Jean-Christophe Baret

Felix Kleinschmidt

Abdeslam El Harrak

Andrew D Griffiths

Kinetic aspects of emulsion stabilization by surfactants : a microfluidic analysis

In classical emulsification processes, surfactants play two roles: first, they reduce the interfacial tension, facilitating droplet deformation and rupture and second, they reduce droplet coalescence. Here we use a microfluidic emulsification system to completely uncouple these two processes, allowing stabilization against coalescence to be studied quantitatively, and independently of droplet formation. We demonstrate that, in addition to the classical effect of stabilization by an increase of surfactant concentration, the dynamics of adsorption of surfactant at the water-oil interface is a key element for droplet stabilization. Microfluidic emulsification devices can therefore be tailored to improve emulsification while decreasing the concentration of surfactant by increasing the time before the droplets first come into contact.

Introduction

Two fundamental processes occur during emulsification: droplet rupture and droplet re-coalescence. The mean droplet size of a kinetically stabilised emulsion system is governed by the relative rates of these two processes [1,2].

Surfactants effect both processes: they reduce the interfacial tension, thereby promoting droplet rupture, and they provide a barrier to re-coalescence via the repulsive interaction between the adsorbed layers on the two colliding drops [2]. However, as droplet rupture and re-coalescence generally occur concurrently during classical emulsification processes, it has proven difficult to study the influence of the surfactant on the two processes independently and the analysis is restricted to averaged parameters measured on large number of droplets, such as droplet sizes in bulk emulsions [1,3]. It has, in particular, proven very difficult to study the effect of the dynamics of absorption of surfactant at the water-oil interface on emulsification. Between the formation of a new droplet and its subsequent encounter with surrounding droplets, surfactants adsorb onto the newly created interface, inhibiting re-coalescence.

If the timescale of the surfactant adsorption is longer than the timescale of the collision, the fresh interface will not be sufficiently covered, leading to re-coalescence and increasing the equilibrium droplet size (EDS). This is of great industrial importance: it leads, for example, to the phenomenon of 'over-processing', often observed using high-pressure emulsification, in which although the energy input during emulsification has been increased, the obtained emulsions have a bigger EDS than expected [1]. Lately, new methods have been developed to prepare monodisperse emulsions [4,5,6]. Microfluidic devices allow the preparation of highly controlled monodisperse [6,7,8], bidisperse [9] as well as multiple emulsions [10,11] or foams [12]. Because droplet-based microfluidic systems [13,14,15] also enable a variety of other operations, all at frequencies of kHz or higher (including splitting [16], fusion [17,18], and sorting [19,20]) they have broadened the range of applications of emulsions into areas such as cell-based assays [21,22] or the synthesis of materials [23]. Microfluidic systems are also an extremely useful tool to perform fundamental quantitative studies of emulsification and emulsion stability, for example, to study droplet formation [24] or coalescence [25]. Here we use a microfluidic emulsification system to completely uncouple droplet formation and droplet re-coalescence by the control of droplet flows along cal-ibrated channels. This allows the stabilization against re-coalescence to be studied quantitatively, and independently of droplet formation. We demonstrate how the stabilization of droplets is modified by kinetics aspects of surfactant diffusion to the oil/water interface and how this knowledge can be used to design improved microfluidic emulsification devices requiring lower concentrations of surfactant to create stable and highly monodisperse emulsions.

Materials and methods

Two types of microfluidic devices (M1 and M2, Figure 1) were prepared by standard soft-lithography techniques [26] in poly(dimethylsiloxane) (PDMS) with channel depths of d 1 = 30µm (M1) or d 2 = 75µm (M2). The PDMS was treated in an oxygen plasma oven (Gala Instrumente) and bound to a glass slide. A commercial surface coating agent (Aquapel, PPG Industries) subsequently dried with N 2 prior to use was used to decrease the wettability of aqueous phase on the channel walls. The microfluidic devices (M1) was designed to study the stability of emulsions generated on chip. It consisted of three parts (see Figure 1 (a)), (i) a classical flow focussing nozzle enabling the production of water droplets in a continuous oil phase [6], (ii) a thin channel of width w = 50 µm and variable length L in which the droplets are separated to prevent collision for a time τ ∝ L and (iii) a coalescence chamber made of an abrupt expansion of the channel (W = 250 µm) in which droplets randomly collide and potentially coalesce. The aqueous phase was a buffered solution (10 mM Tris-HCl, pH8.0), the oil phase a commercial fluorinated oil (FC40, 3M, density ρ = 1.9 10 3 kg/m 3 ) which (i) does not cause PDMS swelling and (ii) does not solubilise most non-fluorinated organic molecules and thereby hinders the exchange of molecules between droplets through phase partitioning. An amphiphilic molecule with a fluorinated tail of a commercial oil (krytox FSH) and a hydrophilic head (di-morpholino-phosphate (DMP)) was used as a surfactant, solublized in the oil at a concentration C (w/w) [21,[START_REF]A1. Fluorocarbon emulsion stabilizing surfactants[END_REF]. The molar mass of the surfactant molecule is M = 6.9 10 3 g/mol. The critical micellar concentration (CM C) in FC40 measured by static light scattering was C CM C = 6 10 -5 g/g (17 µM). Above the CM C, the typical radius of the micelles is ∼ 50 -100 nm1 . Similar surfactants have proven usefull for droplet-based microfluidic applications [START_REF] Holtze | [END_REF]. Volumetric flow rates were controlled using syringe pumps (PHD2000, Harvard Apparatus) and fixed throughout all the experiments in each of the inlet channels to Q o =250 µL/hr. Images of droplets in the microchannels were taken using a standard CCD camera (Guppy, Allied Vision) at 7.5 frames per seconds in region (C). The droplet size distribution was extracted by image processing (Matlab script) of ∼ 1000 frames (∼ 20000 droplets) by counting the number of pixels surrounded by a black ring. The number of pixels was then transformed into the surface area A of the droplet (the apparent radius R of the droplets is simply A = πR 2 ). For channel depth d = 30 µm, droplets of apparent radii larger than ∼ 25 µm are squeezed in the channels as flat pancakes: the droplet area A is therefore proportional to the volume in a good approximation via the approximation of the droplet shape by a cylin-der of height d and radius R (V = Ad). For all the devices used, the droplet radius before coalescence was R 0 = 24 µm ± 5% (for a corresponding area A 0 = 1800 µm 2 ± 10%). For a channel depth d = 30 µm this corresponds to droplets of volume V d ∼50 pL. The microfluidic device (M2) was designed to measure the build-up of surfactant molecules at the oil/water interface.

It is made of a flow focussing junction and an incubation line of 100 µm width (Figure 2b). This device is interfaced with an optical setup to measure droplet fluorescence in an epifluorescence geometry. In this device, the aqueous phase was doped with resorufin at micromolar concentration in PBS buffer solution. Resorufin is used as a fluorescent marker to detect droplets, and acts as a reference for fluorescence intensity. The continuous oil phase is FC40 containing a surfactant made of the same krytox FSH tail, on which a fluorescein isothiocyanate linked to an amine terminated polyethylene oxide hydrophilic head group has been added. The synthesis of this krytox-PEO-Fluorescein surfactant will be presented elsewhere (F. Kleinschmidt et al.

unpublished). This surfactant is fluorescent only when the head group is in an aqueous solution which enables the build-up at the water/oil interface to be monitored directly by the readout of droplet interface fluorescence. It was necessary to adjust the focal plane for each measuring position due to slight deviations from the horizontal of the microfluidic device. After changing the focal plane, the resorufin fluorescence signal was maximised at each measuring position in order to minimize noise. For the analysis, the intensity of the fluorescein signal was scaled by the resorufin signal in order to compensate the intensity variations that arise from the different focal planes. In order to reduce the noise due to the absolute signal intensity an average over 2 consecutive droplets was taken.

Experimental Results

First, we tested the influence of surfactant concentration on the emulsion stability using the microfluidic device M1 (Figure 1 (a)). It is clear that increasing surfactant concentrations lead to an increase of droplet stability. g/g) the droplets are completely unstable: each contact between two droplets leads to coalescence [29]. At intermediate concentrations (10 -3 g/g < C < 2 × 10 -3 g/g, Figure 2 (a)), the droplet size distribution displays several harmonic sub-populations, at multiple integers (i = 2, 3. . . ) of a fundamental population (i = 1): fused droplets have volumes (and here areas) equal to multiple integers of the droplet volume before coalescence: each population is the consequence of a series of individual coalescence events between droplets.

These droplets in region (C) are further destabilized downstream as a result of the increase of the number of collisions resulting in unstable emulsions.

Finally at higher concentrations (C > 2 × 10 -3 g/g, Figure 2(b)) the harmonic intensities decrease and become of the order of statistical noise. These stable droplets in region (C) lead to stable monodispersed emulsions that can be reliably collected and further reinjected in another microfluidic device after long-term storage in syringes (data not shown, see also [21]). Recently the deterministic nature of coalescence has been demonstrated [25]. In our case the relative proportion of each harmonic is the result of a probability of destabilization of the interface between two droplets, the stochastic nature of the process coming from the chaotic nature of the multiphase flow. In the following we will assume that this stochastic phenomenon is the same in all experiments, which is a fair assumption since all experiments are made in devices of identical dimensions and under the same flow rate conditions. The parameter p(1) used to evaluate droplet stability is the proportion of unfused droplets n(1) over the total number of droplets: p(1) = n(1)/ in(i). From a practical view point, droplets are considered as stable for p(1) > 0.999. As expected, increasing surfactant concentration helps to stabilize droplets: at C = 8 10 -3 g/g, no coalescence event were observed for a total of 2.4 10 4 drops.

Second, we varied the length of region (B) in order to study the influence of kinetic effects on emulsion stabilization. The length of the channel in part (B) was set to values between L = 100 µm to L = 5 mm and the droplet-size distribution was extracted for various surfactant concentrations. Since all the experiments were performed at constant total flow rate Q = 3Q 0 and device depth and width d and w, the length L corresponds to an 'incubation' time τ = L×wd/Q during which the surfactant molecules have time to build-up at the oil/water interface. Fixing the surfactant concentration to C = 10 -3 g/g, an increase of the length L lead to a decrease of the number of coalescence event (see Figure 3). The experiment was repeated over a wide range of length and surfactant concentrations (see Figure 4). An increase of L led to a smaller proportion of coalesced droplets (Figure 4), p(1) increased when L increased. In order to quantify the transition, p(1) was plotted as a function of the parameter LC 2 for all the experimental data collected (Fig. 4, the origin of this scaling law will be explained later in this article). We observed a clear transition between the regime of stable droplets and unstable droplets (Fig. 4): experimentaly the separation between the two regimes is in a good approximation represented by Eq. 1:

LC 2 = k (1)
where k ∼ 10 -9 m(g/g) 2 depends on the surfactant used: for other surfactant we observed similar transition but at different values (data not shown).

For values of LC 2 ≫10 -9 m(g/g) 2 the droplets are stable while for values of LC 2 ≪10 -9 m(g/g) 2 the droplets are unstable. This sharp transition showed that two parameters are relevant for the stabilization of a droplet interface:

the surfactant concentration in the oil phase and an additional time-scale corresponding to the droplet incubation time with the surfactant molecules.

In order to demonstrate that this time-scale is linked to the kinetics of build-up of the interface we have used the microfluidic device (M2) with The build-up of the interface is therefore a function of time: the incubation of the droplet along the channel leaves time to the surfactant to adsorb at the oil/water interface. In addition these data show that the surfactant does not accumulate symmetrically on the surface of the droplets. Instead the back end (Figure 5) of the droplet is already highly charged with surfactant at the first measurement position directly after the creation of the droplet.

The droplet interface then gradually fills up with surfactant molecules from the back end towards the middle and finally the front end. This feature of interface in presence of surfactant molecules in a flow or in an electric field can ultimately lead to tip-streaming [30]. These data confirm that the build-up of surfactant at the interface occurs in microfluidic channels on a time-scale of the order of the typical time-scale of droplet manipulation (ms -s). It is clear that this build-up of surfactant at the interface and the kinetics of the surfactant adsorption becomes the key parameters controlling emulsion stability, and are more important than thermodynamic equilibrium parameters such as surface tension or CM C values.

11

In the following we will discuss our experimental observations to explain the behaviour observed in these very simple microfluidic devices. Our aim is to focus on the build-up of the interface as an average over the whole droplet profile, i.e. neglecting the description and modeling of the asymmetric profile observed here. Indeed such an approach would require the description of the motion of molecules at a complex interface in the presence of two flow patterns which is way beyond the scope of the present manuscript. Based on the experimental observations of the dynamic effect of interface build-up, we will discuss the influence of convection and diffusion of micelles and monomers to the droplet/oil interface between the time of droplet production to the time where droplets touch each other. Over the time-scale of droplet production ( 10 -3 s), all of the surfactant is dispersed in the oil volume and effectively none at the oil-water interface. This is confirmed by the experimental observation that the frequency of droplet production is independent of the concentration of surfactant: at short time-scales, there is no effect of surfactant on the surface tension, the droplet production frequency is controlled by the oil/water surface tension only. Over a longer time-scale surfactant molecules migrate to and build-up at the interface. At this stage both concentrations and kinetics of adsorption at the interface are important [31]. To start with, we discuss why, in our opinion, diffusion dominates the kinetics of stabilization by the surfactant. Usually, in order to estimate whether diffusive or convective transport is dominating in a system, the Peclet number P e = U L/D is calculated, with U , L and D as the typical velocity, length-scale and diffusion coefficient in the system. In our case, the Peclet number calculated with a droplet size of 50 µm, a typical speed of 0.1 m/s and diffusion coefficient of 10 -10 m 2 /s (P e = 5000) is larger than one which indicates the predominance of convection.

However in our case, in the reference frame of the droplet, the oil between two droplets is rotating with a laminar flow pattern (Fig. 6) [32,[START_REF] Guenther | Lab-on-a-Chip[END_REF][START_REF] Garstecki | [END_REF]. The flux towards the droplet is then balanced by the flux outwards: the effective transport of elements by convection is not directly linked to the speed of the droplets. However, it could be argued that a certain degree of asymmetry in the oil flow profile could lead to a net flux towards the droplet. Such an asymmetry is for example a known feature for the so-called Taylor bubble which displays stagnation points of the continuous phase streamlines at the edge of bubbles rising in capillaries in a steady continuous phase [START_REF] Guenther | Lab-on-a-Chip[END_REF]. In our case, the continuous oil phase moves at the same speed as the droplet which pushes the stagnation point to the edge of the droplet [32]. Therefore, this asymmetry would be small but could promote the adsorption of surfactant molecules at the back of the droplet which then could explain the asymmetric fluorescent profile obtained in Figure 5. The most effective source of molecule transport in our case will then be diffusive effects: they enable transport of surfactant towards the interface accross the laminar flow lines.

During the flow of the droplet in the channel, the interface adsorbs a certain number of surfactant molecules from the bulk phase. Geometrically, the maximum packing of molecules of typical lateral dimension δ ∼ 2 nm at the interface of a droplet of radius R is achieved with n molecules when 4πR 2 = nδ 2 . Droplets will be stable when the number of molecules at the interface is larger than a fraction 0 < f < 1 of the maximum packing, therefore the stability condition reads:

n 4f πR 2 /δ 2 (2)
As discussed previously, only diffusive effects are considered to describe the build-up of the interface. In the oil, two species are present: free surfactant molecules at a concentration equal to the CM C and micelles which represent the majority of the surfactant concentration C. Considering the sizes of the micelles (∼ 75 nm) the diffusion coefficient D f ree of the free surfactant molecules is much larger than the diffusion coefficient of the micelles D mic and is therefore expected to dominate the diffusion process. The n free surfactant molecules required to stabilize the droplet interface are dispersed in a volume surrounding the droplet over a distance ε of the droplet interface:

n ∼ 4πR 2 εC CM C N A where N A = 6.10 23 mol -1 is Avogadro's number. In a diffusion-limited process, the molecules in this volume will reach the interface in a time t f ree ∼ ε 2 /D f ree which is therefore expressed as Eq. 3:

t f ree ∼ f 2 N 2 A C 2 CM C δ 4 D f ree (3)
Eq. 3 can be further derived to determine the stability transition. Indeed since t = Lwd/Q the stability condition now reads:

L ∼ f 2 δ 4 C 2 CM C DN 2 A × Q wd (4)
The fact that the stability condition does not depend on surfactant concentration is contradictory to the experimental observations (Figure 4). Diffusion of free-surfactant molecules is therefore not the main mechanism of the build up of the interface leading to droplet stabilization. Micelle diffusion has therefore to be considered. Micelles of radius r = 75 nm diffuse much more slowly than free surfactant molecules but when a micelle reaches the interface, the number of molecules involved is given by the number of monomers in a micelle (∼ 4r 2 /δ 2 ≫ 1). Now the n surfactant molecules are present in a smaller volume surrounding the droplet: n ∼ 4πR 2 εCN A and they will pack the interface in a time t mic , the time required for a sufficiently large number of micelles to diffuse to the interface:

t mic ∼ f 2 N 2 A C 2 δ 4 D mic (5)
Eq. 5 can be further derived to determine the stability transition:

LC 2 ∼ f 2 δ 4 DN 2 A × Q wd (6)
Eq. 6 correctly reproduces that the relevant parameter for droplet stabilization is LC We are currently using this technique as a way to characterize surfactants for biological applications (Kleinschmidt et al., in preparation) and we believe that this type of analysis will be of great value to the final users of dropletbased technology.

Practically, microfluidic emulsification has a very interesting advantage. Contrary to bulk emulsification -in which droplet collisions are coupled to droplet production [3] -droplet production and droplet collisions can be decoupled by the use of an 'incubation' channel which enables the surfactant concentration required to stabilize the emulsion to be decreased. The number of micelles in solution after emulsification can be decreased by the use of an 'incubation' nozzle. Since transport phenomena (Ostwald ripening, solubilisate exchange) in emulsions [2] are mediated by micellar transport, the emulsion produced will be less sensitive to these transport phenomena.

Conclusions

In summary, we have observed and quantified the influence of surfactant kinetics on the stabilization of droplets in two-phase flow microfluidics, using two different approaches, one based on a coalescence study and the other based on fluorescence measurement of surfactant build-up at the oil/water interface. The build-up of the molecules at the interface is measured by the increase of the fluorescence signal at the interface and shows an asymmetric profile between the rear and the front of the droplet. The dynamic build-up of the interface is linked to the stabilization of the emulsion produced on-chip: by incubating droplets in a channel where they do not touch, the surfactant is given enough time to pack at the interface leading to the stabilization of droplets with lower surfactant concentration. This dynamic process is mainly governed by diffusion of the surfactant micelles. From our simple experiments we have been able to extract a value for the density of molecules at the interface required to stabilize droplets against coalescence. Finally, we believe that these results and methods will help the design of microfluidic devices for a better control of emulsion properties and for the characterization of surfactant in order to obtain information on typical behaviour of molecules at an interface on a millisecond timescale. In the frame of the droplet, the rotating motion of the oil results in an almost zero net flux of the surfactant towards the droplet interface [32,[START_REF] Guenther | Lab-on-a-Chip[END_REF]. In the vicinity of the droplet, diffusion enables micelles to reach the droplet interface. The number of surfactant molecules in the volume v surrounding the droplet is sufficient to stabilize the interface by simple diffusion of the micelles over the distance ε.

Q o Q o Q o w Q' L (C) (B) (A) w W Q' o Q' o L' Laser line w' (a) (b)

  The fluorescence was measured by exciting the droplet with a single blue laser line (488 nm), oriented perpendicular to the microfluidic channel (See Supplementary Material). It excites both the fluorescein, bound to the surfactant, and the resorufin droplet marker: fluroescence intensities of each of the fluorophores are detected on two distincts PMTs (at 500 -520 nm for fluorescein and at 600 -675 nm for resorufin). We used flow rates Q ′ o = Q ′ w = 200 µL/h for the oil and aqueous phases. The total flow rate in the chan-nel after the flow focussing junction is therefore 600 µL/hr, corresponding to a fluid velocity v = 22.2 mm/s. This resulted in droplets of about 200 µm length. Since the width of laser line estimated from a direct microscope image is about ∼ 10 µm, these elongated droplets enable the measurement of the fluorescence interface at the front of droplet to be separated from the measurement at the back of the droplet. The fluorescein signal shape was determined at four different positions along the channel, starting directly after the droplet creation point and at 2.5, 5, 7.5 and 10 mm from the nozzle.

Fixing

  the length L =1 mm, we analyzed the distribution of droplet sizes in region (C) varying the concentration of the surfactant. At very low surfactant concentration -although still larger than the CM C -( C CM C ≪ C < 10 -3

  the fluorescent surfactant and interfaced the microfluidic chip with the laserinduced fluorescence set-up. Although less efficient for droplet stabilization, it enabled stable droplets to be produced at 0.05 g/g and displayed the same type of behaviour, i.e. an increased stability of the emulsion with LC 2 (data not shown). The surfactant has been designed in such a way that the fluorescence is quenched when the hydrophilic head group is in the oil phase and fluorescent when in water. Therefore the fluorescence of the molecules is linked to the presence of the surfactant at the oil/water interface. For this experiment we produced large elongated droplets at a microfluidic junction with larger dimensions (see materials and methods). The increase of droplet size increased the fluorescent signals coming solely from the molecules at the interface. The profiles of the fluorescein signal along the droplets are presented in Figure5for various measurement points along the incubation channel corresponding to different ages of the droplets since their formation.Directly after the creation the fluorescence profiles of the droplet are very asymmetric: virtually no fluorescent signal is measured in the middle and front end of the droplet and the maximum of intensity is at the back of the droplet (Figure5). Upon following the droplet down the channel the signal gradually rises from the back end towards the middle and finally the front end of the droplet. At the end of the channel (10 mm) the profile is still asymmetric with an excess of surfactant at the back end of the droplet. This asymmetry has also been observed for other flow rates (data not shown).

2 .

 2 In addition, when combining the experimental values D mic = 10 -12 m 2 /s, Q = 750 µL/hr, w = 50 µm and d = 30 µm, and the experimental value of the transition (k ∼ 10 -9 m(g/g) 2 ) we find f ∼ 0.1: the interface is stabilized by a fraction of about 10 % of the maximum packing that can be obtained with 2 nm molecules at the surface of the droplet. This corresponds to a time-scale t mic ∼ 1 -50 ms depending on the surfactant concentration. This timescale corresponds to the one observed in the experiments: a droplet needs ∼ 35 ms to travel a 5 mm long channel of 50 µm width and 30 µm depth. Therefore, the experimental observations are consistent with a model of the interface build-up based on a diffusion limited process involving surfactant micelles. The model enables the fraction of molecules at the interface required to stabilize the emulsion to be extracted from the experimental data.The dynamics of the stabilization is reasonably explained by simple arguments involving micellar diffusion and the analysis performed here enables an estimation of the density of molecules at the interface required to stabilize an emulsion. These results not only show the importance of the kinetics of surfactant adsorption at the interface on stabilization of an emulsion but they also demonstrate that microfluidic systems are an efficient tools to obtain fundamental information on the physical-chemistry of a surfactant molecule.

Figure 1 :

 1 Figure 1: Diagram of the microfluidic devices (M1) and (M2) for surfactant analysis. (a) M1 used for coalescence studies: the device of depth 30 µm consists of three different part: (A) a hydrodynamic flow focussing junction, (B) a channel to keep droplets separated for a length L (w = 50 µm), (C) a coalescence chamber where the droplet undergo stochastic collision for the test of emulsion stability (W = 250 µm). The flow rates are fixed at Q o =250 µL/hr. (b) M2 used for the analysis of surfactant build-up at the interface (the depth of the channel is 75 µm). The droplet production junction is coupled to an optical setup for fluorescence analysis in the incubation channel (w ′ = 100 µm). The flow rates are Q ′ o = 200 µL/hr and Q ′ w =200 µL/hr in order to produce elongated droplets, of length larger than the width of the laser line (in blue).

Figure 2 :

 2 Figure 2: Droplet stability as a function of surfactant concentration C: size distribution of droplets in the coalescence chamber. The length L of the nozzle is L =1 mm (τ = 7.2 ms) for two surfactant concentrations. The area of droplets A are rescaled by the area of unfused droplet A 0 . (a) C = 10 -3 g/g, the emulsion is unstable (A 0 = 1914 µm 2 ), several populations are visible, at areas equal to multiple integers of the unfused droplet area, (b) C = 8 10 -3 g/g, the proportion of fused droplets is less than 10 -4 (A 0 = 1734 µm 2 ): increasing surfactant concentration increases the emulsion stability. For the measurement, droplets touching the edges of the image are discarded.

Figure 3 :

 3 Figure 3: Droplet stability as a function of incubation length L: size distribution of droplets in the coalescence chamber. The concentration C = 10 -3 g/g is constant. (a) L = 1 mm (τ = 7 ms) , the emulsion is unstable (A 0 = 1914 µm 2 ), (b) L = 5 mm (τ = 36 ms), the proportion of fused droplets is less than 10 -3 (A 0 = 2028 µm 2 ): increasing the length of the channel after production helps stabilizing emulsions.

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4: Droplet stability analysis. The ratio of non fused droplets is plotted for five lengths L and various surfactant concentrations C. Both an increase of length and surfactant concentration help to stabilize the droplets: the coalescence rate displays a sharp transition as a function of LC 2 .

A detailled description of this biocompatible surfactant as well as synthesis and caracterization will be published elsewhere(Kleinschmidt et al., unpublished)

For table of contents use onlyKinetic aspects of emulsion stabilization by surfactants : a microfluidic analysis Jean-Christophe Baret, Felix Kleinschmidt, Abdeslam El Harrak, and Andrew D. Griffiths

Acknowledgements

The authors thank B. Hutchison (Raindance Technologies -USA), D. A.

Weitz (Harvard

University -USA), J. Bibette (ESPCI -F) and C. Baroud (LadHyX -F) for stimulating and interesting discussions. J.-C. B. was supported by an EMBO long-term fellowship [ALTF 915-2006]. This work was supported by the European Network MiFem under Contract No. 028417, the Ministre de l'Enseignement Suprieur et de la Recherche, Centre National de la Recherche Scientique (CNRS), Agence National de la Recherche (ANR) (ANR-05-BLAN-0397), and the Fondation d'entreprise EADS.

Supporting Information Available

Sketch of the optical set-up for on-chip fluorescence measurement. This material is available free of charge via the Internet at http://pubs.acs.org.


Meryeme Toto Jamil

Abdelkader Benabou
email: abdelkader.benabou@univ-lille.fr

Stéphane Clénet

Sylvain Shihab

Laure Le Bellu Arbenz

Jean-Claude Mipo

Magnetic ageing investigation of bulk low-carbon silicon steel

Keywords: Magnetic ageing, magnetic losses, precipitation, bulk low carbon silicon steel 1

In this paper, the magnetic ageing of a bulk forged non-annealed magnetic core, used in claw pole synchronous machine, is investigated. The study is carried out by characterizing the material properties of two groups of samples subjected to a thermal ageing at 180 °C that corresponds to the maximum operating temperature of the claw pole rotor. The investigated characteristics are the electrical conductivity, the magnetic properties, the material microstructure and the Vickers hardness. They were characterized along with the ageing time.

The results show that, during the thermal ageing, the hysteresis losses and the Vickers hardness have been affected by the magnetic ageing, whereas the electric conductivity and the normal B-H curve have not been modified. The microstructure analyses showed that carbides precipitates were the main cause behind the magnetic ageing. Moreover, the comparison between the results of two groups of samples revealed the possibility that the magnetic ageing of the material could have started during the manufacturing process of the magnetic core.

Introduction

In electrical machines, ferromagnetic materials are at the heart of electrical energy conversion. Their operating temperature influences their behavior and could affect the performance of the machine. In fact, during the electromechanical energy conversion, the different sources of losses (iron losses, Joule losses) may lead to a significant heating of the machine. The claw pole machine used in the automotive industry is one of these devices that involve high power density in a relatively small volume. For some operating points, the temperature can reach relatively high levels in the claw pole rotor, made from forged magnetic steel, where thermal hot spots reach up to 180 °C [START_REF] Brisset | Thermal modelling of a car alternator with claw poles using 2D finite element software[END_REF]. This increase in temperature combined with the time factor could activate atomic diffusion and precipitation mechanisms modifying the microstructure of steel. Thus, the electromagnetic properties of the material will change irreversibly due to a so-called magnetic ageing. Unfortunately, those changes could be deleterious on the machine energy efficiency.

According to the literature, magnetic ageing is the result of microstructural changes, especially the precipitation and coalescence, mainly at dislocations, of second phase particles (carbides and / or nitrides) [START_REF] Jenkins | Precipitates in electrical steels[END_REF]- [START_REF] Ray | TEM Investigation of Carbide Precipitation in Low Carbon Steels Containing Silicon[END_REF]. These precipitates act as pinning sites for the magnetic domain walls during the magnetization process [START_REF] Jenkins | Precipitates in electrical steels[END_REF]. Particularly, precipitates whose size is close to the domain walls thickness, have the strongest effect [START_REF] Michal | The kinetics of carbide precipitation in silicon-aluminum steels[END_REF], [START_REF] Marra | Magnetic losses evolution of a semiprocessed steel during forced aging treatments[END_REF]. As a result, the coercive force and the hysteresis losses increase [START_REF] De Campos | Consequences of magnetic aging for iron losses in electrical steels[END_REF], [START_REF] Benenson | Kinetics of magnetic aging of low-carbon electrical steel[END_REF], [START_REF] Ray | Magnetic ageing characteristics of low silicon electrical steels[END_REF].

Different parameters influence the kinetic of the magnetic ageing such as the material chemical composition [START_REF] Benenson | Kinetics of magnetic aging of low-carbon electrical steel[END_REF], [START_REF] Ray | TEM Investigation of Carbide Precipitation in Low Carbon Steels Containing Silicon[END_REF], [START_REF] Marra | Magnetic losses evolution of a semiprocessed steel during forced aging treatments[END_REF], [START_REF] Mao | Possible influence of sulfur content on magnetic aging behaviors of non-oriented electrical steels[END_REF], the ageing time and temperature [START_REF] Pardal | Influence of temperature and aging time on hardness and magnetic properties of the maraging steel grade 300[END_REF]. In the case of carbides precipitation, there is no ageing if the carbon presence is below its solubility limit.

Moreover, the silicon acts as a very effective inhibitor of magnetic ageing [START_REF] Leslie | The magnetic aging of low-carbon steels and silicon irons[END_REF]. Its presence in amounts greater than about 1 delays carbides precipitation [START_REF] Benenson | Kinetics of magnetic aging of low-carbon electrical steel[END_REF], [START_REF] Ray | Magnetic ageing characteristics of low silicon electrical steels[END_REF] and in amounts of about 3 or more will restrict magnetic ageing of the material.

The investigation on magnetic ageing listed above deals with semi-processed or fullyprocessed annealed electrical steel sheets. This paper focuses on a full processed non annealed bulk magnetic core having a composition (very low silicon content) and a manufacturing process (hot and cold forging) that strongly differ from those of conventional electrical steels. To our best knowledge, it is the first study dealing with the magnetic ageing of such magnetic steel. The frame of this study relies on two main aspects. Firstly, the investigated material is a low carbon, low silicon steel that has to work under high operating temperatures (180 °C). So, according to the state of the art, its magnetic ageing is an issue that deserves special attention. Secondly, the material underwent several mechanical and thermal constraints during its manufacturing process, especially during the hot and cold forging steps. Considering that the magnetic piece (claw pole rotor) is not annealed during the industrial manufacturing process, it is expected to have a high density of dislocations where the nucleation of precipitates is more likely to occur [START_REF] Ray | TEM Investigation of Carbide Precipitation in Low Carbon Steels Containing Silicon[END_REF].

The present work investigates the magnetic ageing of full processed non annealed bulk magnetic material extracted from a claw pole rotor. The characterization method and the experimental protocol have been defined in accordance with the actual operating conditions of the magnetic core within the electrical device. Thus, the magnetic ageing was performed at 180 °C which corresponds to the operating conditions with the highest level of temperature within the claw pole rotor. The ageing effects on the material properties are investigated in terms of electrical conductivity, magnetic properties, material microstructure and Vickers hardness, all as a function of the ageing time. The paper is organized with a presentation of the characterization methods and experimental protocols. Then, the experimental results obtained from samples extracted from a claw pole are presented and discussed in terms of the ageing effect on the material properties and microstructure. Finally, the impact of the magnetic ageing on two groups of samples extracted from different regions of the claw pole is discussed.

Material and Methods

Material under study

In this paper, the magnetic piece under study is a full-processed claw pole rotor. It is a bulk forged non-annealed magnetic core made from a SAE1006 steel grade. The corresponding chemical composition is presented in Table 1. In a previous study, and as a consequence of the manufacturing process, the claw pole microstructure was found out to be strongly heterogeneous [START_REF] Borsenberger | Contribution à l'identification de l'interaction paramètres procédéspropriétés d'emploi des produits : Application au forgeage et aux propriétés électromagnétiques d'une roue polaire d'alternateur[END_REF]. Thus, to address the issue of claw pole ageing, twelve specimens were extracted by wire electrical discharge machining from the plate of the rotor (Figure 1) where the gradient of grain size variation is the smallest. The choice of the cutting technique is justified by its limited impact on the magnetic properties of the cut pieces [START_REF] Naumoski | Investigation of the influence of different cutting procedures on the global and local magnetic properties of nonoriented electrical steel[END_REF].

Regarding the cutting area, two sets of six-samples each are considered: S.1 samples and S.2 samples with dimensions (35 x 10 x 1) mm 3 and (27 x 10 x 1) mm 3 , respectively. As shown in Figure 2, the S.1 samples are located in front of the claws and the S.2 samples were taken between the claws. The difference of dimensions between the two sets is due to the fact that between the claws, the dimensions of the area do not allow samples longer than 27 mm to be

Experimental

The ageing study was carried out on both sets of samples extracted from the plate of the claw pole. After the initial characterizations, S.1-A and S.2-a samples were kept as a reference for the microstructure analysis while the others underwent isothermal ageing treatment at 180 °C for different total time periods (Table 2). In order to follow the evolution of the electric and magnetic properties throughout the ageing time, the samples were removed from the furnace, at regular time intervals of the heat treatment, and characterized at room temperature. Finally, ten samples (all samples except of S. The magnetic properties of the samples are measured with a specifically developed miniaturized SST (mini SST), as in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF], [START_REF] Jamil | Magneto-thermal characterization of bulk forged magnetic steel used in claw pole machine[END_REF]. Indeed, as mentioned previously (see 2.1), because of the complex shape of the claw pole rotor and its relatively small size, the sample extraction is limited to small dimensions [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF]. The characterization of the B-H magnetic hysteresis loops is based on the flux-metric method.

To measure the magnetic field H inside the sample, two Hall probes are placed next to each other along a line perpendicular to the sample surface, and as close as possible to the sample. Thus, the magnetic fields H 1 and H 2 are measured at two known distances from the sample surface and the magnetic field H at the sample surface is obtained directly by a linear extrapolation.

To measure the magnetic flux density B in the sample, a secondary coil is wound on a plastic support in which the sample is inserted. This way, all the samples are characterized using the same secondary coil to avoid a possible dispersion in the measurements due to a manual winding. Thus, the magnetic flux density B is determined accounting for the compensation of the flux in the air:

( ∫ ( ) ) (Eq 1)
where Ssamp is the cross section of the sample, and are respectively the number of turns, the voltage and the cross-section of the secondary winding, the magnetic permeability of the vacuum and H the magnetic field estimated at the surface of the sample.

For the analyses of magnetic properties, measurements are performed at an excitation frequency of 20 Hz for which the skin depth is expected to be much higher than the sample thickness for this type of material. We will also consider mainly the normal B-H curve that is obtained by collecting the tips (H p , B p ) of centered minor loops and the specific core losses that correspond to the B(H) loop areas.

Regarding the electrical conductivity, the four-point method is employed [START_REF] Arbenz | Characterization of the local Electrical Properties of Electrical Machine Parts with non-Trivial Geometry[END_REF]. In the configuration with a sensor having four aligned needles, a DC current is imposed between the outer pair of needles and the voltage is measured between the inner needles. However, since this method is dependent on the position of the electrical contact points and the shape of the sample, a geometry correction factor is applied as in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF], [START_REF] Smits | Measurement of Sheet Resistivities with the Four-Point Probe[END_REF].

2) Microstructural and mechanical properties

To investigate the presence of precipitated particles and to evaluate the mechanical properties, the selected samples are analyzed using scanning electron microscopy (SEM) and their Vickers hardness characteristics are measured with a 3 kg load. Nevertheless, it must be pointed out that polishing (required for SEM) and hardness measurement were considered as destructive measurements since they modify the stress and strain distribution in the sample and so the magnetic properties. Hence, the hardness variation and the SEM analysis presented below were not performed on the same sample but on different samples from the same group (S.1 or S.2) which are assumed to be similar.

Results of thermal ageing effects on the electromagnetic properties

Thermal ageing effects on the electrical conductivity

The effect of thermal ageing on the electrical conductivity is presented in Figure 3. The characterizations were carried out as explained in Table 3. The four needles technic is no destructive which enables to measure several times the same sample during the ageing process like the sample S1.E and S1.F. According to the homogeneity of the electrical conductivity in the claw pole attested in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF] and [START_REF] Jamil | Magneto-thermal characterization of bulk forged magnetic steel used in claw pole machine[END_REF], all the samples are supposed to have fairly close conductivities before ageing. Therefore, the electrical conductivity measured on the sample S.2-a is representative of those of the other samples. Regarding the uncertainty on the measurement ( 0.18 MS.m -1 ), calculated from the instruments precision and the measurement limitations [START_REF] Jcgm | Evaluation of measurement data -Guide to the expression of uncertainty in measurement[END_REF], it can be noted that the electrical conductivity before and after thermal ageing remained the same. Thus, no significant change in the electrical conductivity as a function of ageing time is observed. This is quite expected as this property depends mainly on the composition of the material which remains the same. To investigate the thermal ageing effects on the magnetic material properties, the claw pole samples were characterized before ageing at 20 Hz frequency. The measured specific losses at 1 T and 1.5 T are listed in Table 4. It appears that the S.1 and S.2 samples exhibit a clear distinct behavior before the ageing process. For example, at 1.5 T the average losses of S.2 samples are about 12 % lower than those of S.1 samples. Also, among each group of samples, a small heterogeneity is observed, with a coefficient of dispersion of 5 %. These characteristics are probably due to the manufacturing process that leads, as already observed in [START_REF] Borsenberger | Contribution à l'identification de l'interaction paramètres procédéspropriétés d'emploi des produits : Application au forgeage et aux propriétés électromagnétiques d'une roue polaire d'alternateur[END_REF], to a heterogeneity of the microstructure (grain size, second phase particles) and residual stress levels that are known to affect the magnetic properties.

Ageing time t(h)

2) Thermal ageing effects on the material magnetic properties

Despite the initial heterogeneity noted in Table 4, the thermal ageing showed a similar behavior for all groups of samples. In fact, the final characteristics after ageing were found to be similar for all the samples. So, thereafter, for clarity of results, the effect of ageing on the hysteresis loop, the B-H normal curve and the losses will be illustrated with the data of sample S.2-e.

In Figure 4 (1), the measured hysteresis loops, at 20 Hz and 1.5 T induction level, are given before ageing (0 h) and after 30 hours of thermal ageing treatment at 180 °C.

Comparing both hysteresis loops, an enlargement of the loop area is clearly observed leading, in the one hand, to an increase of the coercive field, which represents the magnetic field required to demagnetize the sample and, in the other hand, to an increase of the magnetic losses, as illustrated in Figure 4 (3). However, the induction level at saturation and the normal B-H curve, obtained from the tips of minor centered hysteresis loops, are slightly modified (Figure 4 (2)).

3) Ageing index evolution

To further investigate the effect of ageing on the losses, these are decomposed into their hysteresis and dynamic components such as:

(Eq 2)

The hysteresis losses were calculated by extrapolating the specific energy to zero frequency. This has been achieved by considering measurements at four different frequencies, respectively 5 Hz, 20 Hz, 50 Hz and 100 Hz. The dynamic losses were then obtained after subtracting hysteresis losses from the total losses for each frequency. In addition, to describe and quantify the relative variation of the hysteresis losses due to the thermal ageing, the hysteresis loss ageing index (AI_hys) was calculated using (Eq 3):

( ) ( ) (
)

(Eq 3)
where ( ) and ( ) are respectively the hysteresis losses before and after thermal ageing. In Figure 5, the evolution of the index AI_hys is illustrated as a function of

Specific losses P(W/kg)

Magnetic induction B(T)

Non aged 30 hours

(3)

(1) (2)
the ageing time for samples which were aged for more than 30 hours (S.1-D, E, F and S.2-d, e, f) and for 1 T magnetic induction level. The hysteresis ageing index starts to considerably increase after only few hours of ageing. It reaches levels between 8 % and 14 % after about 25 hours of thermal ageing and tends to stabilize after about 30 hours of ageing. The same behavior of the hysteresis ageing index curve was observed on all the samples except for S.1-E, F and S.2-f samples whose ageing index values were lower than 5%. In particular, no significant ageing effect is observed for the samples S.1-E and F. The variability of the measurements prevents from extracting any significant tendency for the ageing index. The origin of such variability will be discussed later in section 5.3. The level reached by the ageing index varies from one sample to another; its values are reported in Table 5.

Comparing the AI_hys of S.1 samples to the AI_hys of S.2 samples, it can be noted that the S.2 samples are more sensitive to ageing. These heterogeneous ageing indexes may be related to the initial microstructural characteristics of the samples that were heterogeneous. The underlying physical origins will also be discussed in section 5.3. In contrast, compared to the hysteresis losses, no significant variation was observed for the dynamic losses. For example, at magnetic induction magnitude of 1 T, the dynamic ageing index AI_dyn, calculated, as in (Eq 3) using dynamic losses at 50 Hz, does not exceed 2.5 %. Indeed, this could be explained by the fact that dynamic losses are mainly related to the electrical conductivity and we have shown experimentally that the electrical conductivity is not impacted by the magnetic ageing.

Consequently, it is expected that the dynamic losses, at least the classical loss contribution [START_REF] Bertotti | General properties of power losses in soft ferromagnetic materials[END_REF], will not be modified by the magnetic ageing.

(1) equipment. The analyses of three selected samples S.2-a, S.2-e and S.2-f, supposed to have similar initial microstructural characteristics, are performed respectively before ageing, after 60 hours and after 205 hours of thermal ageing as reported in Figure 6 and Figure 7. It is shown that before thermal ageing, only few precipitated particles (small white dots) were detected (Figure 6-( 1)), while after ageing treatment the supposed carbide precipitates become more and more apparent and ever more numerous (Figure 6.-(2) and Figure 7).

Moreover, according to the SEM microstructural results, it was noted that even in the samples with low AI_hys (< 5%) or apparently insensitive to ageing, as it is the case for the sample S.2-f in Figure 7, carbide precipitates are also visible. They are visually similar to those of the samples with high AI_hys (like S.2-e in Figure 6-( 2)).

(1) (2)

Magnetic ageing effects on the mechanical hardness

As for the magnetic properties, the presence of carbide particles impacts also the mechanical properties. Thus, the increase of precipitates was corroborated by the mechanical Vickers hardness test. Results of the test are given as a function of ageing time in Figure 8 with the hardness graphs of the S.1 and S.2 samples. First, it is noticed that the S.1 samples are globally harder than the S.2 samples. As previously explained, the difference observed between S.1 and S.2 samples in terms of hardness evolution is also probably due to the inhomogeneity of the claw pole properties induced by the manufacturing process. Second, considering the measurement confidence interval, the hardness observed for the S.

Discussion

Kinetic of the magnetic ageing

To clarify the observed microstructural results, it is important to consider the kinetics of carbon precipitation. In fact, during the ageing treatment, the diffusion mechanisms of the supersaturated carbon in iron α are activated. According to Fick's laws, after 21 hours of treatment at 180 °C, the distance traveled by the diffusing carbon atoms is about 5.65 µm [START_REF] Murry | Aide-mémoire -Métallurgie Métaux, Alliages, Propriétés[END_REF]. Carbon can therefore diffuse and form precipitates of carbides, preferably in dislocations [START_REF] Ray | TEM Investigation of Carbide Precipitation in Low Carbon Steels Containing Silicon[END_REF] which explains the intragranular precipitates observed in Figure 6 and Figure 7.

Moreover, the kinetics of ageing is linked to that of precipitation of carbides.

Consequently, it can be controlled by one or more of the parameters of the precipitated carbides (volume fraction, density, texture and / or size of the particles…). Indeed, it has been reported that precipitates whose size is close to the thickness of the domain wall have the strongest pinning effect on the domain wall movements during the magnetization process [START_REF] De Campos | Consequences of magnetic aging for iron losses in electrical steels[END_REF], [START_REF] Wang | Effect of non-metallic precipitates and grain size on core loss of non-oriented electrical silicon steels[END_REF]. Furthermore, based on the theory of the inclusion of Louis Néel [START_REF] De Campos | Consequences of magnetic aging for iron losses in electrical steels[END_REF], the increase in coercivity was found out to be proportional to the volume fraction of the precipitates. Thus, the kinetics of ageing is the result of the combined effects of the size and the volume fraction of the precipitates. This could further explain the evolution of the indices AI_hyst seen in Figure 5. Three stages can be distinguished. The first presents the initiation state (first 7 hours). At this stage the carbon starts to diffuse and form precipitates. Their fraction and size are very small so their effects on the magnetic properties are limited. This step is followed by a rapid increase in AI (between 7 hours and 20 hours) which corresponds to the growth phase of the precipitates. The size of the precipitates increases significantly, leading to an increase in the volume fraction. Their pining effect on the domain wall movement becomes stronger.

On the other hand, the solid solution becomes depleted of carbon (reduction of supersaturated carbon). The maximum volume fraction of the precipitates is reached, and its value remains constant even in the event of coalescence. As for the size of the precipitates, once it exceeds the thickness of the domain wall, it could not cause more degradation [START_REF] De Campos | Consequences of magnetic aging for iron losses in electrical steels[END_REF], [START_REF] Wang | Effect of non-metallic precipitates and grain size on core loss of non-oriented electrical silicon steels[END_REF], [START_REF] De Almeida | Magnetic Aging, Anomalous and Hysteresis Losses[END_REF]. This explains the trend towards the stabilization (the third stage) observed in Figure 5 after 21 hours of ageing. The same behavior was observed on semi-processed annealed electrical steel (0.034% C and 0.012% Si) in [START_REF] De Almeida | Magnetic Aging, Anomalous and Hysteresis Losses[END_REF] with one significant difference in the ageing times compared to our study. In fact, the highest AI value was reached after more than 100 hours instead of few hours of ageing treatment. Since the chemical composition of the studied materials is quite close, this difference is principally due to the lower temperature of the ageing treatment (150 °C) considered in [START_REF] De Almeida | Magnetic Aging, Anomalous and Hysteresis Losses[END_REF]. Nevertheless, this difference could also be attributed, in part, to the dislocation density which was reduced during the annealing treatment in [START_REF] De Almeida | Magnetic Aging, Anomalous and Hysteresis Losses[END_REF].

The magnetic ageing and the mechanical hardness

Regarding the mechanical hardness, the evolution noted in Figure 8 is due to two phenomena which act on hardness in opposite ways. On the one hand the reduction of carbon in solid solution implies a reduction in hardness, while in the other hand, the precipitation of carbides leads to an increase in hardness. These opposite effects can explain the drop at t=40h of hardness noted on sample S.1 in Figure 8. A similar behavior was also observed by Oliveira Júnior, et al [START_REF] De Oliveira Júnior | Kinetics of Magnetic Ageing of 2%Si Non-oriented Grain Electrical Steel[END_REF] with one significant difference. Indeed, Oliveira Júnior, et al noted that the ageing peaks, measured by Vickers hardness, are reached much earlier than the maximum value of the magnetic losses. This difference was explained by the fact that the size of carbides leading to a maximum effect on the movement of dislocations is much smaller than the size which anchors the magnetic domain walls movement. Yet, it could finally be concluded that even if the hardness and the magnetic ageing result from the same cause, namely the precipitation of carbides, the mechanisms impacting the magnetic properties and the mechanical hardness are not quite the same. Therefore, it is difficult to correlate the evolution of the magnetic ageing and the evolution of the mechanical hardness.

To emphasize this result and make the link with the macroscopic quantities, the iron losses of the samples before and after ageing were compared. In Figure 10, the magnetic losses are given at 20 Hz frequency for the samples S.1-(D, E and F) and S.2-(d, e and f) before and after 30 hours of ageing. Indeed, above 0.8 T of magnetic induction amplitude, the loss curves before ageing show discrepancies between S.1 and S.2 sample groups. However, after the thermal ageing, the dispersion between the losses curves decreases. For example, at 1 T magnetic induction amplitude, the coefficient of variation dropped from 5% to less than 2% as illustrated in Figure 11. The loss curves show a global tendency to converge towards the same final values as observed in Figure 10-(2). This observation strengthens the hypothesis of a more advanced precipitation process in the samples of the S.1 group. Indeed, at the beginning and before the ageing treatment, in comparison to S.2 samples, the S.1 group shows higher iron losses because of a more significant presence of precipitated particles initially formed during the manufacturing process of the magnetic piece. Then, through the thermal ageing treatment applied in the present study, the precipitation process has restarted where it stopped in the S.1 samples, whereas the S.2 samples seemed to have a very limited amount of precipitations before the thermal ageing applied in the present study. Thus, the S.2

samples have exhibited a more sensitive behavior to the ageing treatment, and their iron losses have increased more significantly than those of the S.1 group. However, the compositions of both sample groups being the same, after the stabilization of the magnetic ageing effects, the iron loss curves of both sample groups finally reached the same values.

(1) (2) Figure 10. Specific losses of S.1 and S.2 samples before (1) and after (2) thermal ageing at 20 Hz.

CV (%) B p (T)

Before ageing After ageing

Comparaison between the coefficients of variation of losses Figure 11. Evolution of the coefficient of variation of the losses (all samples considered) before and after ageing (with the ratio of the loss standard deviation on the mean losses value)

Conclusion

The present work has investigated the magnetic ageing of a steel grade used for the manufacturing of massive magnetic parts of claw pole synchronous machine. The composition of the material as well as the operating conditions of the electrical machine (about 180 °C for some operating points) strongly suggest that magnetic ageing should occur.

The obtained results showed a clear evolution of the magnetic properties during the proposed thermal ageing process. Indeed, even if the normal B-H curve is not significantly modified after the ageing process, the losses increase significantly, up to 14 % for some samples. These observations are supported by microstructural analyses showing an increase of carbides precipitates inside the grains. This mechanism explains the loss increase, especially the hysteresis loss contribution, as these microstructural precipitates act as pinning sites for magnetic domain walls during the magnetization process. Moreover, due to the manufacturing process of the investigated magnetic part (the claw pole rotor being obtained from hot and cold forging processes without annealing), heterogeneous properties were observed from one sample to another before the ageing process. The samples, extracted from two different locations in the magnetic piece, exhibit different evolutions of the ageing index.

The possibility of a pre-existing carbide precipitations during the manufacturing process is suspected. Also, the tendency of all samples to have the same magnetic losses at the end of the ageing process supported this hypothesis. The maximum effects of the thermal ageing, at the same temperature of operation of the device, on magnetic losses were achieved after only 21 hours of thermal ageing. Therefore, magnetic ageing may occur rapidly during the first hours of operation of the energy conversion device. In the case of the claw pole alternator application, in the majority of the core, the plates and claws are subjected to a DC excitation.

The major losses in the rotor are due to dynamic ones induced by the flux pulsations at the surface of the claws due to the rotor movement in front of the stators teeth. So, the influence of ageing on the losses may be finally negligible. Nevertheless, for other applications in which the magnetic core is exposed to AC excitation, the influence of ageing on the magnetic properties, especially the losses, should be taken into consideration in the design and performance simulation of the energy conversion device.

Figure 1 .Figure 2 .

 12 Figure 1. Extraction area of samples

Figure 4 .

 4 Figure 4. Magnetic characteristics before (0 h) and after 30 hours of thermal ageing at 180 °C at 20Hz on sample S.2-e. (1) B-H hysteresis loop (for 1.5 T magnetic induction amplitude), (2) Normal B-H curve and (3) Total magnetic losses.

Figure 5 .

 5 Figure 5. Evolution of the hysteresis ageing index as a function of time for 1 T magnetic induction amplitude measurement, (1) S.1 samples and (2) S.2 samples

Figure 6 .Figure 7 :

 67 Figure 6. Precipitate particles (1) before and (2) after 60 hours of thermal ageing at 180 °C (20 µm scale).

Figure 8 .

 8 Figure 8. Vickers hardness evolution (3 kg load) as a function of ageing time for S.1 and S.2 samples

Table 1 .

 1 SAE1006 steel chemical composition.

	extracted. It has been shown that, with our measurement device (see 2.3), developed in [14], a
	variation of length from 35 mm to 27 mm have few influence on the measured magnetic
	characteristics.
				Composition (%)
		% C	% Si	% P	% S	% Mn
	% weight	< 0.06 %	0.07 -0.6 %	< 0.03 %	0.05 %	< 0.35 %

Effect of magnetic ageing on electrical conductivity

	Figure 3. Electrical conductivity evolution as a function of thermal ageing at 180°C with
		measurement uncertainty.
		Samples
	Ageing time	S.1	S.2
	Non aged		a
	14 hours	B, E	b, e
	21 hours	F	f
	27 hours	D, F	d, f
	52 hours	E, F	f

Table 3

 3

. Impact of ageing on the electrical conductivity: Measurement points and characterized samples 3.2. Thermal ageing effects on the material magnetic properties 1) Magnetic losses before ageing treatment

Table 4 .

 4 Initial values of the iron losses at 1 T and 1.5 T

		Iron losses (W/kg)		Iron losses (W/kg)
	Samples		Samples
		P 1 T	P 1.5 T		P 1 T	P 1.5 T
	A	1.93	4.02	a	1.67	3.25
	B	1.72	3.6	b	1.66	3.18
	C	1.68	3.51	c	1.6	3.31
	S.1		S.2
	D	1.79	3.73	d	1.71	3.33
	E	1.82	3.75	e	1.75	3.45
	F	1.89	3.86	f	1.7	3.1

Table 5 .

 5 S.1-A and S.2-a were not mentioned in the table because they did not undergo the thermal ageing. They were used as reference for the microstructural analysis (SEM) Hysteresis ageing index highest values of S.1 and S.2 samples

		14												14
			S.1												S.2
		12	D E											12	d e
			F												f
		10												10
	AI Hys (%)	6 8											AI Hys (%)	6 8
		4												4
		2												2
		0												0
		0	5	10	15	20	25	30	35	40	45	50	55	0	5	10	15	20	25	30	35	40	45	50	55
						Ageing time t(h)									Ageing time t(h)
													1 samples and (2) S.2 samples

*

Acknowledgements

The authors would like to thank Jean-Bernard Vogt from UMET-University of Lille for access to microstructural and mechanical measurement facilities.

Analysis of the S.1 and S.2 groups ageing behavior

In order to investigate the difference in ageing kinetics between the S.1 and S.2 samples, their average grain size was measured using the average grain intercept method (AGI). The average grain size measured on ten of the twelve samples (including the S.1 and S.2 samples) turned out to be quite the same. It varies from 26 to 29 µm. Thus, it was concluded that the grain size could not be the cause behind the observed gap between S.1 and S.2 samples in terms of iron losses. However, the S.2 samples being more sensitive to magnetic ageing than the S.1 samples, one can suspect the presence of already precipitated carbides resulting from the manufacturing process. Indeed, just after the hot forging step (~1100 °C) at the beginning of the manufacturing process and the controlled cooling phase, the magnetic piece is still hot (>200°C) and is air-cooled before the next process steps.

Therefore, considering the massive magnetic piece and its complex geometry, as seen in Figure 2, the region where the S.2 samples have been extracted (close to the radial edge) is more likely to cool down faster than the region where the S.1 samples have been extracted (next to the claws). Thus, given the consideration of a slower cooling rate in the region where the S.1 samples were extracted, the thermal constraints may have triggered more significantly the precipitation of carbides in S.1 samples. Accordingly, the microstructural imaging of the non-aged S.1-A sample is presented in Figure 9. It is remarkable that the white spots, representing the carbides, could exist in this sample group even before the thermal ageing treatment. Therefore, it can be concluded that the magnetic ageing of these samples started right from the manufacturing stage. Consequently, the S.1 sample losses, before the ageing treatment, are susceptible to be higher than those of the S.2 group as it was noted in Table 4.