Resende De Azevedo

Fabienne ⁎ Letourneau

Ré Maria Inês

Antisolvent crystallization of a cardiotonic drug in ionic liquids: Effect of mixing on the crystal properties

Keywords:

) is a poorly soluble drug which has been proposed to have major advantages over other cardiotonic drugs. Poorly water soluble drugs present limited bioavailability due to their low solubility and dissolution rate. An antisolvent crystallization processing can improve the dissolution rate by decreasing the crystals particle size. However, LASSBio-294 is also poorly soluble in organic solvents and this operation is limited. In order to open new perspectives to improve dissolution rate, this work has investigated LASSBio-294 in terms of its antisolvent crystallization in 1-ethyl-3methylimidazolium methyl phosphonate [emim][CH 3 O(H)PO 2 ] as solvent and water as antisolvent. Two modes of mixing are tested in stirred vessel with different pre-mixers (Roughton or T-mixers) in order to investigate the mixing effect on the crystal properties (crystalline structure, particle size distribution, residual solvent and in vitro dissolution rate). Smaller drug particles with unchanged crystalline structure were obtained. Despite the decrease of the elementary particles size, the recrystallized particles did not achieve a better dissolution profile. However, this study was able to highlight a certain number of findings such as the impact of the hydrodynamic conditions on the crystals formation and the presence of a gel phase limiting the dissolution rate.

Introduction

Poorly soluble drugs present limited bioavailability due to their low solubility and dissolution rate, and several strategies have been developed in order to find ways to improve them. Crystallization techniques are widely used in the pharmaceutical industry and antisolvent crystallization has been used to reduce the particle size in order to increase drug dissolution rate [START_REF] Zhao | Controlled liquid antisolvent precipitation of hydrophobic pharmaceutical nanoparticles in a microchannel reactor[END_REF][START_REF] Zhang | Micronization of atorvastatin calcium by antisolvent precipitation process[END_REF][START_REF] Dong | Preparation and characterization of spironolactone nanoparticles by antisolvent precipitation[END_REF]. In this method, the drug is dissolved in the solvent and the formed solution is poured to the antisolvent. This mixing generates high supersaturation that subsequently induces nucleation, simultaneous growth, and possibly agglomeration of crystals. The properties of the final crystalline product such as size, morphology and purity are significantly dependent on the rate, magnitude and uniformity of supersaturation generated during crystallization. Fig. 1 summarizes the main operating parameters and phenomena (nucleation, growth and agglomeration) influencing the crystals properties.

Pharmaceutical drugs are generally crystallized from organic solutions using an antisolvent crystallization technique. However, there is a general consensus in limiting the use of organic solvents because of their negative environmental and health impact. The introduction of alternative solvents such as supercritical fluids [START_REF] Kroon | Crystallization of an organic compound from an ionic liquid using carbon dioxide as anti-solvent[END_REF] and ionic liquids [START_REF] Mizuuchi | Room temperature ionic liquids and their mixtures: potential pharmaceutical solvents[END_REF][START_REF] Smith | Solubilities of pharmaceutical compounds in ionic liquids[END_REF][START_REF] Lourenço | Solubility advantage of Pyrazine-2-carboxamide: application of alternative solvents on the way to the future pharmaceutical development[END_REF][START_REF] Forte | A favourable solubility of isoniazid, an antitubercular antibiotic drug, in alternative solvents[END_REF][START_REF] Vicosa | An innovative antisolvent precipitation process as a promising technique to prepare ultrafine rifampicine particles[END_REF][START_REF] Melo | Ammonium ionic liquids as green solvents for drugs[END_REF] opens new opportunities for the pharmaceutical industry, and also reduces the disadvantages of traditional volatile organic compounds.

Ionic liquids (ILs) are solvents that consist entirely of ions, differently from molecular solvents consisting of only neutral molecules and salt solutions consisting of ions and molecules. ILs are composed of a relatively large asymmetric organic cation and an inorganic or organic anion. The asymmetry of the cation is responsible for low lattice energies of ILs and their liquid state at ambient conditions. In general, they are thermally stable, nonflammable and exhibit very low vapor pressure. The application of ionic liquids as solvents in the crystallization processing of pharmaceutical drugs is still relatively unexplored, which results in a low number of studies in the literature. To the best of our knowledge, the drugs concerned by these studies are methyl-(Z)-α-acetamidocinnamate [START_REF] Kroon | Crystallization of an organic compound from an ionic liquid using carbon dioxide as anti-solvent[END_REF], paracetamol [START_REF] Smith | Crystallisation control of paracetamol from ionic liquids[END_REF][START_REF] Smith | Crystallisation of active pharmaceutical ingredients using ionic liquids[END_REF][START_REF] Weber | The use of cooling crystallization in an ionic liquid System for the purification of pharmaceuticals[END_REF], ibuprofen and flufenamic acid [START_REF] Smith | Crystallisation of active pharmaceutical ingredients using ionic liquids[END_REF], adefovir dipivoxil [START_REF] An | Application of ionic liquid to polymorphic design of pharmaceutical ingredients[END_REF][START_REF] An | Antisolvent crystallization using ionic liquids as solvent and antisolvent for polymorphic design of active pharmaceutical ingredient[END_REF], rifampicin [START_REF] Vicosa | An innovative antisolvent precipitation process as a promising technique to prepare ultrafine rifampicine particles[END_REF] and vancomycin [START_REF] Ha | Effect of an ionic liquid on vancomycin crystallization[END_REF]. Among them, the antisolvent crystallization of rifampicin using 1-ethyl-3-methylimidazolium methyl phosphonate [emim][CH 3 O(H)PO 2 ] resulted in ultrafine amorphous particles with faster dissolution rate.

LASSBio-294 (3,4-methylenedioxybenzoyl-2-thienylhydrazon) is a new bioactive molecule which has been proposed in an attempt to develop new therapies to simplify the treatment of cardiovascular diseases [START_REF] Lima | Synthesis and analgesic activity of novel N-acylarylhydrazones and isosters, derived from natural safrole[END_REF][START_REF] Barreiro | Estratégia de simplificação molecular no planejamento racional de fármacos: a descoberta de novo agente cardioativo[END_REF]. However, as a hydrophobic drug, it exhibits a low solubility and dissolution rate in the gastro-intestinal tract, which limits its effective absorption and bioavailability after oral administration. An improvement of the bioavailability should reduce considerably the dose of the drug to be administered.

Antisolvent crystallization has been used to improve dissolution rate by decreasing the drug crystals particle size. For pharmaceutical drugs poorly soluble also in organic solvents such as LASSBio-294 this operation is limited. However, our group has determined the solubility of LASSBio-294 in seven different imidazolium based ionic liquids and in binary mixtures of water/ILs and this compound showed sufficient solubility in five of the tested ILs, 1-ethyl-3-methylimidazolium methyl phosphonate [emim][CH 3 O(H)PO 2 ] among them [START_REF] Azevedo | Solubility of a new cardioactive prototype drug in ionic liquids[END_REF]. Based on these results, the objective of the present study was to investigate LASSBio-294 in terms of its antisolvent crystallization in 1-ethyl-3-methylimidazolium methyl phosphonate [emim][CH 3 O(H)PO 2 ] as solvent and water as antisolvent and under various preparation conditions. The influence of the mixing mode of the drug solution (ionic liquid-drug) and the antisolvent (water) and the solute concentration in the solvent have been studied. In order to get a fast and homogeneous mixing to obtain uniform distribution of concentration and so small crystals, two pre-mixers (Roughton and T-mixer) were used. A reference experiment without pre-mixer was conducted for comparison. The end crystals properties are particle size distributions, crystalline structure, residual solvent in crystals and in vitro dissolution.

Materials and methods

Materials

The LASSBio-294 was obtained from Cristália Ltda (Itapira, SP, Brazil) and used without further purification. It is in the form of a yellowish solid with a molecular weight of 274.3 g/mol and 99.96% purity. The ionic liquid, 1-ethyl-3-methylimidazolium methyl phosphonate ([emim][CH 3 O(H)PO 2 ]), was obtained from Solvionic (Toulouse, France) and it was used as received ( > 98% pure). Sodium dodecyl sulfate (SDS) was supplied by VWR International (Leuven, Belgium). HPLC grade acetronitrile (Scharlau SL, Spain), methanesulfonic acid (MSA) (Fluka, Buchs, Switzerland) for ion chromatography were used to prepare the mobile phases. Sodium dihydrogen phosphate (NaH 2 PO 4 ) (Sigma-Aldrich, Gillingham-Dorset, England) and sodium hydrogen phosphate (Na 2 HPO 4 ) (Alfa Aesar, Karlsruhe, Germany) of analytical grade were used to prepare the buffers and mobile phases. Water was distilled and purified using Milli-Q Water Purification System (Purelab Classic DI MK2, Elga, UK).

Methods

Crystallization method

First, a LASSBio-294 solution with defined concentration (57, 91 or 159 ± 1 mg LASSBio-294/g solution) was prepared in [emim] [CH 3 O(H)PO 2 ] as solvent at 30 ± 0.5 °C. The anti-solvent crystallization was conducted in a stirred vessel. The stirred vessel has a volume of 200 mL (diameter 6.3 cm), with double jacket equipped with a mechanical turbine stirrer with 8 blades mounted on flat disc throughout the operation. The temperature at 25 ± 0.5 °C was controlled by a water bath (Julabo VC F30). Agitation at 800 rpm was powered using a mechanical stirrer (Eurostar IKA labortechnick 2000 motor). Based on preliminary tests and solid-liquid equilibrium of our ternary system, mass ratios water/[emim][CH 3 O(H)PO 2 ] between 12.5 and 13.9 were used [START_REF] Azevedo | Etude de la cristallisation d′une nouvelle molécule à efficacité cardiotonique dans un mélange liquide ioniqueeau[END_REF]. After 30 min, the particle size distributions were determined. The suspension resulted was filtered (pore size 0.2 µm, polypropylene, Milipore, Bedford, MA, UK). The filter cake was washed with water (500g) to remove the residual solvent. The crystals were dried in vacuum oven (Heraeus Vacutherm-VT-6025) at 50 °C for 3-5 days and then further characterized in terms of crystal structure, morphology, residual solvent and in vitro dissolution. Operating conditions are given in Table 1.

Two mixing mode of solution and antisolvent were tested: a) Indirect addition: the simultaneous addition of the LASSBio-294-[emim][CH 3 O(H)PO 2 ] solution and water in stirred vessel is carried with a pre-mixer (Fig. 2(a)). Initially, water is present in the stirred vessel in order to allow agitation of the suspension leaving the premixer. Note that it induces the creation of a new supersaturation. Two types of pre-mixers, Roughton and T-mixer, were manufactured on the basis of the work of Lindenberg et al. [START_REF] Lindenberg | Experimental characterization and multi-scale modeling of mixing in static mixers[END_REF]. The Roughton mixer has an inlet tube of 1 mm diameter, a mixing chamber diameter of 3 mm and its outlet tube a diameter of 1.75 mm and a length of 15 mm (Fig. 2(b)). The T-mixer has two radial entries with a diameter of 1 mm and its outlet tube has a diameter of 2 mm with a length of 17.5 mm (Fig. 2(c)). Organic and aqueous phases were introduced into the pre-mixer with an infusion pump (Harvard PHD 2000 Infusion, USA) at 40 mL/ min. The maximum supersaturation ratio into pre-mixer is noted S pre-mixer (Table 2). b) Direct addition: the organic solution is introduced rapidly into a stirred vessel containing water. The maximum supersaturation ratio into stirred vessel is noted S stirred vessel (Table 2). Particle size analysis. Mean particle size and particle size distribution were determined by laser diffraction using a Mastersizer 3000 (Malvern Instruments. UK). At the end of synthesis (30 min), a few drops of suspension were added directly into the tank of the laser diffractometry containing water until the laser obscuration level was in the desired range (5-15%). A refractive index of 1.520 was used for the particles (by default use) and 1.33 for the continuous phase (water). The samples circulated in the measuring cell using the instrument's internal stirring system (2200 rpm) and with the help of an ultrasonic probe. Results were expressed as volume percentage (%) according to the particle size diameter (μm). The mean surface diameter, D 2.2.2.5. Dissolution. Dissolution studies were performed assuring sink-conditions (maximal concentration lower than the third of the equilibrium concentration) according to the paddle method (USP) using an Erweka DT60 dissolution apparatus (Erweka, Germany). The stirring speed used was 50 rpm, and the temperature was maintained at 37 ± 0.5 °C (n=3). The dissolution medium (900g) was phosphate buffer pH 7.4 containing SDS 0.5%. This phosphate buffer consisted of The percentage of the dissolved drug was calculated with the ratio between LASSBio-294 dissolved mass for a given time and LASSBio-294 initial mass.

Results and discussion

The experiments were designed to determine, at the end of synthesis, the influence of the mixing mode and the initial solute (drug) concentration on the following properties of the dry solid: particle size distribution, morphology and residual solvent. The experimental yields are higher than 85% but less than the theoretical yield of 99% (Table 1). The theoretical yield is calculated from a mass balance assuming that, in the end of the operation and at the experiment temperature, the solution is saturated. The difference between theoretical and experimental yields is partly caused by the solid's waste into the stirred vessel. X-ray powder diffractograms (Fig. 3) showed that the synthesized LASSBio-294 is crystalline like the raw drug, even if changes in peak relative intensities could be observed in 2θ range 24-27° [START_REF] Azevedo | Etude de la cristallisation d′une nouvelle molécule à efficacité cardiotonique dans un mélange liquide ioniqueeau[END_REF].

Influence of the mixing mode

The influence of the mixing mode is observed with experiments 1, 2 and 3 (Table 1). The mean sizes of the dry solid (D 4,3 and D 3,2 ) are smaller than the initial solid (D 4,.3 =57.9 µm and D 3,2 =29.5 µm). The mean volume size (D 4,3 ) obtained without pre-mixer is higher than those obtained with pre-mixer, but the amount of residual solvent is lower (6920 ppm against amounts higher than 19470 ppm). The mean surface size (D 3,2 ) is unchanged. Particle size distributions and morphologies of the crystals after 30 min of the synthesis are shown in Fig. 4. They present a first peak of less than 1 µm and a second one between 12 and 100 µm corresponding to at least two populations (Fig. 4(a)). Observing the SEM images, the first peak could be attributed to the elementary particles and the second one to the agglomerates. The first peak seems to have always the same width, only its intensity varies: it is identical when using a pre-mixer and less intense when working with a direct addition. SEM images also show that the crystal habit appears to be related to some residual solvent content (Fig. 4(b),(c),(d)): Higher the residual solvent, less defined the edges of the crystals. Therefore, the crystals have a waxy appearance, as already observed in the case of rifampicin [START_REF] Vicosa | An innovative antisolvent precipitation process as a promising technique to prepare ultrafine rifampicine particles[END_REF].

Influence of the initial drug concentration with pre-mixer

The study of the drug concentration in solution was performed with the Roughton mixer (experiments 1, 4 and 5, Table 1). The mean sizes (D 4,3 and D 3,2 ) are identical for two different conditions (91 and 159 mg LASSBio-294/g solution) and slightly lower for the third condition (57 mg LASSBio-294/g solution). The bimodal particle size distributions are shown in Fig. The intensity of the first peak decreases by increasing the initial concentration; in contrast, the second peak remains unchanged regardless the concentration (Fig. 5(a)). Increase of the first peak intensity comes primarily from the supersaturation increase, which induces an increase of the nucleation rate when increasing the initial concentration. The S pre-mixer ranges between 2400 and 8200 (Table 2). The residual solvent decreases as the initial concentration decreases. The crystal habit is always related to some residual solvent content (Fig. 5(b),(c),(d)).

Mixing time and crystals formation mechanism

The mixing time, t mix (s), into Roughton mixer and the macromixing time into the stirred vessel (t macro, turbulent ) were estimated and compared with the induction time (t ind ). The t mix (s) into Roughton mixer is calculated from the equation [START_REF] Lindenberg | Experimental characterization and multi-scale modeling of mixing in static mixers[END_REF]:

where d j is the inlet diameter in the pre-mixer (1 mm), ν the kinematic viscosity after complete mixing and u j the average speed. For a solvent/ anti-solvent ratio different from 1, u j is calculated assuming an equivalent kinetic energy.

For the calculation of the t macro, turbulent into stirred vessel, it was assumed a complete mixing of the two solutions without considering the solid formation (% solid mass to the final time < 2). It is obtained by the following relationship [START_REF] Mersmann | Crystallization Technology Handbook[END_REF]:

⎛ ⎝ ⎜ ⎞ ⎠ ⎟ t T ε =7. 3 macro turbulent , 2 1/3 (2)
where ε is the average power (W) calculated by ε N u D = ( )

π P D T D H 4 3 2 2 with
u the rotation speed of the agitator(s -1 ), N p the power number of the agitator, D the diameter of agitator (m), H the liquid height into the stirred vessel (m) and T the vessel diameter (m). Macromixing time will be greater in the case of a laminar flow. The t ind (s) was estimated from the molecular diameter of the solute d m (m), the supersaturation S and the diffusion coefficient D AB (m 2 /s) [START_REF] Mersmann | Crystallization Technology Handbook[END_REF]:

t d D S = 80 ln ( ) ind m AB 2 (3)
In all cases, given the supersaturation values, the t ind (10 -4 ms) were very low compared with the t mix . Therefore, it could be concluded that the crystal formation process is controlled by the mixing between drug solution and antisolvent.

During the solubility studies, it was found that a gel phase could be formed beyond a certain solute concentration in the ionic liquid [START_REF] Azevedo | Solubility of a new cardioactive prototype drug in ionic liquids[END_REF]. The appearance of crystals observed on the SEM images suggests that the particles obtained are fluid aggregates frozen from a completely segregated mixture. These particles would consist of a gel phase being formed during the mixing of the two phases, however, a crystalline phase was detected by X-ray diffraction. Washing the crystals with a greater quantity of water can change crystal habit. It seems that the gel phase is present at crystals surface.

It would also seem that when the mixing is fast and the initial LASSBio-294 concentration is high, the residual solvent in the final particles is higher. From our experiments we show that, during the process, crystals and gel are formed due to the mixing of the two phases (Fig. 6). It is not possible to determine what phases are formed first. An intense mixing and high concentration of solute seems to favor the gel formation.

Dissolution studies

The in vitro dissolution profiles of raw and recrystallized LASSBio-294 (Experiment 1, residual solvent highest) are compared in Fig. 7. The in vitro dissolution tests were carried out in triplicate. The standard deviation calculated was reported on the figure. The recrystallized LASSBio-294 dissolved significantly slower than the raw LASSBio-294. Both profiles are statistically different for 60 min dissolution test. For example, after 30 min, 31% of the recrystallized drug and 75% of the original crystals are dissolved. The LASSBio-294 is very slightly soluble in water. Its solubility in aqueous medium with SDS 0.5% is improved by micellar solubilisation. Furthermore, the presence of the surfactant reduces the solid-liquid interfacial tension and increases the LASSBio-294 crystals wettability. These effects enhance the dissolution of the LASSBio-294 and could explain the high dissolution rate of the original crystals. Despite a lower mean size, the slower dissolution of the recrystallized drug can be explained by the gel phase presence, which probably slowed the mass transfer and therefore the aggregates dissolution.

Conclusion

In the present study we examined the antisolvent crystallization of a new hydrophobic drug using an ionic liquid as solvent. Despite obtaining a finer powder, the recrystallized drug in vitro dissolution is slower than that of the unprocessed drug crystals. This behavior could be due to a gel phase formation when the drug solution is mixed with the antisolvent. This gel phase induces the appearance of aggregates which are difficult to disperse. A rapid mixing and high initial drug concentration in the organic phase seem favors the gel phase formation and leads to the formation of synthesized particles ILs open new opportunities for the pharmaceutical industry as alternative solvents. However they introduce new difficulties into an antisolvent crystallization method related to the presence of a new gel phase (not observed in the presence of traditional volatile organic solvents) that can slower the dissolution of the recrystallized drug particles even if are smaller in size. Its formation is a limiting parameter and has to be controlled in the process. Therefore, the use of ionic liquids can open future investigations for the pharmaceutical drugs recrystallization keeping in mind the need of control of the gel phase formation. New ways along this line to limit the gel phase formation could be a direct addition of the drug solution in the antisolvent phase. This mode of addition would allow each drop of organic solution to disperse more easily into the aqueous phase before the gel phase formation. Our work in going on to check for these assumptions.

Fig. 1 .

 1 Fig. 1. Main operating parameters (mixing and supersaturation) and phenomena (nucleation, growth and agglomeration) having an impact on crystals properties.

2. 2

 2 .2.4. Residual solvent. A Dionex model ICS-3000 ion chromatograph was applied for determining residual solvent in the crystal by the quantification of cation-IL. This system consists of an autosampler, a degasser, pumps and conductometric detector. A Dionex suppressor LERS 500 (4 mm) for chemical suppression was installed between the conductometric detector and the Dionex IonPac CS17 analytical column (250 mm x 4 mm). A Dionex IonPac CG17 (50 mm x 4 mm) guard column was also installed. The samples were eluted by isocratic elution with acetonitrile-MSA 20 mM mixtures (20:80 (w/w)) at a flow rate of 1.0 mL/min. An injection volume of 25 μL was used. All chromatographic analyses were carried at 35 ± 0.5 °C. Cation-IL concentration in the crystals was determined from solutions prepared with 100% acetonitrile. The concentrations were calculated with linear regression equation (Peak area (μS/min) =0.0165 C (μg/g solution) -0.0495, R 2 =0.9954) obtained with the linear ranges of calibration curve between peak area and the concentration (0.6-144 μg/g solution).

Fig. 2 .

 2 Fig. 2. Scheme of the experimental process to prepare LASSBio-294 particles with premixer (a) and illustrations of the Roughton (b) and (c) T pre-mixers.

Fig. 3 .

 3 Fig. 3. X-ray powder diffractograms of raw LASSBio-294 and recrystallized samples.

Fig. 4 .

 4 Fig. 4. Particles size distribution and SEM images for recrystallized LASSBio-294: Influence of the mixing mode. Roughton mixer, experiment 1 (a) filled diamond and (b) with 23 644 ppm at residual solvent; T-mixer, experiment 2 (a) empty circle and (c) with 19 470 ppm at residual solvent; Without pre-mixer, experiment 3 (a) empty square and (d) with 6920 ppm at residual solvent.

Fig. 5 .

 5 Fig. 5. Particles size distribution and SEM images for recrystallized LASSBio-294: influence of the initial drug concentration. 159 mg/g, experiment 1 (a) filled circle and (b) with 23 644 ppm at residual solvent; 91 mg/g, experiment 4 (a) empty square and (c) with 4 271 ppm ppm at residual solvent; 57 mg/g, experiment 5 (a) filled triangle and (d) with 2 708 ppm at residual solvent.

Fig. 6 .

 6 Fig. 6. Mechanism of formation of crystals: (a) mixing and transfer of solvent and antisolvent, (b) formation of crystals and gel, (c) decrease of phase gel after washing.

Fig. 7 .

 7 Fig. 7. Dissolution kinetic profiles for raw and recrystallized LASSBio-294 (testing conditions: SDS 0.5%, pH 7.4 at 37 ± 0.5 °C, n=3). Filled square (raw LASSBio-294), Empty circle (recrystallized LASSBio-294, Experiment 1).

Table 1

 1 Process conditions and products characteristics.

	Experiment number	Raw drug	1	2	3	4	5
	Concentration (mg/g solution)		159	159	159	91	57
	Water/IL ratio		13.7	13.7	13.9	13.0	12.5
	Mixing mode		Roughton	T-mixer	Without mixer	Roughton	Roughton
	Residual solvent (ppm)	0	23644	19470	6920	4271	2708
	D 4,3 ( ± 1) (µm)	57.9	9.0	8.0	14.0	9.0	6.0
	D 3,2 ( ± 1) (µm)	29.5	2.0	2.0	3.0	2.0	1.5
	Crystallization yield (%)		93.0	88.0	91.1	95.3	85.1

2.2.2. Characterization of products 2.2.2.1.

Table 2 t

 2 ind and t mix values into the pre-mixer and the stirred vessel. Diffusion coefficient of the LASSBio=9.6x10 -11 m 2 /s into stirred vessel and 4.9×10 - 11 m 2 /s into the pre-mixer, diameter molecular of the solute =8.4×10 -10 m.

		Pre-mixer		Stirred vessel
	Experiments	S pre-mixer t ind *	t mix (ms) S stirred vessel t ind *	Re A	t mix (s)
	number		10 4		10 4
			(ms)		(ms)
	1	8126	1.27 0.292 ***
	2	8443	1.26	>
	3	-	-	0.292 ** -14918	0.62 1801 1.21 ****
	4	4256	1.38 0.294 ***
	5	2451	1.48 0.299 ***
	Properties used:
	** Kinematic viscosity after complete mixing: 10 -5 m 2 /s and average speed: 0.52 m/s.
	**** Diameter of the stirred vessel: 0.063 m, Diameter of the agitator: 0.027 m, Liquid
	height: 0.05 m, Agitation rate: 800 rpm, Dynamic viscosity: 5.10 -3 Pa.s, Volume of the
	solution: 0.146 L, Power number of the agitator (function of the Reynolds number of the
	agitator ReA): 4. Despite an intermediate hydrodynamic regime (10 < ReA < 10 4 ), a
	constant power number and equal to 4 was chosen. Indeed, in the Reynolds number
	range of our agitator, this number varies little with power [21].

* ** Not calculated. *

Acknowledgment

The authors would like to thank Cristália Ltda (Itapira, São Paulo, Brazil) for providing the drug LASSBio-294 and CNPq (Brazilian National Research Council) for doctoral fellowship to ResendeAzevedo J. (Proc.200835/2010-6).


François-Xavier De Vaujany
email: devaujany@dauphine.fr

Jeremy Aroles
email: jeremy.aroles@manchester.ac.uk

Pierre Laniray
email: planiray@poitiers.iae-france.fr

Towards a Political Philosophy of Management: Performativity & Visibility in management practices 1

Keywords: Performativity, Visibility, Management practices, Merleau-Ponty, Austin

 in order to show how everyday activity both performs and makes visible the world.

From that perspective, modes of visibility appear as emergent conditions of possibility of performativity itself. We draw some implications for the conceptualization of management practices.

Introduction: Performativity… a disembodied process?

This paper is concerned with the tensions between 'immanent' and 'transcendental' stances and the implications of these tensions for the field of Management and Organisation Studies (MOS). More precisely, we position our paper as an attempt to momentarily 'reconcile' these two stances through a focus on the concept of performativity (sensu Austin) and the Merleau-Pontian concepts of visibility/invisibility and continuity/discontinuity. We set to develop another view of performativity (either complementary or interrelated to an immanent stance), one that re-introduces transcendence in the analysis and yet sees in it something dialogical to the process itself. By drawing from the concepts of visibility/invisibility and continuity/discontinuity [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]/2013[START_REF] Merleau-Ponty | Le Visible et l'Invisible[END_REF], we set out to show how everyday activity both performs and 'makes visible'. Modes of visibility appear as processual conditions of possibility of performativity itself. Such position could consist in seeing organizing processes as constituting the conditions of possibility of their own perception and actions in the flow of everyday activities themselves. What is visible or invisible, continuous or discontinuous in the joint assemblage of people and objects involved in the flow of organizing becomes a key issue in the process of becoming itself, its intercorporeity and emotional dynamic [START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF].

Adopting such an ontological stance allows us to articulate three potential contributions. First, this allows us to focus the description of performativity not only on results (or finalised outcomes) but also on the process itself, which then appears as an emergent perceptual condition of possibility. Second, by inviting us to be more attuned to the complexity, multifacetedness and embodiness of performances, our suggested conceptual stance enables us to explore some of the key aspects of the becoming of work practices, in the context of which collaborative entrepreneurship, communities, emotions, 'doing together', craftsmanship and inter-corporeity are increasingly more important [START_REF] Spinuzzi | Working alone together: Coworking as emergent collaborative activity[END_REF][START_REF] Garrett | Co-constructing a sense of community at work: The emergence of community in coworking spaces[END_REF]. Indeed, work and managerial practices tend to make both the visibility and continuity of collective activities more problematic than ever, with the generalization of open spaces, mobile work, working at home or open innovation [START_REF] Anderson | Makers: The New Industrial Revolution[END_REF][START_REF] Johns | The third wave of virtual work[END_REF]Borg and Söderlung, 2015;[START_REF] Gandini | The rise of coworking spaces: A literature review[END_REF][START_REF] Taylor | A new mystique? Working for yourself in the neoliberal economy[END_REF][START_REF] Bouncken | Coworking-spaces: how a phenomenon of the sharing economy builds a novel trend for the workplace and for entrepreneurship[END_REF]. Finally, the explicit inclusion of a 'transcendental loop' may keep open a wider space for discussions about personal ethic and collective engagement in civic life (Arendt, 1958(Arendt, /1998)). Keeping this conversational space between bodies and stressing the ongoing exploration of the past in the present with a sense of freedom and responsibility is part of what we see as a transcendental dimension in the immanence of processes. This paper is structured as follows. The next section introduces the notion of performativity (as developed by Austin) and presents the Merleau-Pontian concept of visibility in order to articulate a different view on performativity (a view that sets out to 'transcend' the immanence/transcendence dualism). This lays the foundations of our third section, which consists in a reflection on the implications of our conceptual development with regards to our understanding of management and new work practices. We conclude this paper on the political ramifications of our dialogue between performativity and visibility.

Oscillating between or combining performativity and visibility: A Merleau-Pontian invitation

Performativity: Back to key social, material and temporal debates

The notion of performativity lies at the heart of numerous ontological discussions in MOS [START_REF] Orlikowski | Material works: Exploring the situated entanglement of technological performativity and human agency[END_REF][START_REF] Spicer | Critical performativity: The unfinished business of critical management studies[END_REF][START_REF] Cabantous | Rational decision making as performative praxis: explaining rationality's éternel retour[END_REF][START_REF] Guérard | Rethinking the concept of performance in strategy research: towards a performativity perspective[END_REF][START_REF] Wickert | Towards a progressive understanding of performativity in critical management studies[END_REF][START_REF] Gond | What do we mean by performativity in organizational and management theory? The uses and abuses of performativity[END_REF][START_REF] Vaujany | The post-Macy paradox, information management and organising: Good intentions and a road to hell?[END_REF]. These discussions draw from debates within various areas of scholarship, such as linguistics [START_REF] Austin | How to Do Things with Words[END_REF], gender studies [START_REF] Butler | Gender trouble: Feminism and the subversion of identity[END_REF][START_REF] Butler | Bodies That Matter[END_REF] or Science and Technology Studies [START_REF] Barad | Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning[END_REF].

In a sense, this turn towards performativity can be traced back to the work of the British philosopher of language John Langshaw Austin. For [START_REF] Austin | How to Do Things with Words[END_REF], a discourse instantiates the object that it refers to; put differently, 'words do something in the world, something that is not just a matter of generating consequences' (Loxley, 2007: 2). This idea of a performative utterance refers to what [START_REF] Austin | How to Do Things with Words[END_REF] calls a 'speech-act': a sentence is not a simple statement or description of what people are doing; the sentence actually performs the action. [START_REF] Austin | How to Do Things with Words[END_REF] distinguishes between constative and performative sentences. A constative sentence is concerned with facts and built around truth-values. Contrariwise, a performative utterance is not truth-evaluable and is always part of an action simultaneously performed as it is being uttered. As an instance of performative sentence, Austin (1962: 5) proposes the following: 'I bet you six pence it will rain tomorrow'. He also distinguished explicitly from inexplicitly performative sentences. The performative power of discourse will require the actualisation of certain 'felicity conditions' upon which the performative sentence relies [START_REF] Austin | How to Do Things with Words[END_REF][START_REF] Loxley | Transforming or reforming capitalism: Towards a theory of community economic development[END_REF]. For instance, the utterance 'I now pronounce you husband and wife (or wife and wife, or husband and husband)', which produces the social construct of marriage, is often accompanied by certain artefacts (e.g. a suit, a white dress, rings, etc.), specific individuals (e.g. witnesses, the mayor, a priest, etc.) and frequently takes place in a specific and ritualized context (e.g. a town hall, a church, etc.)these form the felicity conditions of the utterance. In that sense, the material underpinnings, mediations or contexts (embodying an institution) connected to a particular speech contribute to making this speech performative. Interestingly, the distinction between 'performative' and 'constative' utterances has been questioned by Austin himself (see [START_REF] Austin | How to Do Things with Words[END_REF] and by critics of his work (see for example [START_REF] Jakobson | Verbal art, verbal sign, verbal time[END_REF][START_REF] Searle | How performatives work[END_REF].

More recent research has stressed the material (i.e. signs can be more than texts and symbols) and temporal (i.e. performativity is present time, as our experience is always performative) dimensions of the notion of performativity (see for example [START_REF] Pickering | The mangle of practice: Time, agency, and science[END_REF]Sedgwick and Parker, 1995;[START_REF] Barad | Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning[END_REF][START_REF] Muniesa | La performativité des sciences économiques[END_REF]. From a performative perspective, agency 'performs'; put differently, in an entangled way, it materially and socially constitutes our world [START_REF] Pickering | The mangle of practice: Time, agency, and science[END_REF][START_REF] Barad | Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning[END_REF]. From a performative stance, there are no pre-defined entities. Agency may inhere in tools such as assemblages of software packages, screens, computers and models that perform design, calculation and even composition [START_REF] Orlikowski | Knowing in practice: Enacting a collective capability in distributed organizing[END_REF][START_REF] Cooren | Textual agency: how texts do things in organizational setting[END_REF]. In the context of Science and Technology Studies (STS) discussions, the concept of intra-action epitomizes this tendency [START_REF] Barad | Agential realist: Feminist interventions in understanding scientific practices[END_REF][START_REF] Barad | Posthumanist performativity: Toward an understanding of how matter comes to matter[END_REF][START_REF] Barad | Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning[END_REF]. Past, present and future are present in activity itself, constituted and constitutive of it with it not being necessarily the intentional effect of a creative human agent: devices can act. Furthermore, performative stances are in clear opposition to 'representational philosophies' [START_REF] Lorino | Research methods for nonrepresentational approaches to organizational complexity: The dialogical mediated inquiry[END_REF]. Representational approaches see language and signs as direct and unmediated representations of reality. In contrast, phenomenological (Heidegger, 1927(Heidegger, /1996;;[START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]/2013), pragmatic (Dewey, 1938(Dewey, /2007;;Peirce, 1903Peirce, /1997) ) and post-Marxist stances link truth to actions and performances.

From a performative perspective, an immanent becoming constitutes the core aspect of ontology [START_REF] Dewsbury | Performativity and the event: enacting a philosophy of difference[END_REF]. This has notably been evidenced through the body of literature lying at the intersection of 'process philosophy' and organisation studies [START_REF] Tsoukas | On organizational becoming: Rethinking organizational change[END_REF][START_REF] Hernes | Understanding organization as process: Theory for a tangled world[END_REF][START_REF] Hernes | A process theory of organizations[END_REF][START_REF] Nayak | Thinking becoming and emergence: process philosophy and organization studies[END_REF][START_REF] Olsen | The relevance and applicability of process metaphysics to organizational research[END_REF][START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF][START_REF] Aroles | Rethinking stability and change in the study of organizational routines: difference and repetition in a newspaper-printing factory[END_REF][START_REF] Helin | The Oxford handbook of process philosophy and organization studies[END_REF] as well as in some STS-inspired perspectives, such as agential realism [START_REF] Barad | Posthumanist performativity: Toward an understanding of how matter comes to matter[END_REF] or the actor-network theory (Czarniawska and Hernes, 2005;[START_REF] Latour | Reassembling the social: An introduction to the actor-network theory[END_REF].

Carefully describing the network and all the mediations identified through a pragmatist inquiry is a key objective when adopting a performative lens. Time is itself ontological (based on duration, manifestation and time reckoning systems) and the researcher can ultimately delimit a 'field of events' [START_REF] Hernes | A process theory of organizations[END_REF]. Through descriptions, everything can look to be mediation but in a world becoming more and more global and liquid [START_REF] Bauman | Liquid modernity[END_REF], subject to continuous changes and dyschronies [START_REF] Alter | La logique de l''innovation ordinaire[END_REF][START_REF] Vaujany | Rules, Practices and Information Technology (IT): A Trifecta of Organizational Regulation[END_REF], the ontology of performativity provides a powerful theoretical stance. Time, necessarily, is the main concern of any ontology of performativity.

Visibility: Exploration of a neglected late Merleau-Pontian concept

Merleau-Ponty (1945/2013, 1948, 1964), who died just one year before the publication of How to do things with words [START_REF] Austin | How to Do Things with Words[END_REF], was particularly interested in the visibility/invisibility and continuity/discontinuity loops at stake in the processes of perception and embodiment. [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]/2013) view of (embodied) perception is by no means representative: perception is not sensation. Perceiving means constructing through senses more than reproducing through senses. As such, seeing is by no means an isomorphic process (Ibid.). Beyond space and materiality, time is also a construction in Merleau-Ponty's work. We spend most of our present time in the past; we re-enact forms and structures already perceived and efficient for our activities. Should we really perceive continuously the world through all our senses (separately), we would quickly be cognitively and emotionally exhausted. [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF]/2013[START_REF] Merleau-Ponty | Sens et non-sens[END_REF][START_REF] Merleau-Ponty | Le Visible et l'Invisible[END_REF]) also suggested two key loops and dimensions in the process of perception. For him, visibilities and invisibilities are key dimensions of our everyday activities. In order to perceive and act, we need to create a lot of invisibilities. As we cannot simultaneously face the innumerable sensations conveyed by our embodied experience of the world, we must put many other things aside. For instance, in order to write these lines, we need to put aside the noise of the street, overcome a pain somewhere in the body, ignore email and phone notifications, etc. According to [START_REF] Merleau-Ponty | Le Visible et l'Invisible[END_REF], visibilities and invisibilities are thus not the opposite of each other; invisibilities are the scaffolding of visibilities and also often what could make visibilities possible and extend them. Time, which is seen by Merleau-Ponty (1954-1955/2003) as the epitome of an institution [START_REF] Terzi | Institution, évènement et histoire chez Merleau-Ponty[END_REF], is a key emotion in the process of balancing visibilities and invisibilities. To write, one needs to put aside nostalgia (a disturbing past) and anxiety (an impeding future). These sensorial invisibilities will then reinforce the visibility of one's activities for oneself.

These visibility/invisibility loops are not just the product of individual necessities (e.g. cognitive); they also have a historicity. Codes of visibility/invisibility evolve over time. For example, a request on Google Maps is probably constitutive of a different temporality and Constitutive of modes of visibility and continuity, expression is both a form of embodiment and an event. The subject is constructed and visible for oneself. What interests Merleau-Ponty 'is the establishment of the event, and not primarily and essentially the establishment of the subject in the event' (Gély, 2000: 355). This establishment of the subject (and one's body) in the event is also present in some research about performativity that shares communalities with Merleau-Ponty's phenomenology. This is notably the case of [START_REF] Butler | Gender trouble: Feminism and the subversion of identity[END_REF] view of embodiment and its relationship with performativity [START_REF] Stoller | Expressivity and performativity: Merleau-Ponty and Butler[END_REF]. The ability to locate gender and organs (and their affordance) is inseparable from the performative movements of society (whereas Merleau-Ponty would stress their emotional and bodygrounded progressive internationalization).

In slight contrast to an ontology of performativity, from the viewpoint of an 'ontology of visibility', researchers should be particularly careful about the variety of things and the degree of 'thingification' that they make of the worlds they investigate and the miscellaneous underlying assumptions and other worlds that relate to them. Relations and identifications will be central to an empirical engagement with the notions of visibility and invisibility. Surprises, anomalies, and breakdowns should be carefully explored in order to make sense of the potentially symbolic and/or material objects that are part of an instrumentation or extension of the corporeal scheme [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF][START_REF] Vaujany | Rules, Practices and Information Technology (IT): A Trifecta of Organizational Regulation[END_REF]. More generally, the researcher is both immersed and situated in a relation of 'care' and 'responsibility' towards the object of the research, which is questioned with regards to all those modalities of understanding that produce and reproduce the worlds that surround it. Ultimately, an 'ontology of visibility' always implies a flow of meaning, which may be a movement from one anthropological system to another, from a natural to a questioning attitude, etc.

The following section briefly summarises in a table the two perspectives aforementioned, namely an 'ontology of performativity' and an 'ontology of visibility'. This comparative summary will lay the foundation of our discussion of the implications of establishing a dialogue between the concepts of performativity and visibility for the field of MOS.

Performativity and visibility: The latter as the embodied description of the former?

If a performative ontology gives sense to the notions of inseparability and relationality (applied by [START_REF] Jones | Untangling sociomateriality[END_REF] to the concept of 'entanglement'), an 'ontology of visibility' provides more room to the notions of embodiment, reversibility and interpenetration. An 'ontology of visibility' shares commonalities with [START_REF] Marx | The Economic and Philosophical Manuscripts[END_REF] view on the alienating dimension of work. [START_REF] Adler | Marx and Organization Studies Today[END_REF] underlines that for Marx, the prototypal activity is practical (the famous Thesis Eleven). [START_REF] Hook | Towards the Understanding of Karl Marx: A Revolutionary Interpretation[END_REF] argues that Marx's and Dewey's understandings of practical activity are very similar. Marx's account situates humans as world makers and shapers who use both concrete and symbolic tools. Material tools, abstract ideas, theories and human desires always mediate material realities. Their relation to collective forms of social organization mediates individuals' relations to such materiality: people construct social reality but not always under circumstances of their own choosing and they do not do so either as idealists or as wholly social animals. They are animals capable of imaginaries, socially constructed but materially more or less enabled or restricted. In short, performativity and visibility can be contrasted the following way (see Table 1).

12

PERFORMATIVITY VISIBILITY (and INVISIBILITY) Definition

The process of constitution (instead of 'representation) of our world through the flow of everyday activities.

The joint process of embodied perception and non-perception and the emergent conditions of possibilities of this process.

Ontological stance

Mainly immanent. Life and organizing are always in the flow. Everyday activities perform our shared reality, which is a duration, a temporality and a sense of 'happening'.

Both immanent and transcendental.

Visibilities-invisibilities are emergent conditions of possibilities (i.e. constituted in and through the flow itself) of the continuities-discontinuities of the process. Continuities-discontinuities are also emergent discontinuities of visibilities-invisibilities in a sense of happening.

Status of an external, pre-existing world

There is no pre-existing world or pre-existing entities. World is always assembled and constituted temporally, materially and socially through activities.

There is no pre-existing world, but there are conditions of possibilities immanent to the flow itself (i.e. a transcendence in the immanence or a transcendental dimension in immanence/process). Key references [START_REF] Austin | How to Do Things with Words[END_REF] and [START_REF] Searle | How performatives work[END_REF] description of linguistic performativity and felicity conditions; [START_REF] Pickering | The mangle of practice: Time, agency, and science[END_REF] notion of 'performative idioms'; [START_REF] Barad | Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning[END_REF] view of intraaction, performativity and material discursive practices. Merleau-Ponty's (1954-1955/2003) lectures at the Collège de France and his description of visibilities/invisibilities, continuities/discontinuities (Merleau-Ponty, 1964). [START_REF] Butler | Gender trouble: Feminism and the subversion of identity[END_REF][START_REF] Butler | Notes toward a performative theory of assembly[END_REF] view of gender as performative.

Table 1: Performativity versus visibility

Performativity and visibility: Implications for MOS

This section is articulated around the three potential contributions of this paper, as stated in the introduction. The positioning of visibility as a strong ontological stance raises the question of the ontological relationship between the concepts of performativity and visibility; can they be complementary? Are they interrelated? The second contribution is to articulate a different view (post-Kantian) on the notion of condition of possibilities, which may lead to research that would be more in phase with contemporary trends in work practices (e.g. new forms of collaborative work, etc.). Lastly, we also see this work as resulting in more reflexive discussions about ethics with regards to MOS.

Ontologies of performativity and visibility: Complementary or interrelated views of practices and processes?

Performing requires making visible and invisible things as well as both continuing (i.e. using pre-reflexive perceptions reproduced in present time) and setting up discontinuities (something is 'happening' inside and beyond these continuities). Everyday activities are both in the flow and immanent, and the flow itself requires and produces the phenomenological conditions of its continuity and duration. As explained by Merleau-Ponty (1960: 305), 'in this network of calls and answers, where the beginning metamorphoses and accomplishes itself, there is a duration that belongs to no-one but to everyone, a 'public duration', the 'rhythm and proper speed of the event of the world' that, according to Péguy, would be the theme of a true sociology'.

Compatible and complementary stances see in performativity and visibility two distinct ontologies that are (more or less) harmonious. A stance stressing the importance of embodiment versus one which does not give an importance anymore to sense-making and embodiment may result in the second perspective (i.e. complementarity) [START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF].

Flesh is a different matter, and its involvement in the process of becoming may lead to a specific ontology, which is complementary to that of performativity. From the viewpoint of MOS, this has some clear and practical implications. A non-embodied and non-flesh-focused view of performativity may lead to a stress on assemblages viewed and enacted for and by themselves. The text of the assemblage, as revealed through the dialogical process of writing and inquiring, is at the heart of the study. For instance, exploring the performativity of a new search engine, a balanced score card, a new managerial practice will flow itself. In contrast, a flesh-grounded and embodied description of performativity is likely to lead to a more sensemaking and inter-corporeate-oriented description of the process of becoming. One possible drawback is a possible over-focus on human agency and 'emotional flow' [START_REF] Merleau-Ponty | Phenomenology of Perception[END_REF].

We contend that these two views are more than simply compatible or complementary; they are interrelated. In that sense, we join Merleau-Ponty's (1960: 267) reflexion: 'The truth is that the relationships between the natural and the transcendental attitudes are not simple, are not side by side or sequential, like the false of the apparent and the true'. We see the process of becoming as both immanent and transcendental in the sense that the process produces its own conditions of possibilities. Visibility/invisibility loops and continuity/discontinuity modes emerge in the flow itself of everyday activities, which is more and more at stake in contemporary work practices of digital mobility, coworking, Do It Yourself or working at home where individual need to set up and maintain their emotional, cognitive and social work bubbles.

Visibility-invisibility and continuity-discontinuity loops as condition of possibility of performativity

The notion of condition of possibility is often linked to Kantian and neo-Kantian views of reality [START_REF] Russon | The Spatiality of self-consciousness: Originary passivity in Kant, Merleau-Ponty and Derrida[END_REF]. Time, space, God and divinity appear as conditions of absolute possibilities to do something or formulate a thought. They are absolute and pure categories likely to help us build knowledge beyond sensible experience (see [START_REF] Kant | Critique of pure reason[END_REF][START_REF] Kant | Critique of pure reason[END_REF]Kant, , 1783Kant, /2002)). Other philosophical approaches have defended empirical or realistic views of transcendence; this is notably the case of Critical Realism, as advocated by [START_REF] Archer | Realist social theory: The morphogenetic approach[END_REF]. These approaches aim to identify empirically and creatively (imagination and abduction have an important role to play) grounded conditions of possibilities for agency (e.g.

'generative mechanisms').

To avoid the epistemic fallacy (i.e. conflating epistemology with ontology, transitive and intransitive dimensions of knowledge), researchers would thus need to consider jointly a phenomenological world (of reflexivity), a locus of subjective time and a 'real' world, both the 'real' construction that is the emergent effects of individual activities, the context of upcoming agencies, a locus of objective time. This would lead to the idea that performativity itself is a process 'conditioned' by endogenous mechanisms (i.e. neurologic generative mechanisms) that underlie perceptions. This is not what we suggest in the context of this paper. Both philosophical stances (Kantian and critical realist) put aside the notions of embodiment and becoming. As noted in the introduction, we are concerned with the ways in which we may be able to endow the notion of performativity with a sense of embodiment and sensations. As such, we defend emergent views on the conditions of possibilities of managerial practices, part of the flow itself, as co-constituted by the flow of everyday activities.

Let us take a contemporary example. Entrepreneurs involved in the practice of pitching their business models in a coworking space make visible some logics, some specific entrepreneurial metaphors and the urgent temporality of their entrepreneurial project. They make more invisible some implementations and partnerships necessary to move forward and materialize their project. They suggest how discontinuous their project might be, but to do so they need to rely on the routines of entrepreneurship and the place where they perform their pitch. At the very moment of their pitch, they feel their audience, make invisible some things they wanted to say because the previous entrepreneurs mentioned it, and if they want to make visible the originality of their project, they have to remove what appeared 20 minutes ago as a key idea. The performativity of their speech relies on a complex entanglement of visibilities and invisibilities unfolding as the utterance progresses. In short, during their pitch, they have to co-create the conditions of possibilities of their communication and make joint differences and repetitions.

In a sense, this could be related to Merleau-Ponty's (1960: 283) take on loneliness as necessarily related to togetherness: 'Saying that the ego 'before' others is alone implies situating it with regards to the ghost of another, at least it involves perceiving an environment where others could be. The true and transcendental loneliness is not this one: it occurs only if the other is not conceivable, and this requires that there is not a self to claim this loneliness.

We are truly alone, provided that we are not aware of it; it is precisely this ignorance that is our loneliness.'

Senses, perceptions and embodiment: Towards an ethic of performativity with visibility?

Making visible raises the question of for whom and to what purpose (at the risk of perhaps overstating human agency). It also implicitly and immediately raises the question of invisibility. What and who is put aside in the visibility and ordering of everyday activities? In other words, what and who gets annexed, silenced and other-ed in this process of performing visibilities and invisibilities. As noted by Thøgersen (2014: 29), 'what we actually express is not primarily a matter of our own intentionsa will-to-speakbased on ready-madethoughts; but rather a matter of our immediate emotional grounded response to our surroundings and hence also based on whether the opportunities for certain expressions exist within our current surroundings, within our current experience of the world'.

An ontology of visibility brings with it alterity, otherness and togetherness [START_REF] Descola | The Ontology of Others[END_REF]. It also creates a locus for reflexivity, as it anchors becoming into 'inter-corporeity' (more than flesh). Emotions we jointly feel, affects we invest in are the main matter of everyday ethics. Their positive or negative presence/absence need to be illuminated and discussed in the key agora of our cities. [START_REF] Butler | Notes toward a performative theory of assembly[END_REF] thus stressed the importance of public gathering and the performativity of numerous bodies assembled in a public space. This has always had a political effect that is largely leveraged today by social media and microblogging [START_REF] Sergi | Making mundane work visible on social media: a CCO investigation of working out loud on Twitter[END_REF][START_REF] Vaast | Social Media Affordances for Connective Action: an Examination of Microblogging Use During the Gulf of Mexico Oil Spill[END_REF]. For Merleau-Ponty (1945: 417), 'My freedom, the fundamental power which I enjoy of being the subject of all my experiences, is not distinct from my insertion in the world. It is a fate for me to be free, to be unable to reduce myself to anything that I experience, to maintain in relation to any factual situation a faculty of withdrawal, and this fate was sealed the moment my transcendental field was thrown open, when I was born as vision and knowledge, when I was thrown into the world'.

Conclusion: Towards a political philosophy of management?

The work (in particular the later work) of Merleau-Ponty has been the subject of numerous misunderstandings, in particular his view of embodiment. His focus on embodiment constituting the assemblage. This requires making them continuously accountable of their agency [START_REF] Sartre | Being and Nothingness: An essay on phenomenological ontology[END_REF][START_REF] Sartre | Being and Nothingness: An essay on phenomenological ontology[END_REF]. This is sometimes difficult in the context of what appear as radical post-humanist [START_REF] Hayles | How we became posthumans: Virtual bodies in Cybernetics, Literature and Informatics[END_REF] and highly temporal views of agency and management.

Another view stresses the pre-reflexivity, emotions, perceptions and inter-corporeity at the heart of becoming [START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF]. Narration is then quickly a hermeneutic for and by itself [START_REF] Ricoeur | Time and Narrative[END_REF]. However, this view can lead to managerial approaches (e.g. of design) more focused on bodies and embodiment [START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF][START_REF] Vaujany | Re-inventing management research with learning expeditions[END_REF] and can then perform a world less engaged in the possibilities of material agencies at large, that of the materiality performed, encountered by the assemblage itself. Putting together the two ontologies of performativity and visibility in management (which we see as co-authors as more than 'complementary' but interrelated) is a fascinating task for future research in management. A task we see as performative by itself. Performative for the best we hope.

  enacts a different institution to that of the walk of the flâneur in the Haussmannian Paris of the 19th century. It was probably easier to 'feel' the infrastructure related to the place and the underlying domination mechanisms (in particular through collective conversations but also through intensive immersions into the city) in the case of the flâneur than in the context of individual immersions into Google requests and the complex set of algorithms behind it. The same relation underlies continuity & discontinuity (Merleau-Ponty, 1964) and activity & passivity (Merleau-Ponty, 1954-1955/2003); far from being oppositional, they mutually constitute each other.

and inter-corporeity is not a way to introduce another matter that would be flesh itself (Reynolds and Roffe, 2016) 2 . Merleau-Ponty wanted, most of all, to stress the importance of reversibility and emotional flow and to place them at the heart of the process of becoming [START_REF] Küpers | Phenomenology of the embodied organization: The contribution of Merleau-Ponty for organizational studies and practice[END_REF]. The flow can be seen as pure immanence (with probably a pure Bergsonian view). It can also be viewed as a dialogical process: interrelated transcendental-immanent dialogical loops. Embodiment is a condition of possibility of experience, or rather, is at the heart of the emergent conditions of possibilities of experience (their continuities and visibilities).

If the former view places a greater focus on the risk of an overstress of temporal dynamics as constituted by the assemblage itself and time as a textual, aspatial and 'aemotional' narrative, the latter increases the risk of overstating human agency, emotions and pre-reflexive narratives. All this is far from being neutral politically and entices us to engage more than ever with the political philosophy wished by Arendt 3 (1958/1998).

What is the world of work and management we wish to constitute and make visible through our empirical and conceptual descriptions and what are the tools we use for this task?

As noted by Arendt (1958: 26), 'homo faber could be redeemed from this predicament of meaninglessness ... only through the interrelated faculties of action and speech, which produce meaningful stories as naturally as fabrication produces use objects'. Furthermore, with the view of a world made of assemblages and discourses, the political engineering of this world is also a question of performing and making visible the 'right' assemblages. This also implies discussions and texts questioning the responsibility of all those individually 2 Furthermore, it is not a way to put aside instruments, techniques and the materiality of our world. Instruments and materiality are part of the experience and of our pre-reflexivity. Merleau-Ponty sees them as relevant mainly if they are part of the broader process of visibility-invisibility, continuity-discontinuity and passivity-activity that is at the heart of the emergent conditions of possibilities of collective activity. He also believes in the ontology and materiality of our world, but suggests that we temporally live in a present that is often ahead of 'real' matter and the 'real' world (we are inhabited by past mediations). We re-cognize and re-activate perceptions more than we sense the world. We come close to matter 'as it is' in a pure experience, mainly when something wrong happens. What's going on? Instruments and objects at hands then take their shape, colors and matters in the field of our experience. 3 See van [START_REF] Van Diest | Managing Freely Acting People: Hannah Arendt's Theory of Action and Modern Management and Organisation Theory[END_REF] and [START_REF] Nielsen | The Oxford handbook of process philosophy and organization studies[END_REF] on the relation between Arendt's work and MOS.


H Helouvry

N Macedo Portela Da Silva

J-J Letourneau
email: jacques.letourneau@mines-albi.fr

F Baillon

F Espitalier

Microscale Two-phase Flow Behaviour Between an Ionic Liquid and Supercritical Carbon Dioxide

). Since ionic liquids are almost non-volatile, the mass transport occurs from SC-CO 2 towards this ionic liquid. This two-phase flow system is observed with a high-speed camera. An image processing of the images is performed in order to calculate the global two-phase flow geometrical parameters: frequency, velocity, size, gap length, volume and surface. The influence of operating conditions (continuous flow rate, dispersed flow rate, temperature and pressure) on the physical properties of the system has been studied. The observed results show a special behaviour of our two-phases flow system: the length, the volume and the velocity of dispersed phase drastically decrease along the capillary. Figure 1: Co-axial injection of SC-CO 2 in [BMIm + ][PF 6 -] continuous phase -P = 11.4 MPa (inlet); T = 318 K; ! !" ! = 0,11 mL.min -1 ; ! !"#$%& ! = 0.09 mL.min -1 in a 530 µm ID micro-capillary 34 cm CO 2 BMImPF 6

INTRODUCTION

As solvents, ionic liquids are intended to be used in green chemistry processes. Among their characteristics, non-volatility and non-flammability make them safer and less damaging to the environment, compared to traditional volatile solvents. Although several studies show that some of them are toxic and irritant, this is explained by their decomposition in the presence of water, ionic liquids have potential to make chemical processes less harmful for environment by reducing waste and energy consumption. Major impediments to their industrial usage concern their price and their viscosity which is know to be high, between 0.010 and 0.500 Pa.s at ambient temperature. Impurities may influence in both ways: water decreases viscosity of hygroscopic ionic liquids [START_REF] François | Doctoral Dissertation, Utilisation de l'électrophorèse capillaire (EC) pour la caractérisation des liquides ioniques (LI) et intérêt des LI comme nouveaux milieux de séparation en EC[END_REF] whereas solid solutes increase it. Another green solvent, which is known to drastically decrease mixture viscosity when used as cosolvent, is the carbon dioxide at supercritical conditions (SC-CO 2 ). We choose to saturate ionic liquids with SC-CO 2 and use this mixture as a super green solvent. The mixture viscosity can be considerably reduced compared to pure ionic liquid: for instance at 25 MPa the mole fraction of CO 2 in 1-butyl-3-methyl-imidazolium hexafluorophosphate ([BMIm + ][PF 6 -]) reaches 80% and the viscosity is reduced by 90% [START_REF] Adamou | Properties measurement of the binary ionic liquid BMImPF6/SC-CO2 Part 2: Viscosity[END_REF].

As mentioned before, the second main impediment to ionic liquid usage is its price. Ionic liquids are so numerous (more than 1000 on the Sigma-Aldrich catalogue) that the screening of a good candidate to be used as solvent for a specific solute is really expensive, even more when combined with high pressure CO 2 processes. That is why microsystem technology has been chosen. Intrinsic small volume has an interest in research and development of economical, innovative and intensified processes. The microscale allows the use of few quantities, therefore it's also an advantage to reduce the study's time. Furthermore, micro quantities present an interest in the case of toxic product. And finally, microsystem technology presents an advantage for heat and mass transfer due to the large surface area-tovolume ratio in comparison to conventional reactors.

Another advantage of the microscale is to allow the exploration of high-pressure processes because the smaller dimensions represent less mechanical stress on the material. On this basis a micro-reactor has been setup to allow the study ionic liquid -SC-CO 2 -solute mixture under pressure [2]. This transparent micro-reactor uses an uncoated microcapillary entrapped in resin to ensure its robustness under high-pressure (20 MPa with a 550 µm ID capillary).

Our study involves in time the selective solubility of rare earth in ionic liquid -CO 2 mixture. This mixture behaviour will be studied in our two-phase flow micro-reactor. In a first time, modifications have been made on it and a second prototype has been setup. The present communication concerns this second prototype and the tests that have been done with the two-phase system: [BMIm + ][PF 6 -] -SC-CO 2 . [BMIm + ][PF 6 -] is hydrophobic non-watersoluble due to its PF 6 -anion, and make it a good solvent for extraction. Firstly, the ripening and improvements of the manufacturing technique for the high-pressure microfluidic device is presented. And secondly, some experimentation and observations on supercritical CO 2 dissolution in [BMIm + ][PF 6 -] are shown.

MATERIALS AND METHODS

Materials and manufacturing step

For our study, a homemade micro-reactor, shown in figure 2, is used. It is based on the capillary microfluidic technology with coaxial injection. It is design to study intermittent (or separated) two-phase flow under a maximum pressure of 20 MPa for the biggest capillary inner diameter used, which is 530 µm.

A poly(methyl methacrylate) (PMMA) block is purchased with dimension of 270 x 140 x 20 mm. PMMA is a thermoplastic easy to machine, with the excellent optical property of transparency. The chassis is then performed in this block using a digital milling machine (Charlyrobot -Charly4U CNR3). Lubrication is required to prevent overheating of the PMMA, that it could cause deformation during machining work. First, the blank (20 mm thickness) is cutting at the micro-reactor dimensions (260 x 110 x 20 mm), and then a square hole is done allowing to etch the polyimide coating (region A in figure 2: this is the area corresponding to the video viewing). Then channels are engraved with 1/16 inch hemispherical diameter -these channels entrap the capillary and the resin

The micro-reactor consists in a cylindrical fused-silica tubing (Polymicro, USA). Tubing is coated with polyimide cladding as a protection and provides a great flexibility to manipulate the capillary without breaking it. This coating has to be removed to have a real transparent observation zone (region A in figure 2). The sleeves adapted to the capillary are plugged on the capillary (region B in figure 2). Their external diameter is 1/16 inch, precisely adapted to plug it into the channels. Thus, the capillary is fixed on the chassis. The two capillary's extremities stand out in the metal union side. In this state the capillary is ready for the next A B C step: etching the coating. Polyimide coating is burnt on the area provided. A delicate cleaning phase is necessary to remove the ash: a fine brush is used allowing the capillary become transparent for video viewing.

Stainless-steel connectors for high pressure applications (Upchurch Scientific, USA) are used to connect the capillary reactor to the external network pipes (pumps etc.). A tee is used to feed the tubular reactor with the continuous phase. Two unions allow connecting with the inlet for the dispersed phase, and with the outlet for the resulting mix.

Epoxy resin (EP 601-LV, Polytec, France) has been selected for its optical properties, its resistance (shear strength 80 N.mm -2 ) and its fluidity (240 mPa.s). This resin is used for optic applications. An excellent adherence with PMMA has been reported. The microcapillary is then embedded in this resin. The capillary has a maximum inner diameter of 530 µm and an outer diameter of 665 µm. A second capillary is used to inject the dispersed phase with a coaxial configuration. Its inner diameter is 200 µm and the outer one is 350 µm.

Finally the micro-reactor is put into a transparent box and immerged in a circulating heat transfer fluid. The box has been setup to force the fluid circulation everywhere around the micro-reactor. Inlet/outlet for this heat transfer fluid is shown in figure 2 (region C).

Main advantages

This device presents different advantages.

First, it's the price: 200 €. The lifetime of micro-reactors is not indefinite. This is highlight when different chemical is applied or when systems work under high pressure. Its lifetime heavily depends on the number of utilisation or more precisely on the number and the way pressure drop/increase are done. That is why its low price allows it to be seen as a disposable device.

This micro-reactor has the further advantage of a circular cross-section compared to the square cross-section presented by on-chip microsystems. In fact, the resulting axial symmetry of the flow has both the advantage to drastically simplify CFD simulation and to allow efficient and reliable measurements with image acquisition.

Another advantage is its resistance. It is even the main objective of this device. It was conceived to resist to pressure up to 20 MPa.

Although, this device doesn't entirely fulfilled one of the main objective: the transparency. Indeed, the epoxy resin combined with the PMMA covering panel absorb almost all radiations in IR and UV regions.

In order to compact their total channel length, the 2D design of on-chip based microdevices presents a very small radius of curvature. Thanks to the 3D design path of our capillary-based micro-reactor, the minimal radius of curvature of the presented configuration is 3 cm and has to be compared to the 100-500 mm radius of curvature of the on-chip 2D design. The curvature effect can lead to flow instabilities or to coalescence of the dispersed phase and can even be used to separate phases. This effect is stronger when the fluids densities difference is greater, which is true for SC-CO 2 -ionic liquid systems, and when the inner diameter is larger, which is also our case. For this device the Bond number: Bo = ∆! ! ! ! ! /! with ! ! = !/! !"#$ , is calculated with centrifugal acceleration. Considering identical mixtures, with identical operating conditions and with the same channel surface sections, the Bond number of the on-chip microdevices (Rcurv = 0.3 mm) is 100 times higher than of the presented device (Rcurv = 30 mm).

The design strategy presented enables to set up microdevices as long as 3 m. Moreover, the chassis configuration can be easily modified to enable devices of 10 m capillary length or more. This strategy fulfils almost all the criteria required to incorporate a successful macro-tomicro interface design [START_REF] Fredrickson | [END_REF].

Experimental section

Micro-reactor is integrated into a high-pressure circuit, powered by syringe pumps (ISCO 260 ISCO 100 D and HLX) to reach pressure up to 20 MPa in the system. The pumps are filled with [BMIm + ][PF 6 -] (99.9%; Solvionic, France) and with CO 2 (purity 99.995%; Linde, France). Each pump controls the volume flow rates and the two streams feed the microreactor, the CO 2 being coaxially injected forms the dispersed phase. These pumps as well as the micro-reactor are temperature controlled. A third syringe pump (ISCO 260 D) placed on the micro-reactor output line serves to maintain and control the output pressure in the system.

After the intermittent two-phase flow being stabilised, the detailed formation of the flow is registered by a CCD camera (Baumer HXC13) with a resolution of 1280 x 1021 pixels 2 . The videos can be acquired at 2000 frames per second. The scene is backlighting with LED lamps with a total light intensity of 2200 lumen.

RESULTS

As shown in figure 1 and3, the CO 2 transfers in the continuous phase and the drop size decreases all along its move in the capillary. The shape of the drop changes and allows to distinguish two regions beyond the generation zone. In the first one convection keeps acting on the transfer of the CO 2 and in the second one drops look like sphere and are transport in a Poiseuille flow, the transfer is only diffusive.

Another observation concerns the presence of a film. The viscous ionic liquid sticks to the inner capillary surface and forms a thick film surrounding a less viscous tube where the drops circulate faster with a bullet-like shape. It has also been noticed that the film thickness decreases along the capillary as it can be shown in figure 4.

The system cumulates several distinctive aspects that includes:

1. The global behaviour change with pressure: At 8MPa CO 2 acts as a gas but at 15MPa it acts as a liquid. 2. When SC-CO 2 (supercritical carbon dioxide) is dissolved in [BMIm + ][PF 6 -], the continuous phase properties considerably change. For example, at 18 MPa and 308 K as the mole fraction of CO 2 varies from 0 to 90 %, the density varies from 1400 to 2100 kg.m -3 and the viscosity varies from 0.13 to 0.013 µPa.s. It has been observed that most of the CO 2 dissolves in the continuous phase during its move on the first So, in this region the continuous phase splits in two parts: the film which is viscous and moves slowly and the Taylor zone entrapped between two drops formed by an almost saturated phase ten times less viscous, which slips on the film. 3. The film thickness is really large and can be predominant at low CO 2 flowrate. 4. The film thickness decreases rapidly and tends to disappear.

In the same way as mentioned properties drastically changed with CO 2 dissolution, the refractive index follow the same trend. So, it has been possible by adapting the backlighting to make visible the toroidal flow in the Taylor zone as it is shown in Figure 5.

CONCLUSION

The specific behaviour of a two-phase flow under pressure of a CO 2 /ionic-liquid system has been partially explained. It has been possible thanks to a homemade and cheap microdevice. This microdevice was fabricated using capillary microfluidic technology with integrated connections. An optically-clear epoxy resin was applied on the microdevice in order to combine optical transparency and mechanical resistance. An experimental high-pressure setup was designed. This setup was implemented to operate and generate stable two-phase flow and to overcome the difficulties due to restricted optical access, pressure adjustment, and temperature control. Thus, this system enables fast process control and detection and is able to produce homogeneous conditions. Consequently, the described microfluidic high-pressure setup is an optimal configuration for a fast study of processes.

In future, this study will permit the applicability of high-pressure operations in a simple microcapillary device. In particular, it will enable to investigate the mass transfer under pressure of supercritical CO 2 in ionic liquids in presence of solutes.

Figure 2 :

 2 Figure 2: The transparent high pressure micro-reactor -coaxial injection, L = 3 m, ID = 536 µm, ID injection = 100 µm

Figure 3 :

 3 Figure 3: Experiment done at P = 9.8 MPa ; T = 318 K ; ! ̇!" ! = 0,09 mL.min -1 ; ! ̇!"#$%& ! = 0.11 mL.min -1 . Injection position is shown at z = 0 mm.

Figure 4 :

 4 Figure 4: Decrease of the film thickness: in less than 2 cm it decreases from 23 to 1% of the inner diameter.

Figure 5 :

 5 Figure 5: (at the top) Several toroidal shapes of the flow in the Taylor zone between the CO 2 drops and their evolution on the first 1 cm. (left) Magnification of a zone. (right) Schema showing flow streamlines and the CO 2 transfer magnitude.


Romain Guiheux
email: romain.guiheux@irt-m2p.fr

Sophie Berveiller
email: sophie.berveiller@ensam.eu

Régis Kubler
email: 2regis.kubler@ensam.eu

Denis Bouscaud
email: denis.bouscaud@ensam.eu

Etienne Patoor
email: etienne.patoor@georgiatech-metz.fr

Quentin Puydt
email: quentin.puydt@irt-m2p.fr

Pierre Osmond
email: pierre.osmond@mpsa.com

Bastien Weber
email: bastien.weber@arcelormittal.com

Denis

Shot peening analysis on trip780 steel exhibiting martensitic transformation

Keywords: shot peening, residual stresses, TRIP steel, martensitic transformation, finite element simulation

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

Introduction

In the last years, due to increasing ecology and environmental constraints, a search for lightweight structures has been carried out, leading to the use of more complex geometries and new materials. In that context, TRIP (TRansformation Induced Plasticity) steels are of particular interest as the due to their good mechanical properties to weight ratio [1]. They are often used in the automotive industry for reinforcement parts of the vehicle (bumper, door beam…). To increase life duration, critical parts are shot peened. The specific mechanical behaviour of TRIP steels is due to their microstructure: they contain residual austenite that can transform into martensite when a stress is applied. This mechanism is responsible for hardening of the steels. The beneficial effect of shot peening on metastable austenitic steels was recently established by Fargas et al. [2], resulting in extensive austenite to martensite phase transformation. Numerous analytical models and numerical approaches based on finite element analysis have been developed to simulate the shot peening process. Reviews of the wide variety of numerical models can be found in Rouhaud et al. [START_REF] Rouhaud | Handbook on Residual Stress[END_REF] and Sherafatnia et al. [4]. Only few experimental studies have been published up to now dealing with the impact of shot peening on metastable austenitic steels [5][6][7]. The first model taking into account the TRIP effect during peening was proposed very recently by Halilovic et al. [8]; it was developed for an austenitic steel AISI 304 peened steel with a single laser shot using a large strain formulation of transformation plasticity.

Objectives

In this study, part of the CONDOR project of IRT M2P, we aimed to study and model the influence of the martensitic transformation occurring during shot peening on the behaviour of a TRIP steel at the phase scale. Shot peening was applied to TRIP 780 steel specimens (2 mm thick, 15% of initial residual austenite) by a Wheelabrator turbine machine for different peening conditions using steel shot media. Residual stresses in each phase and residual austenite fraction was studied after shot peening. A semi-physical numerical model, coupling the mechanical and thermodynamical behaviours, was developed at the scale of the phases following the work of Kubler et al. [9]. The main objective was to understand and predict the effect of shot peening on the mechanical fields in the different phases of TRIP780 steel taking into account plastic hardening and martensitic transformation.

Methodology

The studied steel is a cold-rolled commercial TRIP 780 steel provided by ArcelorMittal in the form of a 2 mm thickness sheet. Its chemical composition is provided Table 1; it has a complex microstructure (Figure 1) composed of ferrite, bainite and residual austenite. The volume fraction of austenite is about 15%. The yield strength and ultimate tensile strength are respectively 560 and 780 MPa. Shot peening (SP) was performed on rectangular samples of 60x60x2 mm 3 , using a Wheelabrator turbine machine. The diameter of the steel shots used was 400 µm, with an exposure time of 16 s.

The SP intensity was measured by the arc height of Almen specimens (A type), corresponding to F19A. The coverage rate was 230%. In order to take into account the effect of forming process, SP was performed on two kinds of samples: the as-received one and a pre-strained one obtained by tensile straining at a total strain of 10%. The retained austenite contents after SP were determined from the X-ray diffraction peak intensities of four hkl planes with Cr-Kα radiation: {200} and {220} for the austenite, and {220} and {211} for the BCC phases. Residual stresses were analysed by X-ray diffraction (XRD), using the classical sin 2  method (NF EN 15305); residual stress in the austenitic phase was measured using Mn-Kα radiation. For the {311} crystallographic planes, the Elastic RadioCrystallographic constants (ERC) values are ½ S2 = 7.18 x10 -6 MPa -1 and S1 = -1.20x10 -6 MPa -1 . Ferrite, ferrite of the bainite and martensite have quite the same diffraction positions; therefore, it is not possible to separate each contribution. We determine the average residual stress over these phases, named BCC residual stress, using Cr-Kα radiation. For the {311} crystallographic planes, the ERC values are ½ S2 = 5.92 x10 -6 MPa -1 and S1 = -1.28x 10 -6 MPa -1 .

In order to get the in-depth profile, material removal was performed by electrolytical polishing in a saline solution. As it may induce a stress relaxation, experimental values of residual stresses were corrected from layer removal using the Sikarskie's correction [10].

Results and analysis

Experimental results

Before SP, the retained austenite content was measured at 12% in the as-received steel; residual stresses were homogeneous in both phases and rather weak (lower than 100 MPa). After prestraining, the austenite content has decreased to 9%. Residual stresses of about 20 MPa were obtained in both phases and in both directions (tensile and transverse ones). The hardness has also increased from 270 HV0.3 to 320 HV0.3. Figure 3 shows the residual stress profile in the BCC (a) and the FCC (b) phases determined by XRD.

In the BCC phases, for the as-received sample, the residual stress state at the surface is in compression (about -490 MPa). It increases to a maximum of -510 MPa at a depth of 15 µm; then it decreases gradually with increasing depths. It is almost zero at around 250 µm; tensile values are expected for larger depths. The pre-strained sample shows the same profile. There is only a difference of 50 MPa at the surface. However, considering stress uncertainty, stress values can be assumed the same on both samples, as well as the affected zone depth. Due to the weak intensity of the austenite peaks, no accurate measurements could be obtained in the first 50 µm as for the fraction measurement. As stress correction from material removal requires the knowledge of the surface stress value, we were not able to perform it. So values are the measured ones, not the corrected ones as for the BCC phases. Austenite exhibits also compression state: at a 100 µm depth, the stress of the as-received sample is -600MPa; this compression value is larger than in the BCC phases (-490MPa at the top surface). The stress decreases gradually with increasing depths and becomes almost zero at 250µm as for the BCC phases. The stress decrease seems to be faster for depths larger than 120µm. This inflexion point corresponds to the depth where the austenite content has increased back to its initial value. Therefore, the austenite stress state is rather constant in the zone affected by the martensitic transformation and varies much more when the austenite is stable. However this effect seems to be less pronounced on pre-strained samples; it would be of interest to have more measurements to confirm this issue.

Numerical simulation

A semi-physical numerical model, coupling the mechanical and thermodynamical behaviours, was developed at the scale of the phases following the work of Kubler et al. [9]. It consists in a thermoelastoplastic model with phase transformation. A Representative Volume Element (RVE) of a set of four components was selected in order to model the behaviour of the steel: ferrite, bainite, residual austenite and martensite. Complete description of the model can be found in [START_REF] Guiheux | Comportement d'aciers à transformation de phase austénite-martensite pour la simulation du grenaillage de précontrainte[END_REF]. Thus the mechanical behaviour of each constituent and the martensitic transformation kinetics can be determined.

A finite element simulation of shot peening with consecutive impacts of spherical media has been developed using the specific behaviour law implemented in a VUMAT subroutine in Abaqus Explicit.

The dimensions of the simulated sample are large enough to be considered as a semi-infinite medium (Figure 4). Due to symmetry conditions with respect to the (XZ) plane, only one half of the sample was modelled. Four among six lateral faces of the impacted workpiece were constrained in displacement along their normal directions; only the upper impacted surface was set free to deform.

The mesh size was chosen to ensure acceptable computational time with regards to a convergence of the residual stress profiles. The mesh is made of hexahedral elements with reduced integration C3D8R in the upper part, and of tetrahedral elements C3D4 in the bottom part. The shot behaviour is assumed to be elastic. The shots are positioned following a deterministic hexagonal pattern to obtain the experimental coverage rate (230%) according to an analytical law estimating the impact radius. Microstructural and mechanical fields were calculated at a given depth by averaging the corresponding values on all the nodes located at the same depth under the impact zone. The austenite content and residual stresses in each constituent were determined; this allows calculating the macroscopic stress using a mixture law (Figure 5a). In order to compared simulated data with experimental ones in the case of the non-deformed steel, the mean stress over the BCC phases was also calculated (Figure 5c); for austenite, a direct comparison can be made (Figure 5d). Simulated results fit quite well to the experimental austenite fraction; nevertheless a shift of 30 µm is observed: the austenite fraction gets back equal to the initial value at 120 µm (resp. 150 µm) for experimental (resp. simulated) values. At the top surface, the fraction was too low to be detected by XRD; the model predicts a quite constant value in the first 50 µm, around 5%. Residual stress profiles are in good agreement with experimental data. The BCC phases stress is decreasing more rapidly when the martensite fraction decreases too. As for the austenite profile, a shift of 30 µm is observed between both profiles. Note that the value at the surface is not well predicted as in many models as it is very sensitive to contact conditions. In the austenite, the difference between experimental and simulated values seems to be higher but one has to keep in mind that experimental values are not corrected from matter removal. If we consider that it should induce an increase of 150 MPa (as in BCC phases), then predicted values are quite good. The advantage of simulation is that it gives access to the entire profile of austenite stress.

Conclusions

The microstructure and mechanical fields were studied on a cold-rolled TRIP 780 steel after conventional shot peening, and with or without pre-strain; for the first time, results were compared to numerical simulations at the phase scale.

1. The pre-strain does not affect residual stresses in the different phases nor the affected depth but it shifts the austenite fraction value towards lower values. 2. All the constituents were found in compression; the maximum value reached in the austenite was -800 MPa while around -500 MPa in the BCC phases. 3. The stress variations are maximum in the zone affected by the martensitic transformation.

Figure 1 :

 1 Figure 1: Microstructure of the TRIP 780 steel. Austenite corresponds to white grains.

Figure 2 :Figure 3 :

 23 Figure 2: Evolution of residual austenite content as a function of depth for as-received (0%) and pre-strained (10%) samples.

Figure 4 :

 4 Figure 4: Shot peening simulation. (a): mesh used for calculation. (b): shots distribution at the sample surface.(nR : number of shots row impacting the sample)

Figure 5 :

 5 Figure 5: Shot peening of the non-deformed TRIP 780 steel. Simulated macroscopic stress in x direction (a). Experimental vs. simulated austenite volume fraction profile (b), residual stress profiles in the BCC phases (c) and in austenite  (d).

  good agreement was obtained with numerical simulation of the martensitic transformation kinetics and residual stresses.

Table 1 :

 1 Chemical composition and estimated phase volume fraction [ArcelorMittal data]

	Chemical composition (wt%)	Estimated phase volume fraction (%)
	C	Si	Mn	Austenite	Ferrite	Bainite	Martensite
	0.209	1.61	1.64	15	70~75	10~15	0


Nayane Macedo Portela Da Silva

Hugo Helouvry

Jean-Jacques Letourneau

Fabien Baillon

Fabienne Espitalier

Mass transfer modelling between supercritical carbon dioxide and an ionic liquid in a micro-two-phase flow

Mass transfer modelling between supercritical carbon dioxide and an ionic liquid in a micro-two-phase flow

N. Macedo Portela da Silva a , H. Helouvry a , J.-J. Letourneau a* , F. Baillon a , F. Espitalier a a Université de Toulouse, Mines Albi, CNRS UMR 5302, Centre RAPSODEE, Campus Jarlard, 81013 ALBI Cedex 9 * Jean-Jacques.Letourneau@mines-albi.fr Microreactors and supercritical fluids have great potential to intensify chemical processes, making them safer, cleaner and more efficient. An additional advantage of the small length scale is the potential for high-pressure applications due to lower mechanical stress in the microreactor material. The hydrodynamic and the mass transfer of two-phase flow under high pressure in a micro-capillary have been modeled. The model can take advantage of the 2D axisymmetry due to the cylindrical geometry of the capillary. This model allows an indirect estimation of binaries physicochemical properties such as mass transfer coefficientestimations which are based on the geometrical values characterizing the two-phase flow such as velocities, frequency, sizes and volumes. To obtain these values, an accurate image processing is done on the high-speed camera images, which take advantages of the microreactor's transparency [START_REF] Espitalier | Doctoral Dissertation Mines Albi -INP[END_REF][START_REF] Macedo Portela Da Silva | [END_REF] . The binary mixture [BMIm + ][PF 6 -] / supercritical carbon dioxide (SC-CO 2 ) have been chosen as the model system. Under pressure, the unidirectional transfer of CO 2 in [BMIm + ][PF 6 -] induces significant changes in physico-chemical properties of continuous phase: viscosity decreases (divided by ten) and density increases (1.5 fold). Due to the wide variations of the continuous phase properties along the capillary, size and shape of the dispersed phase bubbles are simultaneously modified. In the generation region, the bubbles of SC-CO 2 are squeezed and look like bullet-shaped bubbles moving quickly through the capillary and between them the gap of continuous phase is almost saturated. Internal circulations arise within the bubbles. This Taylor flow region is surround by a thick film of viscous [BMIm + ][PF 6 -] pressed against the capillary's inner surface. This film is not stagnant because slugs exert considerable shear stress on it, which keeps the film moving at a low velocity. Furthermore, a significant slip velocity has been identified located between these two regions. As the CO 2 diffuses in this wall-film its viscosity decreases by one order of magnitude and its thickness decreases until it disappears further down the capillary. The droplet's size decreases too and its shape evolves to become spherical. The mean velocity decreases and the flow behavior evolves in a Poiseuille flow. The aim of this study is to further develop a microsystem able to do screening of ionic liquids with solute under pressure of fluidizing CO 2 . For this kind of system the prediction of the hydrodynamic behavior, mass transfer and physic-chemical properties (which drastically vary in a few centimeters) is a key to develop applications in which ionic liquids are involved as a solvent [3] .