation

Gas concentration measurements by means of metal oxide microsensors represent a promising issue due to several advantages (size, low cost, power consumption, reliability…).

However, improvements are required to increase performances of complete experimental systems including microsensor and testing chamber at least. This paper deals with the study of different size and shape configurations of gas testing chamber, by coupling 3D unsteady modelling and experiments in the case of a SnO 2 sensor with ethanol gas flow. The influence of the testing-chamber design on the gas flow hydrodynamics and on the system response is shown. A new 3D-printed prototype chamber (boat-shape design), as compared to the commonly used testing chamber (cross-shape design), leads to an increase of the dynamics, an enhancement of the gas concentration homogeneity and a significant reduction of flow recirculation and dead volumes. In this work we have shown that the optimization of the test chamber (volume and shape) makes it possible to get as close as possible to the real electrical characteristics of the sensor. Consequently thanks to these new achieved characteristics, the performances of the whole system are improved.

Introduction

In the last few years, gas sensors attracted a great attention in numerous application fields such as environmental monitoring, industrial production and safety, medical diagnosis, military and aerospace [START_REF] Gobbi | Rapid diagnosis of Enterobacteriaceae in vegetable soups by a metal oxide sensor based electronic nose[END_REF][START_REF] Galstyan | Porous TiO 2 -Based Gas Sensors for Cyber Chemical Systems to Provide Security and Medical Diagnosis[END_REF][START_REF] Kaushik | Organic-Inorganic Hybrid Nanocomposite-Based Gas Sensors for Environmental Monitoring[END_REF][START_REF] Singh | Flexible Graphene-Based Wearable Gas and Chemical Sensors[END_REF]. These electronic devices offer a wide variety of advantages over traditional analytical instruments such as small size, easy manipulation, low costs and low power consuming [START_REF] Pummakarnchana | Air pollution monitoring and GIS modeling: a new use of nanotechnology based solid state gas sensors[END_REF][START_REF] Wongchoosuk | Portable electronic nose based on carbon nanotube-SnO 2 gas sensors and its application for detection of methanol contamination in whiskeys[END_REF]. Metal oxides represent a very promising material for such kind of applications; they possess a broad range of electronic, chemical, and physical properties that allow them to be widely used and investigated in the detection of volatiles and other gases [START_REF] Mirzaei | Detection of hazardous volatile organic compounds (VOCs) by metal oxide nanostructures-based gas sensors: A review[END_REF][START_REF] Yamazoe | Environmental gas sensing[END_REF][START_REF] Miller | Nanoscale metal oxide-based heterojunctions for gas sensing: A review[END_REF]. In this context, one of the most interesting metal oxide is tin oxide (SnO 2 ), an ntype semiconductor with a direct wide band gap 3.62 eV at 300 K [START_REF] Marikutsa | Nanocrystalline tin dioxide: Basics in relation with gas sensing phenomena. Part I. Physical and chemical properties and sensor signal formation[END_REF][START_REF] Esmaeili-Bafghi-Karimabad | Photo-catalyst tin dioxide: synthesis and characterization different morphologies of SnO 2 nanostructures and nanocomposites[END_REF][START_REF] Vallejos | Aerosol assisted chemical vapour deposition of gas sensitive SnO 2 and Au-functionalised SnO 2 nanorods via a non-catalysed vapour solid (VS) mechanism[END_REF], and a variety of potential applications such as transparent conducting electrodes, solar cells and most importantly in gas sensing technology [START_REF] Behrendt | Highly Robust Transparent and Conductive Gas Diffusion Barriers Based on Tin Oxide[END_REF][START_REF] Ke | Low-Temperature Solution-Processed Tin Oxide as an Alternative Electron Transporting Layer for Efficient Perovskite Solar Cells[END_REF][START_REF] Wang | Low-temperature plasmaenhanced atomic layer deposition of tin oxide electron selective layers for highly efficient planar perovskite solar cells[END_REF][START_REF] Zhang | Room temperature hydrogen gas sensor based on palladium decorated tin oxide/molybdenum disulfide ternary hybrid via hydrothermal route[END_REF][START_REF] Xiao | Improvement of NO 2 gas sensing performance based on discoid tin oxide modified by reduced graphene oxide[END_REF]. The detection mechanism of these sensors relies on the change of the metal oxide resistance induced by absorption or desorption of gas molecules [START_REF] Das | SnO 2 : A comprehensive review on structures and gas sensors[END_REF][START_REF] Roman | Micro and nano transducers for autonomous sensing applications[END_REF].

Most of the published works focused on the enhancement of a sensor response by using nanostructures, catalyst nanoparticles or by the miniaturization of the transducers [START_REF] Annanouch | Aerosol-Assisted CVD-Grown WO 3 Nanoneedles Decorated with Copper Oxide Nanoparticles for the Selective and Humidity-Resilient Detection of H 2 S[END_REF][START_REF] Zhang | Nanostructured Materials for Room-Temperature Gas Sensors[END_REF][START_REF] Roman | Micro and nano transducers for autonomous sensing applications[END_REF].

However, to develop a performing metal-oxide gas-sensor, it is essential to ensure a qualified sensor response measurement.

In addition, note that most of the chemical/physical processes (i.e. mentioned above) occurring at the sensor surface are all influenced by the testing chamber and so it influences the behavior of the sensor in terms of stability, sensitivity and reliability. Lezzi et al. have studied the influence of gaseous species transport on the CO gas sensor responses [START_REF] Lezzi | Influence of gaseous species transport on the response of solid state gas sensors within enclosures[END_REF]. They simulated the filling of the test chamber with CO diluted in air, and the time evolution of the CO concentration at any point inside the chamber. More recently, Viccione et al. have modeled the fluid dynamic behavior of a sensor chamber in order to guarantee homogeneous flow conditions. The average volume fraction of the inflow gas sample nearby the sensor, the stagnant or recirculating zones were discussed as function of the chamber geometry and the injected flow rate [START_REF] Viccione | Fluid Dynamic Simulation of Odour Measurement Chamber[END_REF].

Little efforts have been devoted to the development of optimized testing chambers. Thus, there is a need and a great demand to develop an optimized testing chamber before starting the measurements in order to improve the gas sensor responses (dynamic, amplitude and sensitivity).

In view of the complexity of the transport mechanism as well as the gas concentration diffusion inside the chambers, it is likely that a mathematical modeling will provide an important support for the design optimization studies. This design should remove dead volumes, offer a homogenous gas concentration around the sensor and reduce the gas flow velocity as well as the developments of recirculations. Moreover, the suggested model has to be confronted with experiments in order to determine the discrepancy and to validate the applied model. This paper reports the fabrication, modeling, simulation and experiments of a new chamber design, which is compared to a classical one, used in our laboratory. Experimental studies involving the measurements by means of SnO 2 sensor with ethanol gas, were performed.

Experimental

Gas sensors

SnO 2 sensing layers (50 nm in thickness) were directly deposited by reactive radio frequency (RF) magnetron sputtering over the microsensors platform realized at IM2NP laboratory. The substrates were cleaned with acetone and then with ethanol, dried with air, and then placed inside the shadow mask. A metal target of 99.99% purity with a diameter of 76.2 mm and thickness of 3.18 mm was used. The temperature of the substrate was kept constant during film deposition at room temperature. The sputtering atmosphere consisted of argon (Ar) and oxygen (O 2 ) gas mixture and the RF sputtering power was fixed to 200 W.

The morphology and structure of the obtained SnO 2 films were determined by the deposition conditions parameters and the annealing temperature. More details are found in [START_REF] Lawson-Gadayiglo | New approach to non-invasive monitoring of alcohol by perspiration using MOX multi-sensors[END_REF]. our laboratory [START_REF] Othman | Efficiency of new ozone filters for NO 2 sensing and air depollution[END_REF] and fabricated using clean room facilities and various micro-fabrication steps including photolithography, metallization and backside etching (DRIE) of the substrate to define the membrane. This latter has a size of 400 μm × 400 μm. It carries interdigitated electrodes and two heaters. The gap between the electrodes is 4 μm, the resistance of each heater is 100 Ω and the temperature coefficient is 3 10 -3 /K.

Testing chambers

Gas-sensing tests were carried out in two different chambers. The first one called crossshape chamber (Figure 2) was made of stainless steel with a total volume of 0.3 L and gas flow range between 0.1 L/min and 1.5 L/min. Besides, it has an inlet and an outlet, and the sensor optimal position is at the center, in front of the gas flow direction.

The second chamber (the new one), called boat-shape chamber, is illustrated on Figure 3. It was designed via Sketchup software (Figure 3.a) and fabricated from polylactic acid (PLA) using a 3D printing machine. The total volume was around 2.35 10 -3 L and the gas flow range between 0.01 L/min and 0.5 L/min. It has a boat shape (Figure 3.b) with planar inlet and outlet. Additionally, the optimal sensor position is at the center of the boat back-side, in the same plane as the gas flow direction.

Gas sensing tests

Gas sensing tests were carried out in both testing chambers, using a continuous flow rate of 100 sccm. The sensors were exposed to different concentrations of ethanol vapor, delivered by an autonomous mass flow system, during 1 min and subsequently the chamber purged with air until the initial baseline of the resistance was recovered. The power consumption of each sensor-heater was maintained to 53 mW leading to an optimal working temperature equal to 300 °C. A Keithley 2450 source meter was used to measure the electrical resistance of the sensors. The measuring system (sensor + testing chamber) was kept inside a thermosregulated chamber, in order to control the ambient temperature of the whole system.

The sensor response was defined as R=Ra/Rg, where Ra is the sensor resistance in air at the steady state and Rg represents the sensor resistance after 1 min of the gas mixture exposure [START_REF] Stoycheva | Micromachined gas sensors based on tungsten oxide nanoneedles directly integrated via aerosol assisted CVD[END_REF].

The response time was defined as the time required for the sensor to reach 90% of the sensor response, and the recovery time as the time needed to reach 10% of the initial resistance baseline after the analyte was purged [START_REF] Annanouch | Aerosol-Assisted CVD-Grown WO 3 Nanoneedles Decorated with Copper Oxide Nanoparticles for the Selective and Humidity-Resilient Detection of H 2 S[END_REF].

Results and discussion

Modeling and simulation results

Modeling and simulations are essential steps to be considered during the design and optimization of the testing chamber. Due to the complexity of the gas transport mechanism, it is compulsory to determine its dynamics inside the testing chamber. This study allows us to determine what is happening at the sensor surface level, in term of gas flow velocity, gas flow direction, gas concentration diffusion, etc. For as followed, we assume that the sensor dynamic range is very large compared to that of the flow (i. e. in relation to the temporal and spatial evolutions of the flow transporting the target gas). Additionally, we assume that the sensor does not have any influence on the nature of the gas flow. To know the velocity as well as the path of the gas flow inside the two chambers, we used the multidisciplinary STAR-CCM+ software [START_REF] Fulpagare | Rack level transient CFD modeling of data center[END_REF], which is able to simulate complex industrial problems or physical phenomena. The flow is modeled by a finite volume method solving the 3D unsteady Navier-Stokes equations of a laminar incompressible flow, with no-slip boundary conditions everywhere, except on the inlet and outlet. The Navier-Stokes equations are expressed as the following system of equations (1,2):

(

where u stands for the flow velocity, p the pressure, the kinematic viscosity, the density and t the time.

The boundary conditions were fixed as an inflow in the upstream direction, and an outflow in the downstream limit of the domain. The inflow boundary condition consisted of a uniform velocity profile while the outflow condition lead to set both of the pressure and viscous stresses to zero. This outflow condition, imposed in a weak sense, authorized the disturbances to leave the domain.

The choice of the laminar flow model can be justified by the evaluation of the Reynolds number (3), which is equal to Re= 35 (for a flow rate of 100 sccm, the inlet velocity is equal to 0.13 m/s for a pipe diameter of 4 mm) and consequently much lower than the critical Reynolds number of the order of 2000 [START_REF] Rouvreau | Laminar junction flow at low Reynolds number: influence of the upstream region on the comparison between experiments and calculations[END_REF].

(

) 3
Figure 4 depicts the obtained results. In the cross chamber, the gas flow jet is introduced by the left, through a 4 mm diameter inlet pipe, and then impacted the support of the sensor (perpendicular to the gas flow direction), leading to the occurrence of a recirculation torus around the jet flow (as shown by the streamlines in Figure 4.a). The gas ejected from the torus continued flowing through the entire chamber with trajectories and/or residence times very long (due to the design and the big volume of the chamber). At the end, the gas exited from the outlet in the right side. Because of this geometry, the jet impacted the sensor surface with a high velocity around 0.1 m/s, the induced recirculations had long residence times and the presence of dead volumes limited the dynamics of the flow.

To overcome these drawbacks, the dynamics of the testing chamber must be decreased and the gas residence time should be increased. For this purpose, we suggested the boat chamber, which was already described in section 2.2. Figure 4.b shows the velocity simulation results. The velocity at the sensor surface is almost zero. There were no recirculations around the sensor except small ones produced from the sudden expansion of the flow at the entrance of the chamber (unavoidable due to encumbering). Moreover, the dead volumes and the residence times were highly reduced compared to the cross chamber.

Another parameter which is important during the testing chamber conception: is the gas concentration diffusion. It allows us to know the temporal evolution of the target gas concentration at the sensor surface. Based on this information, we can get an idea about the true gas concentration detected by the sensor and its real experimental response.

For this matter, the target gas concentration was simulated by a passive scalar injected at the upstream of the test chamber. Its value can vary between 0 and 1 (in our case, the value 1 correspond to 50 ppm of ethanol). The passive scalar transport is modeled by solving a convection -diffusion equation ( 4).

(

) 4
where c is the value of the passive scalar and D is the diffusion constant of ethanol in air.

The resolution of the coupled Navier-Stokes and convection-diffusion equations permits us to know the ethanol concentration at any time and whatever point inside the test chamber.

Therefore, the gas concentration will be followed at a point located in the center of the sensor surface.

The target gas (experimentally air with 50 ppm of ethanol, numerically modeled by a passive scalar of value 1) was injected at the entrance of the computational domain (a few centimeters upstream of the entrance in the test chambers) at t = 134 s, which we can considered as the beginning of gas exposure (t = 0 s). Figure 5.a shows the evolution of the gas concentration in both chambers as a function of time.

For the cross chamber, after a short delay of 5 s due to the arrival in the test chamber and the crossing through the upstream pipe of the cross chamber, a sharp slope between t = 5 s and t = 10 s was formed, which corresponds to the convection of the passive scalar by the flow.

In this first step, the gas concentration was about 10 ppm, which can be explained by the establishment of the Poiseuille velocity profile in the circular pipe, and also by the widening of the flow inside the enormous dead volume of the chamber (sudden expansion). Beyond t = 10 s, a slower increase of the curve, towards 25 ppm of ethanol, was noticed, due to the convection of the passive scalar induced by the recirculation torus and the slow progressive filling of the cross chamber. After 60 s, we stopped the injection of the passive scalar (no more injection of ethanol): we observed then a decrease of the curve with two different slops. The first one (sharp slope), corresponds to the extinction of the passive scalar and the second one (slower slope), results from the emptying of the cross chamber (big volume and a lot of dead volumes). For the new design model, the behavior of the passive scalar value on the sensor surface was very different from that of the cross chamber. As shown in Figure 5a, from the beginning of the injection (after the delay similar to that of the cross chamber), the ethanol concentration reached rapidly the set point value (50 ppm) in less than 2 s and remained stable throughout the injection time (60 s). After that, when the injection was stopped, the gas concentration dropped instantaneously to zero (due to the emptying of the weak volume of the boat chamber with nearly without dead volume). Thus, the new design has highly enhanced the dynamics of the filling and emptying of the chamber. Besides, the set point concentration can be attained rapidly.

As mentioned in section 2.2, the cross-chamber volume is about 100 times larger than that of the boat one. In order to verify whether chambers with equal volumes and different shapes would contribute greater to find out the dynamics of the gas flow and the optimal setups for testing sensors, we modeled the flow in a small cross-chamber (volume equal to 0.00235 L). Figure 5b depicts the obtained results. The shape effect was always present, the slope was initially greater in the case of the small cross-chamber, while the maximum concentration (50 ppm) was rapidly obtained in the case of the boat-chamber (about four times faster).

In order to achieve 50 ppm of ethanol using the cross chamber, we have increased the exposure time to 4 min and we have tested three different flow rates: 100, 250 and 500 sccm. The obtained simulation results are depicted in Figure 6. As we can observe, we need more than 4 min to reach 50 ppm of ethanol. In contrast, this time can be reduced by increasing the flow rate.

Experimental results (validation)

SnO 2 thin film has been successfully deposited onto the sensor transducer, via RF magnetron sputtering technique. More details about the sensing layer deposition have been provided in the previous section 2.1. It is worth noting that all the experimental measurements were realized by using these fabricated sensors.

Herein, we exposed our sensor to 50 ppm of ethanol, during 60 s, using only the best and the worst configurations, respectively Boat chamber (0.00235 L) and Cross chamber (0.3 L).

Figure 7 displays the sensor responses as a function of time. In the boat chamber, the responses were highly enhanced, with fast response and recovery times (4 s and 89 s, respectively). In contrast, in the cross chamber, the sensor dynamics were undoubtedly hided by the dynamics of the flow. Additionally, the response and recovery times were five times higher than those of the boat chamber.

Based on the simulation results (Figure 5), it is clear that the sensor followed the gas concentration diffusion behavior inside the chambers. Indeed, in the boat one, the responses were corresponding to 50 ppm of ethanol, however in the cross one, the responses were answering to only 25 ppm of ethanol, due to the effects of the size and the design of the chamber. In this case, it would take more than 10 minutes to reach the 50 ppm target.

Thus, there is a good accordance between the experimental and the simulations results, which successfully validates the proposed boat-shaped chamber model.

Figure 8 displays the sensor responses for three different concentrations of ethanol ranging from 1 ppm to 10 ppm, as a function of time, in both chambers. From these results, it is evident that using the new design, the sensor responses are better (higher amplitude/value) whatever the tested concentration. This allows us to quantify smaller concentrations of ethanol with higher sensitivities and faster responses. Besides, these results demonstrated how much the testing chamber can influence the sensor behavior and its metrological characteristics (response amplitude, response time, sensitivity, detection limit).

Figure 9 shows the sensor response as a function of ethanol concentration in the range of 1 to 50ppm. The responses follow a power function behavior which is common for semiconductors metal oxide gas sensors. Indeed, when the concentration is increased, the response curves toward the x abscissa direction. For the boat chamber, the sensor responses increased from 2.7 to 11, for an interval of concentration ranging from 1 ppm to 50 ppm of ethanol. In contrast, a small change of the response was seen in the case of a cross chamber (i.e. from 1.2 to 4.5). These results are in agreement with the hydrodynamic model discussed previously. Indeed, in the case of the cross chamber, hydrodynamics can only achieve about 50% of the injected concentration.

We have exposed our sensor towards 25 ppm of ethanol inside the boat chamber, using different injection times of 1 s, 5 s, 10 s, 20 s and 30 s. In parallel, we have modeled these injections using the boat chamber model (to be closer to the experimental conditions, we replaced the Heaviside function for the introduction of the passive scalar by a slope of few seconds to reach the maximum). The obtained results are depicted in Figure 10. Clearly, there is a good agreement between the proposed chamber model and the real sensor responses towards different ethanol exposure times. The dynamics of the gas transport coordinates very well with the real behavior of the sensor. It is worth noting that the sensor reached the steady state after 10 s of exposure. Consequently, with the boat chamber, the exposure time could be decreased.

As it is mentioned before in section 2.2, the boat chamber was fabricated from PLA using the three-dimensional printing machine. In order to study the PLA walls adsorption effect on the gas sensor responses, we have realized a second chamber, from stainless steel (INOX), with similar design and dimensions. After that, we have carried out measurements with the same sensor in both chambers (PLA and INOX) using 25 ppm of ethanol during 1 min. Figure 11 depicts the obtained results. We can observe that there is no difference between the obtained curves. We have exactly identical response amplitudes with similar response and recovery slopes. Thus, the adsorption and desorption phenomena at the PLA test chamber walls seem negligible and do not affect the sensor response. Despites, it is worth noting the excellent repeatability of the sensor responses.

Conclusion

In this work, we showed how the testing chamber design can affect the real behavior of the gas sensor. We proceeded by using two different approaches: numerical and experimental.

In the first one, we demonstrated that the cross chamber suffered from many defects such as the presence of recirculations, a lot of dead zones and the perpendicular position of the sensor with respect to the flow, which hided the real sensor response. Moreover, we founded that the new design (boat chamber) solved all these problems and increased a lot the chamber dynamics.

In the second approach, we observed a good accordance between the numerical and the experimental results. The sensor showed excellent results using the boat chamber in contrary to the cross one. The sensor detected very small concentrations of ethanol (1 ppm) with good sensitivity, the detection limits shifted toward ppb level and the response and recovery times were highly fast (4 s and 89 s, respectively). Finally, we demonstrated that the adsorption and desorption phenomena at the PLA test chamber walls seem negligible and do not affect the sensor response.

Highlights

The influence of the testing chamber design on a gas sensor response Modeling and simulation of the gas transport mechanism inside a testing chamber for gas characterization.

Modeling of a gas flow by a finite volume method solving the 3D unsteady Navier-Stokes equations High sensitive SnO2 ethanol sensor *Research Highlights

Figure 1

 1 Figure 1 depicts the microelectromechanical systems (MEMS) based microsensor platform

Figure. 1 .FigureFigure 2 .

 12 Figure. 1. MEMS-based microsensor platform (patent FR 13 59494, 2013 -US20160238548A1, 2016)

Figure 3 .Figure 4 .Figure 5 .

 345 Figure 3. Design in the left-hand section (a) and Photographs of the boat chamber in the right-hand section (b)

Figure 6 .

 6 Figure 6. Ethanol volume fraction (set up ethanol concentration/ real ethanol concentration) simulation in the cross chamber (0.3 L) versus time injection for different gas flows: 100-250-500 sccm

Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 .

 7891011 Figure 7. Experimental gas sensor responses toward 50 ppm of ethanol with an injection duration of 60 s, using

Acknowledgments:

The authors would like to acknowledge NANOZ, a company specialized in gas sensors; SATT Sud-Est, "Accelerator of Technology Transfer", which is a key player in regional economic development associated with innovation and Mr. T. FIORIDO for his technical support.

Conflicts of Interest:

The authors declare no conflict of interest.

Corresponding author: Prof. Marc Bendahan, marc.bendahan@im2np.fr; Tel.: + 33 (0)4 91 28 91 55