G Lefebvre

L Galet

A Chamayou

Dry coating of talc particles with fumed silica: Influence of the silica concentration on the wettability and dispersibility of the composite particles

Keywords:

Work of adhesion

Even though dispersion operations have been the object of several investigations, the importance of the various parameters and especially the physicochemical and surface properties are rarely treated. Dry particle coating can be used to create new-generation materials by combining different powders exhibiting different physical and/or chemical properties. In such processes relatively large particles (host particles) are mechanically coated with fine particles (guest particles), without using solvents and subsequent drying, to create new functionalities or to improve initial characteristics. The purpose of this study is to modify the surface of Talc particles by dry coating with different concentrations of hydrophobic Silica (Aerosil R972®), to examine the effect of the coating on the wettability of the coated Talc particles and to study the effects on the dispersibility of these same composite particles. Dry coating is found to modify the surface of Talc particles and to control their wettability and dispersibility in aqueous solutions.

Introduction

Talc is widely used in many industrial areas such as paper, paints, ceramics, cosmetics and pharmaceutics; and is insoluble in water making it a good model material for this study. For economic and environmental reasons, dry particle coating is a very promising method for surface modification for many industries as it does not involve solvents and subsequent drying. In this process, materials with relatively large particle size (host particles; 1 μm-500 μm) are mechanically coated with fine particles (guest particles; 0.01 μm-50 μm) in order to create new functionalities or to improve their initial characteristics [START_REF] Yoshihara | Hybridizationtechnology for surface modification of powders without binders[END_REF]. Typical applications of dry coating include modification of flowability, wettability (hydrophobic/hydrophilic properties), solubility, dispersibility, flavour, etc. The guest particles being necessarily small, means that Van der Waals interactions are strong enough to obtain a stable ordered mixture and the mechanical forces applied by the coating device keeps them firmly attached to the larger host particles. Either a discrete or continuous coating of guest particles (Fig. 1) can be achieved depending on the operating conditions such as processing time, mechanical action, weight fraction of guest to host particles and the physical properties of the used particles [START_REF] Pfeffer | Synthesis of engineered particulates with tailored properties using dry particle coating[END_REF]. This process has been successfully used to modify the surface properties of Silica particles [START_REF] Ouabbas | Surface modification of silica particles by dry coating: characterization and powder ageing[END_REF][START_REF] Thomas | Modeling the mean interaction forces between powder particles. Application to silica gelmagnesium stearate mixtures[END_REF].

In a previous study on the kinetics of the dispersion of Talc powder in liquids, Galet et al. [START_REF] Galet | The importance of surface energy in the dispersion behaviour of talc particles in aqueous media[END_REF] showed that there was a relationship between the optimum stirring power and the total work of dispersion of Talc. This study is extended here by examining the effects of changes in surface properties of Talc powder by dry coating with silica nano-particles. This type of Silica has two interesting properties. Firstly, such surface coatings by nano-silica guest particles bring only a negligible change in size of the Talc host particles. Secondly because of their very small size and their small refraction index, these Silica particles are not detectable by the optical fiber used for the dispersion kinetics measurements (see Experimental Part) and do not interfere with the measurement signal. The hydrophobicity of Talc particles, modified by coating with Silica, will be estimated by contact angles measurements of the different samples with pure water.

Materials and methods

Powders and their characterization

Talc, (Mg 3 Si 4 O 10 (OH) 2 ), is a hydrated magnesium sheet Silicate presenting a lamellar structure. Fine Talc powders with narrow particle size distributions are generally obtained by air jet milling and turbo classification. As grinding can change the surface properties of particles, a single type of Talc mined in France has been used: Talc 00 (Luzenac, France), micronized with a 100 AFG fluidized bed air jet mill. This Talc will be called Talc 9000 (in reference to the micronization conditions). The particle size (d 50 ≈ 7 μm) of this Talc has been determined using a Malvern Mastersizer 2000 (dry dispersion in air). Its specific surface area, calculated with the BET model using a Micrometrics® Asap 2010, is 5.2 m 2 /g. Fumed hydrophobic silica (Aerosil R972® Silica) with a specific surface area of 114 m 2 /g has been supplied by Degussa. Its surface has been modified by dimethyldichlorosilane to make it hydrophobic. The true solid densities of Talc 9000 and Aerosil R972® were obtained using a Micrometrics AccuPyc 1330 helium pycnometer, they are respectively: 2.75 g/cm 3 and 1.95 g/cm 3 .

The uncoated and coated Talc particles were examined with scanning electron microscopy (SEM) to study the surface morphology and particle shapes before and after coating. The lamellar shape of Talc particles can be seen on Fig. 2 a whereas image b shows highly agglomerated silica particles (agglomerates size ≈ 250 nm). The primary particle size is about 16 nm.

Coating process

A Cyclomix high shear mixer has been successfully used to carry out coating [START_REF] Pfeffer | Synthesis of engineered particulates with tailored properties using dry particle coating[END_REF][START_REF] Ouabbas | Surface modification of silica particles by dry coating: characterization and powder ageing[END_REF][START_REF] Ouabbas | Particle-particle coating in a cyclomix impact mixer[END_REF]. The apparatus used here is a vertical high shear mixer (Fig. 3), supplied by Hosokawa Micron B.V. with a nominal volume capacity of 1 L. Industrial versions are available with capacities of up to 1 m 3 . The working principle of the Cyclomix differs markedly from other mixing techniques by the specific interaction between the product being mixed and vessel wall. The powders (host and guest particles) are loaded at the top of the conical mixing vessel to a filling ratio 66%. The high rotation speed of the paddles (2240 rpm) forces the particles to the wall where the conical shape of the vessel forces the product from the lower to the upper zone of the vessel. At the top, the product flows inwards and downwards into the centre of the vessel. This flow pattern gives fast macromixing. During the upward motion, the particles are accelerated by the paddles and intensively mixed by friction with the vessel wall. At the end of the process, the totality of the powder (Talc + Silica) contained in the Cyclomix is recovered for the experiments. The processing time used in this work was 10 min. The values of the Silica concentration were in the range from 0% to 10% in weight.

Wettability measurements

The critical surface energy of coated and uncoated Talc 9000 particles was first estimated by the Stevens Method [START_REF] Stevens | Wettability of powders[END_REF]. In this the wettability of powders is determined by sprinkling the powder on liquids having a range of surface tensions obtained by varying the proportions of isopropanol and water (colored by methylene blue) mixtures. This test gives a "wetting number", which is the surface tension γ LV of the mixture with a minimum of isopropanol content, that wets the powder in less than 1 min. A powder is considered as wetted by a liquid if it has either sunk into the liquid or if remains at the surface, but is colored by methylene blue. Surface tensions of the mixtures were measured with a tensiometer Kruss® K12 using the Wilhelmy plate method.

The contact angles of the powders were then measured by the sessile drop method (performed with a tensiometer ILMS-GBX) by deposing a small drop (five drops per sample) of 10 μL of pure water on tablets formed from powder. The tablets were made by a compression under a load of 30 kN using an Instron® press. The shape of the drops was observed and used to determine the contact angles. These contact angles values were used to calculate the work of adhesion using the Eq. ( 1):

W a = γ LV : 1 + cos θ ð Þ ð 1Þ

Measurement of dispersion kinetics

Measurements of dispersion kinetics of uncoated and coated Talc particles in water were performed using a three baffled stainless steel reactor (10.5 cm diameter) with a 3.5 cm diameter dispersion stirrer (deflocculating). An optical fiber sensor was used to measure the dispersion rate of particles in water. This non-commercial device was For a given concentration of particles, the signal decreases when the particles size increases [START_REF] Bergougnoux | Characterization of an optical fiber bundle sensor[END_REF]. Preliminary studies [START_REF] Goalard | Etude physico-chimique du procédé de dispersion des poudres libres et agglomérées en milieu liquide[END_REF] show that the position of the sensor in the reactor has no influence on Wetting number range (mJ m -2 ) 37.2-37.7 35.9-37.2 35.9-37.2 34.5-35.9 34.5-35.9 34.5-35.9 34.5-35.9 34.2-34.5 34.2-34.5 33.6-34.2 31.9-33.6

the relative dispersion kinetics. In our experiments the sensor was located at 2 cm from the bottom of the reactor. The linearity of sensor response to changes in solids concentration has been validated in separate experiments and the sensor calibrated to determine the response to a given concentration of powder. The maximum response when the powder is fully dispersed is used to normalize the results of each experiment to fractional dispersion values. To be sure that the signal obtained at the end of an experiment corresponds to the total dispersion, the stirring speed is increased to the maximum to disperse all the particles. This maximum response is referred to as R∞. The sensor response to the dispersion of the powder in a liquid, is merely an arbitrary voltage R which can be related to the concentration of dispersed particles by calibration if the dispersion profile has to be developed. For a constant size, the extent of dispersion, X(t), is defined in Eq. ( 2).

X t ð Þ = R t ð Þ R∞ = C t ð Þ C∞ ð2Þ
The stirring speed was 1500 rpm. According to the Eq. ( 3) the corresponding stirring power in the liquid is 1000 W m -3 .

P = N P ρN 3 d 5 ð3Þ
Table 2 Results of wettability (contact angles measurements) and dispersion speed (S: slope at the origin of the kinetics).

Silica concentration (% w/w) 0 0.5 Where P = power dissipated (W m -3 ), N P = power number given by the stirrer supplier (1.06), ρ = liquid density (1000 kg m -3 ), N = stirring speed (25 s -1 ), d = stirrer diameter (35.10 -3 m).

Results and discussion

Surface morphology

The SEM photos (Fig. 4) show a discrete and uniform coating in which all the Silica particles play a part. During the observations, no single or agglomerated free Silica particles were observed on the support. The increase of the silica concentration on the Talc surface appears clearly in these pictures. For all the samples, some parts of the Talc surface remain free except for the 10% concentration for which almost all the surface is recovered by Silica.

Wettability measurements

The results of wettability measurements as a function of Silica concentration are listed in Table 1 (Stevens method) and Table 2 (Sessile drop method).

Table 1 shows that the surface tension of the water/isopropanol mixture has to be decreased to wet the powder meaning that the wetting number decreases when the concentration of hydrophobic silica guest particles increases. Table 2 presents the values of contact angles and work of adhesion as a function of the silica concentration. From 0% to 10%, the contact angles increases from 53°to 133°, which confirms the increase in hydrophobicity of the composite particles caused by the presence of hydrophobic Silica. This trend is illustrated by the behavior of water drops on the tablets (Fig. 5). The work of adhesion, related to the affinity between the particles and the liquid (water), decreases with increase in silica concentration.

In the following Section 3.3 (Dispersion kinetics) the relation between the work of adhesion and the dispersion kinetics will be discussed.

Dispersion kinetics

Fig. 6 shows the dispersion kinetics of the uncoated and coated Talc particles with different silica concentrations. The presence of silica modifies the dispersion kinetics of Talc 9000: the higher the silica concentration, the lower is the rate of dispersion. For 0.5% silica concentration, the dispersion stays unchanged and complete dispersion is obtained at the same time as with the uncoated particles (about 1200 s). When the silica concentration is increased from 1% to 10%, the work of adhesion decreases from 116.3 mJ m -2 to 22.8 mJ m -2 and the dispersion rate, characterized by the slope at the origin (S) of the dispersion kinetics (see Fig. 6) decreases from 2.59 ms -1 to 0.17 ms -1 (see Table 2). For silica concentrations higher than 5%, the general aspect of the dispersion kinetics is changed and for the 10% concentration a threshold value seems to have been reached at which the stirring power used is no longer sufficient to obtain a complete dispersion. For this silica concentration, a plateau is reached at about 80% dispersion (20% of the powder remains at the surface of the water) at between 5000 s and 7000 s (not shown in this figure), and the stirring power has to be increased to obtain a total dispersion.

Increasing the silica concentration from 0 to 5% leads to a strong decrease of the work of adhesion (from 116.3 mJ m -2 to 55.3 mJ/m 2 ) which is accompanied by a big decrease in the rate of dispersion characterized by S, from 2.59 ms -1 to 0.41 ms -1 (see Table 2 and Fig. 7). The same increase of 5% in the silica coating (from 5% to 10%) leads to a smaller decrease of the work of adhesion from 55.3 mJ/m 2 to 22.8 mJ/m 2 and a smaller decrease in the rate of dispersion (from 0.41 ms -1 to 0.17 ms -1 ). Thus, the first modification of the surface of Talc 9000, characterized by small additions of coating silica (0.5%-4%), has a strong influence on the rate of dispersion. The influence of larger quantities of silica (5%-10%) on S is less. For example in the experiments with 7% and 10% Silica, S is almost the same, but with 10% silica only 80% of the particles are dispersed and the stirring power has to be increased to complete the dispersion. One hypothesis S = Slope at the origin dX(t)/dt at t=0 is that for high concentrations of silica (greater than 4%), almost all the Talc is covered by silica and we reach a critical work of adhesion.

Up to the values of 4% silica concentration, the experimental curves can be fitted (Figs. 8 and9) by a two parameter exponential model presented elsewhere [START_REF] Galet | The importance of surface energy in the dispersion behaviour of talc particles in aqueous media[END_REF][START_REF] Kravtchenko | A novel method for determining the dissolution kinetics of hydrocolloid powders[END_REF][START_REF] Larsen | A novel method for measuring hydration and dissolution kinetics of alginate powders[END_REF] and given in Eq. ( 4), where k (ms -1 ) characterizes the dispersion rate and A corresponds to the final stage of the dispersion. The value of A approaches 1 when all the particles are dispersed in the liquid.

X t ð Þ = A 1-e -kt ð4Þ
On the one hand, for silica concentrations from 0% to 4%, the decrease in the work of adhesion leads to a decrease in the rate of wetting (and also the rate dispersion) but the wetting is not considered as a "limiting step" at the stirrer speed used. On the other hand, for the silica concentrations greater than 4%, the shape of the dispersion kinetics changes, particularly over the first thousand seconds (for example between 0 s and 1000 s for the 10% concentrations in Fig. 6). One of the future objectives will be to find another model for such kinetics, including another parameter characteristic of this limiting wetting step.

Conclusion

This study indicates that it is possible to change the dispersion properties of Talc particles by coating them with hydrophobic Silica (Aerosil R972®) using a Cyclomix as dry coating device. The coating obtained is a discrete coating of silica on the surface of Talc particles and it makes the Talc more hydrophobic. This is confirmed by the measurements of the work of adhesion determined by the sessile drop method on tablets of powder. An important result of this study is that the work of adhesion can be related to the dispersibility of the particles system in water. At silica concentrations of between 0 and 4% Silica concentrations, the dispersion kinetics can be fitted by two parameter model where the values k and A relate respectively to the rate of dispersion and the height of the plateau. One of the future objectives is to determine a fit for higher Silica concentrations (between 5% and 10%) where there is an initial wetting step before the dispersion. This causes either an increase in the time for complete dispersion or a decrease of the quantity of powder finally dispersed.

Fig. 1 .

 1 Fig. 1. Dry particle coating principle.

Fig. 2 .

 2 Fig. 2. (a) Talc particles (×3200) and (b) Aerosil R972® particles (×12,600).

Fig. 3 .

 3 Fig. 3. Scheme of the Cyclomix high shear mixer.

Fig. 4 .

 4 Fig. 4. SEM pictures (×6400) of uncoated Talc particles (a) and coated particles with different concentrations of Silica: 1% (b), 2% (c), 3% (d), 4% (e), 5% (f), 7% (g) and 10% (h).

Fig. 5 .

 5 Fig.5. Pictures at t 0 of water sessile drops on uncoated Talc tablet (a) and coated Talc tablets with different concentrations of Silica: 0.5% (b), 1% (c), 1.5% (d), 2% (e), 3% (f), 4% (g), 5% (h), 7% (i) and 10% (j).

Fig. 6 .

 6 Fig. 6. Dispersion kinetics of Talc coated with different concentrations of Silica (P = 1000 W m -3 ).Fig. 8. Correlation between raw data and the fit (2% Silica concentration).

Fig. 8 .

 8 Fig. 6. Dispersion kinetics of Talc coated with different concentrations of Silica (P = 1000 W m -3 ).Fig. 8. Correlation between raw data and the fit (2% Silica concentration).

Fig. 7 . 9 .

 79 Fig. 7. S (slope at the origin dX(t)/dt at t = 0) as a function of work of adhesion. Fig. 9. Fits of the kinetics until the 4% concentration.

Table 1

 1 Results of Stevens method.

	Silica concentration (% w/w)	0	0.5	1	1.5	2	2.5	3	4	5	7	10


I Murrieta-Pazos

L Galet

C Rolland

J Scher

C Gaiani

Interest of energy dispersive X-ray microanalysis to characterize the surface composition of milk powder particles

Keywords: Dairy powders Energy dispersive X-ray technique Surface composition Composition gradients EDX, energy dispersive X-ray, ESEM, environmental scanning electron microscopy, NMC, native micellar casein, NWI, native whey isolate, SEM, scanning electron microscopy, SMP, skim milk powder, WMP, whole milk powder, XPS, X-ray photoelectron spectroscopy

Energy dispersive X-ray (EDX) is a technique rarely used for organic powders. Nevertheless, this technique is of great interest in the characterization of milk particle surface. In order to validate the method, the EDX technique was tested on pure milk components, on model powders composed of different ratio of lactose/whey proteins and on whole milk powders presenting or not free fat at the surface. For all these powders, satisfactory results were obtained with correct experimental atomic percentages in comparison with expected theoretical percentages. The technique was then applied to skimmed and whole milk powders sieved in 4 fractions. The surface and the core (cut particle) were analyzed by EDX and compared. A relationship between the particle size and the surface composition was observed. X-ray photoelectron spectroscopy (XPS) often used to characterize milk powder surface, however no differences were observed between surface and core composition using this method. The depth of analysis by EDX is far more significant (1 m) in comparison to that of the XPS (5 nm); hence it was concluded that the analysis of cut particle by EDX was not interesting since too close to the results obtained at the surface. Finally, the technique was coupled with XPS and successful hypothesis concerning composition gradients were done.

Introduction

Milk powders are produced by spray drying milk from a feed to contain uniformly distributed components. Nevertheless, it has been demonstrated by various authors [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF][START_REF] Nijdam | The effect of surface composition on the functional properties of milk powders[END_REF][START_REF] Shrestha | Effect of protein concentration on the surface composition, water sorption and glass transition temperature of spray-dried skim milk powders[END_REF][START_REF] Kentish | Milk skin formation during drying[END_REF] that these components were redistributed during the droplet formation process. The resulting particles present an heterogeneity between the surface and the core. In addition, the surface/core heterogeneity may be accentuated by packaging, storage and/or transport conditions [START_REF] Gaiani | Native phosphocaseinate powder during storage: lipids released onto the surface[END_REF][START_REF] Kim | Surface composition of industrial spray-dried milk powders. 3. Changes in the surface composition during long-term storage[END_REF][START_REF] Fitzpatrick | Glass transition and the flowability and caking of powders containing amorphous lactose[END_REF]. In turn, it is now generally well accepted that the particle surface composition has a strong impact on powder functional properties (reconstitution properties [START_REF] Forny | Wetting, disintegration and dissolution of agglomerated water soluble powders[END_REF], stickiness [START_REF] Shrestha | Effect of protein concentration on the surface composition, water sorption and glass transition temperature of spray-dried skim milk powders[END_REF], flowability [START_REF] Kim | Effect of surface composition on the flowability of industrial spray-dried dairy powders[END_REF], floodability, oxidation [START_REF] Vignolles | Free fat, surface fat and dairy powders: interactions between process and product[END_REF]. . .). As the food powder production increases new and innovative methodologies are required to understand the behaviour of these powders regarding their functional properties. For this, a growing number of interesting methods allowing the surface characterization of milk powders has been used recently or are under development [START_REF] Murrieta-Pazos | Food powders: surface and form characterization revisited[END_REF].

During the two last decades, the most used technique to characterize the surface of dairy powders was the X-ray photoelectron spectroscopy (XPS). XPS provides elemental (atomic percentages) and chemical (binding percentages) information for the first 5-10 nanometres below the particle surface [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF][START_REF] Shrestha | Effect of protein concentration on the surface composition, water sorption and glass transition temperature of spray-dried skim milk powders[END_REF][START_REF] Kim | Surface composition of industrial spray-dried milk powders. 3. Changes in the surface composition during long-term storage[END_REF][START_REF] Faldt | The surface coverage of fat on food powders analyzed by ESCA (electron spectroscopy for chemical analysis)[END_REF][START_REF] Gaiani | How surface composition of high milk proteins powders is influenced by spray-drying temperature[END_REF][START_REF] Kim | Surface composition of industrial spray-dried milk powders. 1. Development of surface composition during manufacture[END_REF][START_REF] Kim | Surface composition of industrial spray-dried milk powders. 2. Effects of spray drying conditions on the surface composition[END_REF][START_REF]Characterisation of spray-dried emulsions with mixed fat phases[END_REF]. From the atomic values, the determination of the principal components percentages (protein, lactose and lipids) present at the powder surface can be done with the help of a matrix formula [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Faldt | The surface coverage of fat on food powders analyzed by ESCA (electron spectroscopy for chemical analysis)[END_REF]. Another classical approach was also possible with the development of scanning electron microscopy (SEM). Investigations performed by SEM may indeed present some disadvantages as: information about components is difficult to obtain (if not used in conjunction with EDX). In addition, samples have to be coated with a conductive material (creation of artefacts). By SEM, different surface content in lactose, lipids and/or proteins were related to differences in surface topography. For example the powders were more or less shrivelled, smooth. . . [START_REF] Mistry | Effect of lactose and protein on the microstructure of dried milk[END_REF]. Nevertheless, quantitative information is impossible to obtain in this way. Surface investigations were also possible by solvent extraction, but these techniques were only produced interesting results for powders containing fat [START_REF] Vignolles | Free fat, surface fat and dairy powders: interactions between process and product[END_REF]. EDX is another powerful technique allowing an elemental analysis of the surface (as well as XPS). This technique, contrary to XPS, allows the surface characterization at a deeper level from the first micron to the five first microns. In addition, EDX allows a very localized characterization in the particle whereas the area of XPS analysis is larger (300 × 700 m) [START_REF] Briggs | Practical surface analysis[END_REF]. Recently, environmental scanning electron microscopy (ESEM) images were combined with EDX analysis. The environmental mode allows examination of the specimen without the necessity to coat and then eliminates the inteference of sample coating during chemical analysis. The EDX analysis system works as an integrated feature of an ESEM equipment and cannot operate on its own. Its characterization capabilities are due in large part to the fundamental principle that each element has a unique atomic structure allowing X-rays to be identified uniquely from one another. An EDX spectrum is a plot of how frequently an X-ray is received for each energy level. The higher a peak in a spectrum, the more concentrated the element is in the sample. In the field of food powders, EDX was rarely used [START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF][START_REF] Murrieta-Pazos | Food powders: surface and form characterization revisited[END_REF][START_REF] Laskin | Automated single-particle SEM/EDX analysis of submicrometer particles down to 0.1 m[END_REF]. Only few authors used this technique to investigate the chemical composition of dairy powders [START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF]. Even if this technique seems to be very promising, these first results need in depth validation.

For this purpose, industrial skim and whole milk powders were used. In addition, pure milk components were purchased to validate the methodology. The aim of this paper is to test a recent and innovative technique called EDX and to see if this technique can be used to characterize the surface or the composition gradient of dairy powders.

Materials and methods

Materials

Two industrial milk powders obtained from Lactalis (Laval, France) were studied. Proteins and lactose content were determined by Kjeldahl method and enzymatic kit (Enzytec Lactose/d-Galactose, Diffchamb SARL, Lyon, France) respectively. Fat content was determined with a Röse-Gottlieb extraction and ashes were measured after incineration at 550 • C (from the American Dry Product Institute, 2002). Moisture content was determined by weight loss after drying 1 g of powder at 103 • C for 5 h (from the American Dry Product Institute, 2002).

The following compositions (% w/w) were measured respectively for skim milk powder (SMP): water (3.8), proteins (37.1), lactose (52.0), lipids (1.4) and ashes (5.7) and whole milk powder (WMP): water (3.9), proteins (26.2), lactose (36.7), lipids (27.3) and ashes (5.9).

For method validation, powders containing pure components were used. To study milk proteins, native micellar casein (NMC) and native whey isolate (NWI) powders were used. NMC powder was obtained from International Dairy Ingredient (IDI, Arras, France). This industrial powder (Promilk 872B) is obtained by microfiltration from milk and presents a high percentage of native micellar casein (more than 88% w/w). NWI powder (Prolacta 90) was provided by Lactalis (Laval, France) and present more than 90% wt/wt whey. Monohydrated lactose was purchased from VWR-Prolabo (Fontenay sous Bois, France) and Anhydrous Milk Fat (AMF) was obtained by centrifugation of melted butter.

Whole milk powder without free fat

The free fat was defined as the fat that was not entirely coated and stabilized by surface-active elements or a matrix containing proteins and lactose [START_REF] Vignolles | Free fat, surface fat and dairy powders: interactions between process and product[END_REF]. The free fat is located both at the surface and in inner parts of a powder particle surface. The free fat was extracted [START_REF] Kim | Melting characteristics of fat present on the surface of industrial spray-dried dairy powders[END_REF] with some adaptations. Petroleum ether was added to 10 g of powder in a 1:5 (p:p) proportion. After mixing for a period of 5 min at 300 rpm, the solvent was eliminated by filtration. After 5 extractions, the powder was dried under fume cupboard and ready for further analysis.

Particle sieving

Between 10 and 20 g of powders were sieved in a Retsh sieving device (Retsch GmbH AS200 digit, Haan, Germany). The sieving duration was 20 min at a power of 60 in the machine scale. Powders corresponding to different sizes were obtained by using sieves corresponding to 40, 80, 125 and 160 microns.

X-ray photoelectron spectroscopy

XPS is a quantitative spectroscopic technique that measures the elemental composition up to 5 nm depth. It provides elemental and chemical state data in solid samples. XPS is performed in an ultrahigh vacuum (10 -8 kPa) which may limit the technique in the food industry and specifically for liquids. Nevertheless, it is not an inconvenient in the case of food powders. The use of XPS was extended for the last 20 years to the surface composition of dairy powders. From the C, O and N percentages, the contents in protein, lactose and fat at the surface were calculated with a matrix formula already used in a great number of studies [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Gaiani | Native phosphocaseinate powder during storage: lipids released onto the surface[END_REF][START_REF] Faldt | The surface coverage of fat on food powders analyzed by ESCA (electron spectroscopy for chemical analysis)[END_REF][START_REF] Gaiani | How surface composition of high milk proteins powders is influenced by spray-drying temperature[END_REF][START_REF] Jayasundera | Surface modification of spray dried food and emulsion powders with surface-active proteins: a review[END_REF].

The XPS analyses were carried out with a Kratos Axis Ultra (Kratos Analytical, Manchester, UK) photoelectron spectrometer. The instrument uses a monochromatic Al K␣ X-ray source. The powder samples were attached to the sample holder with a double side conductive tape. The analyzed area was about 700 × 300 m. Spectra were analyzed using the Vision software from Kratos (Vision 2.2.0). Quantification was performed using the photoemission cross-sections and the transmission coefficients given in the Vision package.

Energy dispersive X-ray analysis

EDX equipment

Powder samples were characterized with an EDX analyzer coupled to a ESEM XL30 (Philips) microscope instrument operating at 20 kV and equipped with an EDAX EDX detector with an atmospheric thin window and a link analytical system. An average elemental composition of the samples was obtained by a data collection at 3 different m 2 sized windows (5 m 2 ) on the powder surface. Samples analyzed by this technique were not metallized EDX is a technique coupled with ESEM to enable the analysis of the atomic composition of the sample. It works in a depth of approximately 1 m of EDX for the determination of the surface content in lactose, protein and lipids

The application of the technique to dairy powder has been adapted from XPS data treatment [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Shrestha | Effect of protein concentration on the surface composition, water sorption and glass transition temperature of spray-dried skim milk powders[END_REF][START_REF] Jayasundera | Surface modification of spray dried food and emulsion powders with surface-active proteins: a review[END_REF][START_REF] Faldt | The surface composition of spray-dried protein-lactose powders[END_REF][START_REF] Faldt | Spray-dried whey protein/lactose/soybean oil emulsions. 2. Redispersability, wettability and particle structure[END_REF]. Here, the relative atomic concentration of carbon, oxygen and nitrogen at the surface (∼5 m) of the powder was quantified and used in a matrix formula to calculate the relative surface content P, L and F in proteins (P), lactose (L) and fat (F). Experimental values obtained from the reference samples (casein, whey proteins, anhydrous milk fat and monohydrated lactose) are estimated and used to carry out these calculations. By solving the matrix, (␣P), (␣'L), (␣"F), respectively the proteins, lactose and fat surface contents are determined.

Results and discussion

Powders characterization by ESEM-EDX

Pure milk components

The structure of NWI (Fig. 1A) and NMC (Fig. 1B) powders observed by ESEM are typical of spray dried powders. More or less agglomerated powders were observed for NWI whereas individual almost spherical structures can be appreciated for NMC powders. The largest size of agglomerated NWI particles (around 100 m) compared to NMC particles (around 50 m) which are in agreement with the values found by static light scattering (data not shown). On NWI powders, a higher heterogeneity in particle size in comparison with NMC powders was noticed. All the particles present a smooth surface and the presence of dents was observed. Typical structures (less spherical and more irregular) were observed for lactose particles with the presence of small crystals at surface (Fig. 1C). In the case of AMF (Fig. 1D), a drop of molten fat was placed on the support. As the temperature in the ESEM chamber was near to 5 • C, a solid film was formed. No additional specific details were observed.

For lactose, three points (red arrows) were analyzed on the same particle and are represented before and after analysis (Fig. 2A1-B1). After analysis, local degradation of the lactose can be observed. These degradations are representative of the fragility of the lactose structure and may also cause problems during the analysis. Indeed, the EDX analysis is sensitive to the angle of analysis with respect to the detector. Such penetration of the electron beam in the particle could prevent a good spread of X-rays to the Fig. 2. Scanning electron micrographs before (A) and after (B) EDX analysis of lactose monohydrated powder (×800) (1), native whey isolate powder (×400) (2), native micellar casein powder (×1600) (3) and anhydrous milk fat (×200) (4). detector. The particle shape can be also a parameter of influence. Ideally, the sample should be analyzed as a tablet, to get a flat and not-hilly surface to permit an ideal angle of response. However, the aim of this work was to study the surface of the particles, as such, the powder should be directly placed in the support. The results of the three points analyzed are shown in Table 1. For lactose, which is a carbohydrate molecule, only carbon and oxygen were found as expected. This is a classical composition of carbohydrate. By consequence, these analyses may confirm the efficacy of the EDX technique to detect the elements that actually make up organic particles. Nevertheless, when looking to the carbon value for lactose, an overestimation was immediately observed. However, the atomic concentration ratios (C: 79.2 and O: 20.0) were not in agreement with the expected stoichiometric values (C: 50 and O: 50). This overestimation of carbon is common when using X-ray techniques [START_REF] Gerin | Performance of XPS analysis of model biochemical compounds[END_REF][START_REF] Rouxhet | XPS analysis of bio-organic systems[END_REF]. The C peak intensity was more important and may be due to carbon contaminant and impurities collected from the atmosphere during the sample transfer into the EDX chamber or during product manufacturing. Nevertheless, the standard deviation does not vary significantly. This means that there is a good reproducibility of the results for a given particle.

The points of analyzes performed on the NWI particles are presented before and after analysis (Fig. 2A2-B2). In contradiction with the lactose powder, no degradation of the material occurred. The structure of NWI seemed to be more resistant than the lactose one and was not affected by the X-ray beam. This resistance can help to reduce variations in the results and also enable multiple analyses on one single particle. In Table 1, the atomic concentrations obtained at the surface of NWI powder are presented. In addition to C and O elements, the presence of nitrogen (expected as NWI is a protein powder) and minerals are detected. In milk powders, proteins are the only molecules that can have nitrogen element in their composition. Consequently, the N percentage is directly proportional the protein percentage in the powder surface. Sulfur is the most abundant mineral in NWI [START_REF] Gaiani | Milk proteins differentiation and competitive adsorption during spray-drying[END_REF]. As expected, the atomic concentration in NWI did not vary significantly; this confirms a more resistant material which allows a better reproducibility of the analysis (in comparison with lactose).

For NMC powders, Fig. 2A3-B3 shows respectively the localization of 2 points of analysis before and after analysis. The dot a was performed on a small particle close to a bigger one (dot b). After the analysis, it can be observed again that there was no degradation of the material constituting these proteins. In this protein, carbon, oxygen and nitrogen are again observed but the quantity of mineral was higher as micellar casein is known to be rich in calcium and phosphorus in comparison with NWI [START_REF] Gaiani | Milk proteins differentiation and competitive adsorption during spray-drying[END_REF]. The standard deviation was minimal; by consequence the reproducibility of the analysis for this sample was very good (Table 1).

Finally, the analysis was also performed on the AMF (Fig. 2A4-B4). The state of this component is not a particle but a thin film. It can be clearly observed that degradation is caused by the analysis. This effect was fully expected; as the texture was very soft due to a melting point around 40 • C which makes it very fragile. Consequently, it can easily change its stat to become liquid. However, a good reproducibility in the analysis was achieved (Table 1). It can be also appreciated that only carbon and oxygen are detected in the analysis with a very high atomic concentration of carbon. These results correspond to the theoretical atomic composition of AMF.

Industrial milk powders

Fig. 1E and F show the general structural aspect of WMP and SMP respectively. The powders analyzed were both characterized by heterogeneous particles. Usually a smooth surface is appreciated in WMP mainly due to surface covered by free fat [START_REF] Vignolles | Free fat, surface fat and dairy powders: interactions between process and product[END_REF]. On the other hand, a more rigid and wrinkled surface is observed for SMP mainly due to the presence of a lactose-protein matrix and less surface fat. These appearances were characteristic and were already widely observed by others [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Nijdam | The effect of surface composition on the functional properties of milk powders[END_REF] and also by the authors on the same powders [START_REF] Murrieta-Pazos | Comparative study of particle structure evolution during water sorption: skim and whole milk powders[END_REF].

Variation of analysis (by particle and by day)

The EDX analysis is not typically used in organic samples like dairy powders. Up to now, it was not really clear if different particles could have different atomic elements at the surface. In order to interpret the results correctly, it was very important to obtain a good repeatability. Consequently, measures at the surface of different particles and measures realized on different days were performed (Table 2). The variations from one day to another can be explained by the pollution in the microscope chamber. This may occur if some samples with high carbon content were prior analyzed; further analysis may be altered. Averages of more than 10 analyses on different particles on more than 4 different days were performed for each pure milk component as presented. The influence of the particle on the reproducibility was correct for NMC, NWI and AMF (a S.D. maximum of 2.8 for the Oxygen). Only the results for lactose presented higher deviation. Concerning the day of analysis, the repeatability was very good whatever the pure component analyzed.

Analysis of pure milk components powders

Determination of experimental values on pure milk components

Experimental EDX values obtained after analysis of at least 13 points on pure milk components are presented in Table 3. It can be observed that values for carbon were systematically overestimated in comparison with theoretical values. Consequently, the nitrogen and oxygen were underestimated. Nevertheless, this carbon overestimation is well known for X-ray techniques like XPS [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Rouxhet | XPS analysis of bio-organic systems[END_REF]. Lactose values are particularly far from the theoretical ones in comparison with proteins and AMF. As seen in Fig. 2, lactose was also the only sample presenting degradation after analysis. This could explain higher chamber pollution by carbon atoms. This is why it is necessary to integrate the experimental values of each pure component in the equation system, to take into account the error associated to each pure component.

Experimental values of the same pure components obtained by XPS and EDX present also some differences (Table 3). Usually, XPS values are closer to the theoretical ones than EDX. This could be explained by less precision of the EDX analysis and a carbon pollution affecting the analysis.

Analysis of binary mixtures

To corroborate values obtained by EDX, it was necessary to test known mixes and to compare the obtained results with their real composition. Binary mixtures of lactose and whey proteins were prepared and analyzed by EDX under a pellet form after freeze drying of the solutions. As the area of analysis is small (5 m 2 ), the sample must be homogeneous enough at that scale. The choice of lactose and whey proteins was done for this reason, as these compounds are soluble in water and can produce quite good homogeneous solutions. The aspect of the three pellets were observed by ESEM and were quite similar whatever the concentration. The surface seems to also be homogeneous (images not shown). The composition of the surface components was obtained from the equations system (1, 2 and 3) fed by the atomic percentages. The three equations system considers three atoms (O, C and N) and three families of molecules (sugar, protein and lipid). This is the reason why two types of results were presented in Table 4. If three elements are calculated (lactose, proteins and lipids) by the use of the three equations (presented in Section 2), it can be observed that lactose is systematically underestimated and fat is present (whereas AMF was not added in these mixes). Two explanations are possible for these results. First, the overestimation of fat and the underestimation of polysaccharide are inherent to this technique as already observed with the XPS technique [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF]. Second, NWI powder contains residual lipids due to the methods of production [START_REF] Gaiani | How surface composition of high milk proteins powders is influenced by spray-drying temperature[END_REF]. These residual lipids may be located at the surface of the tablets and artificially increase the fat percentage. The reality could be between these two hypotheses. If only equation 3, corresponding to nitrogen, was used a correct prediction is done for the 3 mixtures (70/30, 50/50 and 30/70).

In order to go further, three components mixture containing fat were produced. However, homogeneous pellets were impossible to obtain with AMF (data not shown). The analysis was sometimes located on a zone containing a lactose/protein matrix and sometimes on a fatty zone making the analysis non reproducible.

Application of the technique to the surface and core composition of milk powders

Skim milk powder

After validation of the EDX methodology, this technique was used to analyze the surface and core of SMP. In order to do so, industrial SMP were sieved in five different fractions. The objective of this size classification was to keep a standard depth of analysis. As it was already mentioned, the analysis works in a depth of 1-5 microns approximately. Hence the particle diameter could influence the results of the analysis. From the literature [START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF], it is already known that a milk particles' surface is formed by a thin fat layer, then a skin rich in lactose-protein and finally a lactoseprotein matrix including some fat globules. However the thickness of these layers is unknown. The layers could have different thickness according to the particles size; consequently a classification by size was necessary.

Details of some repetition for different sieved fractions are presented in Table 5. For all the sizes observed, differences between surface and core are not significant. For example, there was no significant increase in the amount of lactose at the core, however XPS analyses confirmed the presence of more lactose in the core [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Kim | Surface composition of industrial spray-dried milk powders. 2. Effects of spray drying conditions on the surface composition[END_REF][START_REF] Faldt | Spray-dried whey protein/lactose/soybean oil emulsions. 1. Surface composition and particle structure[END_REF]. Still by XPS an opposite localization for fat is also systematically observed, but not here. The explanation may be that the surface analysis by EDX was much deeper than the surface analysis by XPS; hence the surface analysis by EDX may be equivalent to the core analysis by EDX or very close in atomic percentages. Concerning the effect of particle size, no clear tendency was observed between small and large particles.

Whole milk powder

Some representative examples of atomic composition at the surface and core of sieved particles are shown in Table 5. Again no differences were observed between the surface and the core. With this technique, the depth of analysis is around 1-5 m and not 5 nm like for the XPS methods. So, the strong overrepresentation of lipids at the surface of WMP observed by others may be linked to the thickness of fat. One hypothesis may be that the fat at the powder surface is thin enough to be detected by XPS but a mean was done by EDX with other components.

For SMP, a heterogeneity was observed in the distribution of the components in the particle. For example, the quantity of lipids increases in comparison with SMP. This indicates that the method is sensible to variation in lipids content. But aberrant values are also found. As it was previously explained it can be caused by a zone of analysis containing only one or two components (lactose/protein). Over 10 analyses were performed by size on a large number within the particle to obtain an accurate mean.

Contrary to SMP, significant differences are observed with the particle size. Whatever the localization of analysis (surface or core) the fat percentage decreased with increasing size and increasing lactose percentage.

Analysis of defatted powder

After the analysis of SMP and WMP, it was necessary to corroborate the sensibility of the analysis to fat in the sample. As it was already mentioned, productions of mixtures with three components were not performed due to non homogeneity in the pellet. As an alternative, the WMP was treated in order to change its lipid surface composition. An extraction of the surface fat was done [START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: agglomeration effect[END_REF][START_REF] Vignolles | Free fat, surface fat and dairy powders: interactions between process and product[END_REF] and permitted to establish the sensibility of the method for fat.

WMP without free fat and sieved between 80-125 m and 125-160 m were analyzed and an example of the zones measured are shown on Table 6. The surface compositions calculated from the atomic percentages are given again. As expected, the fat content decreases significantly while proteins and lactose increased. This is a very important point to validate the method, because even if lipids are generally overestimated; the trends observed are valuable.

Interest of the technique for milk powder

Different results when analysing the core of particles were expected as the core of milk powders presents a complex structure with a lactose-protein matrix and more or less lipid deposits. In addition, results for the surface composition were expected to be more reproducible and it was not the case. One explanation may be that surface measurements by EDX are deeper than XPS. And finally, by EDX, measures done in the core (by cutting the particles) may be very close to measures done at the surface. It is very important to take into account that most of the EDX analyses are performed at a theoretical 1-5 m from the surface. This depth is important for a milk particle and depending on the zone analyzed very different results may be obtained. In addition, if the sample is fragile (a lot of lactose) a structure degradation may occurred due to the electron beam. The methodology presented before in this work permits characterization of the surface and the core of the milk powders by EDX. But it could be interesting to couple this methodology to another technique: XPS. As the depth and the area of analysis are totally different, coupling these two techniques may allow a better knowledge of the composition gradient.

Table 7 detailed the atomic and component percentages for WMP and SMP. The surface was determined by XPS (5-10 nm) and EDX (1-5 m). The core was determined only by EDX by cutting one particle. In order to obtain more information, results for WMP without free fat were also added (surface by XPS and EDX; core by EDX).

To obtain the values of EDX an average of all the analysis was done (mean for different particles and different sieves). For XPS, these results are the mean of three independent experiments.

Gradients for skim milk powders

By observing the atomic percentages, the mineral gradients are remarkable. A significant increase of mineral percentage was observed from the surface (XPS), to the narrow surface (EDX) and finally the core (EDX cut particle). The C, O and N elements were not interpreted directly; as no interesting information can be obtain from these values. When C, O and N percentages are inserted in the matrices formula, the percentage in lactose, proteins and lipids is calculated. The lactose gradient was also evident with a decrease from the surface (42%) to the narrow surface (28%) and the core (27%). Fat was more important in the core in comparison with the surface and no real tendency was observed for proteins.

Gradients for whole milk powders

Again a clear trend appears for minerals in WMP. At the surface (XPS), minerals were not detected. At the narrow surface (EDX), minerals appeared in small quantities. After free fat removing, few minerals (K, Ca) were present at the surface of the powder (XPS). Finally, when cutting the particle and further analysing by EDX some mineral appeared in higher quantity: Mg, Na. This mineral distribution corresponds with the abundance of each element in milk. Potassium and calcium are the most abundant and consequently the first to be detected; and so on. The surface (XPS) was totally covered by lipids. When the analysis was done at the narrow surface (EDX), less fat (29%) and more lactose (36%) and proteins (32%) appeared. In the core (after cutting the particle), the same percentages were observed. This means that the core composition and the narrow surface contain the same elements at the same proportions.

The free fat extraction was interesting and gave us more information. The surface by XPS of the deffated particle was different in comparison with the raw particle. As expected less fat, more lactose and proteins were observed. When the analysis was done by EDX (narrow surface), the tendency was the same but the percentages were closer to the core composition with less fat.

Conclusion

The ESEM-EDX technique is a good choice to study the structure of milk powders as images can be easily obtained without vacuum and labelling. In addition, it is possible to focalize the analysis on a zone of interest thanks to the microscope (fat globule, crystallized lactose. . .). Coupling the EDX and XPS technique seems to be also very interesting and promising for SMP and WMP. More powders will be analyzed in the future to see if it is possible to generalize to all dairy powders. Indeed, information on the surface gradients was obtained and the components repartition was coherent with expected results and literature.

Nevertheless, the EDX technique presents some problems of repeatability. But these problems are inherent to the technique as the zones analyzed are very small and as the depth of analysis is important. Consequently, depending on the localization of the analysis zone different results may appear. However, by analyzing a great number of particles at different locations; it is possible to optimize this repeatability.

I

  C = ˛P.I CP + ˛'L.I CL + ˛′′ F.I CF (1) I O = ˛P.I OP + ˛'L.I OL + ˛′′ F.I OF (2) I N = ˛P.I NP + ˛'L.I NL + ˛′′ F.I NF (3) where I C , I O , I N are the mole fractions of carbon, oxygen and nitrogen in the sample surface, obtained from the areas of the C 1s, O 1s and N 1s EDX peaks. I CP , I CL , I CF are the percentages of carbon in proteins, lactose and fat; I OP , I OL , I OF are the percentages of oxygen in proteins, lactose and fat and I NP , I NL , I NF are the percentages of nitrogen in proteins, lactose and fat.

Fig. 1 .

 1 Fig. 1. Scanning electron micrographs (×200) of reference pure components: native whey isolate powder (A), native micellar casein powder (B), alpha-lactose powder (C) and anhydrous milk fat (D), and of commercial powder: whole milk powder (E) and skim milk powder (F).

3. 4 .

 4 Interest of coupling XPS and EDX for the determination of milk powder gradient composition 3.4.1. Objectives

Table 1

 1 Atomic composition (%) of the reference powders analyzed by EDX in 3 points (represented by a, b and c in Fig.2) for NWI, Lactose and AMF and in 2 points for NMC.

	Powder	Atomic composition (%)	Points of analyze			Average	S.D.
			a	b	c
	Native whey isolate	C	74.37	77.96	75.67	76.0	1.9
	powder	N	11.80	10.35	12.58	11.6	1.1
		O	11.17	9.06	10.12	10.1	1.1
		P	0.30	0.30	0.20	0.3	0.1
		S	1.37	1.45	0.96	1.3	0.3
		K	0.52	0.43	0.25	0.4	0.1
		Ca	0.47	0.45	0.22	0.4	0.1
	Lactose powder	C	80.71	81.75	81.22	81.2	0.5
		O	19.29	18.25	18.78	18.8	0.5
	Native micellar casein	C	75.15	75.15	-	75.1	0.0
	powder	N	9.41	9.52	-	9.5	0.1
		O	10.67	10.74	-	10.7	0.1
		P	1.45	1.23	-	1.3	0.2
		S	0.70	0.71	-	0.7	0.3
		K	0.24	0.28	-	0.3	0.0
		Ca	2.38	2.37	-	2.4	0.0
	Anhydrous milk fat	C	94.58	94.91	94.96	94.9	0.3
		O	5.42	5.09	5.04	5.1	0.3

Table 2

 2 EDX average data the same day on different particles and on the same particle during different days for lactose powders, native whey isolate powders (NWI), native micellar casein powders (NMC) and anhydrous milk fat (AMF).

		Atomic concentration for various pure components (%)
			Lactose	NWI	NMC	AMF
	Average on different particles (more than 10) Average on different days (4 days)	C O N P S K Ca C O N P S K Ca	74.0 ± 7.3 20.6 ± 3.1 -----77.9 ± 2.7 22.1 ± 2.7 -----	72.4 ± 2.2 12.8 ± 2.8 13.8 ± 1.4 0.2 ± 0.1 0.8 ± 0.3 0.2 ± 0.1 0.2 ± 0.1 73.0 ± 2.7 13.4 ± 1.8 12.3 ± 1.9 0.2 ± 0.1 0.9 ± 0.3 0.3 ± 0.1 0.3 ± 0.1	73.5 ± 1.5 12.2 ± 1.2 10.7 ± 1.0 1.2 ± 0.1 0.5 ± 0.1 0.2 ± 0.1 1.7 ± 0.5 73.5 ± 1.5 10.7 ± 0.7 12.2 ± 1.4 1.2 ± 0.1 0.5 ± 0.1 0.2 ± 0.0 1.7 ± 0.4	94.9 ± 0.3 5.1 ± 0.3 -----93.9 ± 1.4 6.1 ± 1.4 -----

Table 3

 3 Theoretical and experimental values for XPS and EDX measures on pure milk components.

		Theoretical values for the atomic	Experimental values for the atomic composition obtained from Table 1 (%)
		composition (%)
					EDX			XPS
		C	O	N	C	O	N	C	O	N
	Lactose	50	50	0	79.2	20.8	0.0	62.7	37.3	0.0
	Caseins	65	19	16	76.0	12.8	11.2	69.8	16.3	13.9
	Whey proteins	65	19	16	73.3	12.8	13.9	68.0	18.0	14.0
	Total milk proteins a	65	19	16	75.5	12.8	11.7	-	-	-
	Anhydrous milk fat	89.1	10.9	0	93.8	6.2	0.0	87.0	12.3	0.7
	a Calculated by taking into account 17% whey proteins and 83% casein.

Table 4

 4 Composition of binary mixtures calculated from the equation system (Eqs. (1)-(3)).

	Equation	Ratio Lactose/Protein	70/30	50/50	30/70
	Eqs. (1)-(3)	Lactose Protein AMF	62 ± 6 34 ± 3 4 ± 3	40 ± 6 54 ± 2 6 ± 5	13 ± 5 74 ± 5 13 ± 3
	Eq. (3) only	Lactose Protein	67 ± 4 33 ± 4	46 ± 1 54 ± 2	28 ± 5

Table 5

 5 Core and surface composition determined by EDX on different size fractions (0-40; 40-80, 80-125 and 125-160 m) of skim milk and whole milk powders.

		Skim milk powder								Whole milk powder
		Surface composition (%)		Core composition (%)		Surface composition (%)		Core composition (%)
		1	2	3	4	Mean ± SD 1	2	3	4	Mean ± SD 1	2	3	4	Mean ± SD 1	2	3	4	Mean ± SD
	Particle size 0-40 m
	Lactose Proteins AMF Minerals	30 78 -9 1	24 80 -6 2	14 81 1 4	18 70 7 5	22 ± 5 77 ± 3 -2 ± 5 3 ± 1	23 53 19 6	40 49 0 10	23 45 22 11	8 79 11 2	23 ± 8 57 ± 2 13 ± 8 7 ± 2	21 29 50 0	30 29 39 2	26 24 47 3	16 33 48 3	24 ± 4 29 ± 2 46 ± 3 2 ± 1	29 23 45 2	28 25 44 2	11 56 30 3	17 45 35 3	21 ± 7 38 ± 13 39 ± 6 3 ± 0
	Particle size 40-80 m
	Lactose Proteins AMF Minerals Particle size 80-125 m 33 37 81 53 -17 6 3 5	33 61 1 5	35 60 2 3	34 ± 2 64 ± 8 -2 ± 7 4± 1	5 71 23 1	36 50 7 7	22 74 2 2	17 80 -2 5	20 ± 8 69 ± 9 7 ± 7 4 ± 2	28 30 39 3	21 61 14 3	15 66 19 1	18 41 37 4	21 ± 4 49 ± 14 27 ± 10 3 ± 1	28 30 39 3	21 61 14 3	15 66 19 1	18 41 37 4	21 ± 4 49 ± 14 27 ± 10 3 ± 1
	Lactose Proteins AMF Minerals	32 54 10 4	30 54 10 6	24 65 7 4	18 54 22 4	26 ± 5 57 ± 4 12 ± 5 4 ± 1	40 54 2 4	23 62 9 6	39 46 9 5	37 50 8 5	34 ± 5 53 ± 5 7 ± 2 5 ± 1	33 23 41 4	33 23 41 4	28 36 31 6	25 49 22 4	29 ± 4 33 ± 10 34 ± 7 4 ± 1	33 23 41 4	33 23 41 4	28 36 31 6	25 49 22 4	29 ± 4 33 ± 10 34 ± 7 4 ± 1
	Particle size 125-160 m
	Lactose Proteins AMF Minerals	28 59 10 3	44 53 -1 4	24 65 7 4	18 54 22 6	28 ± 7 58 ± 4 10 ± 6 4± 1	23 62 9 6	33 49 12 5	28 47 19 6	11 70 15 4	24 ± 6 57 ± 9 14 ± 2 5 ± 1	46 31 19 4	49 37 11 4	13 60 24 3	19 40 35 5	32 ± 15 42 ± 9 22 ± 7 4 ± 1	46 31 19 4	49 37 11 4	13 60 24 3	19 40 35 5	32 ± 15 42 ± 9 22 ± 7 4 ± 1

Table 6

 6 Surface composition measured by EDX of whole milk powder before and after free fat extraction.

		Before free fat extraction			After free fat extraction
		1	2	3	4	Mean ± SD	1	2	3	4	5	6	Mean ± SD
	Particle size	80-125 m
	Lactose Proteins AMF Minerals	36 29 32 3	38 26 33 4	44 27 26 4	42 32 23 4	40 ± 3 28 ± 2 28 ± 4 3 ± 0	46 42 8 5	38 30 27 4	36 39 20 4	41 41 15 4	39 29 28 5	46 41 8 5	42 ± 4 37 ± 5 17 ± 8 4 ± 1
	Particle size	125-160 m
	Lactose Proteins AMF Minerals	45 27 24 3	56 33 9 3	36 44 16 4	39 40 17 5	44 ± 6 36 ± 5 16 ± 4 4 ± 1	46 36 1 7 4	38 44 9 5	36 41 17 5	45 39 6 3	46 45 6 3	46 42 5 3	42 ± 4 41 ± 6 9 ± 9 4 ± 1
	ESEM image obtained during analysis

Table 7

 7 Gradients in whole and skim milk powders by coupling XPS (surface depth around 5 nm), EDX on raw particles (surface depth around 1 m) and EDX on cut particles (core).

			Whole milk powder				Skim milk powder
			Surface				Core
			Before free fat extraction	After free fat extraction		Surface		Core
			XPS	EDX	XPS	EDX	EDX	XPS	EDX	EDX
	Atomic composition (%)	C O N K Ca Cl S P Na Mg	87.4 ± 1.8 11.6 ± 1.2 1.0 ± 0.6 -------	78.6 ± 1.9 13.6 ± 1.5 4.5 ± 1.9 0.3 ± 0.1 0.1 ± 0.0 0.6 ± 0.2 0.2 ± 0.1 0.8 ± 0.2 0.6 ± 0.2 0.2 ± 0.0	77.1 ± 1.1 19.9 ± 0.6 2.9 ± 0.2 0.2 ± 0.0 0.1 ± 0.0 -----	77.1 ± 1.7 14.5 ± 0.8 4.3 ± 0.6 0.3 ± 0.0 0.3 ± 0.4 0.9 ± 0.1 0.3 ± 0.0 0.7 ± 0.1 1.0 ± 0.0 0.8 ± 0.0	77.8 ± 4.2 13.5 ± 2.7 5.2 ± 2.1 0.3 ± 0.1 0.1 ± 0.1 0.6 ± 0.2 0.3 ± 0.1 0.6 ± 0.2 1.0 ± 0.5 0.8 ± 0.5	65.1 ± 0.5 26.5 ± 0.3 7.2 ± 0.1 0.5 ± 0.4 0.2 ± 0.0 0.2 ± 0.2 0.1 ± 0.0 0.1 ± 0.0 --	73.6 ± 2.2 13.9 ± 1.9 7.8 ± 2.2 0.45 ± 0.7 0.2 ± 0.0 1.0 ± 0.4 0.4 ± 0.1 0.7 ± 0.3 1.2 ± 0.6 0.9 ± 0.4	73.7 ± 3.0 13.5 ± 2.1 6.9 ± 1.6 0.4 ± 0.1 0.2 ± 0.1 1.1 ± 0.5 0.4 ± 0.2 1.0 ± 0.5 1.6 ± 0.9 1.3 ± 0.7
	Component composition (%)	Lactose Proteins AMF Minerals	-3.2 ± 2.5 2.2 ± 2.7 101.0 ± 1.7 -	36.1 ± 14.1 32.6 ± 13.4 29.4 ± 12.9 3.3 ± 0.7	24.7 ± 1.0 18.8 ± 1.5 56.4 ± 0.7 0.3 ± 0.0	41.7 ± 3.8 38.3 ± 4.9 17.5 ± 7.9 4.3 ± 0.6	31.7 ± 13.2 36.9 ± 11.0 28.5 ± 14.1 3.7 ± 1.3	42.2 ± 1.1 54.0 ± 1.5 2.7 ± 0.8 1.1 ± 0.7	28.2 ± 16.2 64.3 ± 21.2 4.5 ± 17.8 4.9 ± 2.5	27.5 ± 16.5 57.8 ± 18.2 7.5 ± 23.7 6.0 ± 3.0

Acknowledgments

ANR funding from programme "Reactive Powder" are gratefully thanks. In addition, first author thanks CONACYT as well as SEP scholarships in Mexico for financial resources. LCPME laboratory (Laboratoire de Chimie Physique et de Microbiologie pour l'Environnement, Nancy) is thanks for performing XPS analyses. The authors appreciated the work of Adetoke D. Ogunsanya in the correction of the English in the manuscript.


LES in a Concentric Annular Pipe: Analysis of Mesh Sensitivity and Wall Pressure Fluctuations

S. Bhattacharjee, G. Ricciardi and S. Viazzo

Introduction

Annular pipe flows have varied application in the domains of nuclear reactors, heat exchangers, drilling operations in oil industry etc. The first part of the paper (Sect. 2) presents a comparison of large eddy simulations (LES) of turbulent flow in a concentric annular pipe for 5 different mesh resolutions. Results are compared with benchmark DNS data. The second part (Sect. 3) presents its interesting application of pipe flow in the nuclear field. Inside a pressurized water nuclear reactor (PWR) core, flow-induced vibrations due to spacer grids can cause damage to the structure. Understanding this behavior is a challenge. Here the effect of a 'simplified'circular spacer grid on the vortex induced vibrations of the pipe is investigated. LES was performed with the CFD code Trio_U [START_REF]Trio_U-Computational Fluid Dynamics code version 1.7.0: French Alternative Energies and Atomic Energy Commission (CEA)[END_REF] which uses a hybrid finite volume based finite element approach [START_REF] Bieder | Qualification of the CFD code Trio_U for full-scale reactor applications[END_REF]. Simulations were carried out on the Airain and Curie supercomputers at the Computing Center for Research and Technology (CCRT), Bruyères-le-Châtel, France [2].

Mesh Sensitivity Analysis for LES in a Concentric Annular Pipe

The outer and inner diameters of the pipe were 60 mm and 30 mm respectively. The radius ratio, i.e., the ratio between the inner and outer radii was 0.5. Water flowed through the pipe in axial direction. A schematic diagram is shown in Fig. 1. The hydraulic diameter, defined as HD = 4 A f low /P wet , was 0.03 m where A f low is the surface area of duct cross-section and P wet is the wetted perimeter. The bulk velocity was 0.298 m/s. Reynolds number based on the bulk velocity and hydraulic diameter was 8900. The length of the domain was 0.24 m, i.e., 8 times hydraulic diameter. Fully structured tetrahedral meshes were generated with Gmsh [START_REF] Geuzaine | Gmsh-A three dimensional finite element mesh generator with built-in pre-and post-processing facilities[END_REF] and Trio_U's internal meshing tool. The grid was more refined near the boundary in radial direction to study the near-wall behavior (Fig. 2). It was uniform in axial and azimuthal directions. Five different mesh resolutions were considered. Table 1 shows the number of grid points as well as the grid resolution in wall units in each direction for each simulation. Figure 3a-f illustrate the stretching of the tetrahedral elements relative to each other. Space discretization was done with the second order centered stabilized "EF_stab" scheme [START_REF] Kuzmin | Multi dimensional FEM-TVD paradigm for convection-dominated flows[END_REF] and time discretization with the second order explicit Adams-Bashforth scheme. The wall-adaptive local eddy viscosity (WALE) model [START_REF] Nicoud | Sub-grid scale stress modeling based on the square of the velocity gradient tensor[END_REF] was used to model the universal small scale eddies. In cases where the grid resolution near the wall is not of order 1, the Reichardt wall law [START_REF] Hinze | Turbulence[END_REF] was used.

Due to the regular pattern of the grid, a constant velocity profile as initial condition was not sufficient to generate turbulence. So a fully developed turbulent flow field from another simulation (on a coarser mesh) was used as initial condition. Periodic boundary condition was applied axially. A momentum source term was added to maintain constant flow rate. Two point correlation coefficient between the velocity component in the streamwise (axial) direction is plotted in Fig. 4. It falls to zero at half a period suggesting that the streamwise domain length is sufficient. No-slip condition was imposed on the inner and outer walls.

Results

The turbulent statistics were collected after the flow stabilized. The averaging was done over 25 flow traversals. For the case F2, standard deviation of radial and axial velocity was computed as shown in Fig. 5. It is in good agreement with experimental data of [START_REF] Nouri | Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli[END_REF]. A comparison of mean velocity profiles for 4 different simulations in Table 1 is presented in Fig. 6a. Comparison of the coarse C1 profile with F1 shows an improvement due to the refinement in all directions. The F2 mesh was created with the same number of elements as F1 but the resolution in azimuth was doubled and that in axial was halved. The profile for F2 agrees well with DNS of [START_REF] Chung | Direct numerical simulation of turbulent concentric annular pipe flow Part 1: Flow field[END_REF]. UF mesh also shows similar profile as F2. Hence one could go up to the resolution in wall units of the order of 10 in axial, 3 in azimuthal and 1.3 in radial to reproducing the benchmark result. It should be noted that the total number of elements was maintained for cases F1, F2, UF. The above sensitivity analysis shows that the mean velocity profile has a stronger dependence on azimuthal resolution compared to axial resolution for the 4 said meshes. A similar test was made with the coarse mesh. The azimuthal resolution in C1 was doubled to create C2 mesh. Again, Fig. 6b shows a significant improvement in the profile from C1 to C2.

Pressure Fluctuations in an Annular Pipe with a Circular Grid

A realistic PWR core has a square spacer grid. However, creation of a square grid inside an annular pipe would lead to unstructured mesh (at least in its vicinity if we implement hybrid meshing). Since the aim is to understand the physics of the problem, we implemented a circular grid instead. As a result, generation of a fully structured mesh was possible. Also the domain became symmetric. This improved the speed of simulation. In order to make it more realistic, the ratio of hydraulic diameters between the inner and outer flow areas was kept the same for both types of grids. The pipe with the circular grid is shown in Fig. 7. The length of the domain was 0.2688 m, i.e., approximately 9 hydraulic diameters. Table 2 presents the grid resolutions in different directions. An attempt was made to keep in consideration the acceptable resolutions obtained in Sect. 2.1. However, as seen from Table 2, some compromise had to be made due to lack of computational time and resources. The domain consisted of 20.7 million tetrahedrons and simulation was carried out on 710 parallel processors. All numerical parameters were the same as in Sect. 2 except the boundary conditions at the inlet and outlet. A fully developed

Results

Instantaneous velocity fluctuations were analyzed in terms of power spectral density (PSD) at 3 heights: 0.6 HD upstream, 1 HD downstream and 3 HD downstream. Figure 8 shows that the amplitude of fluctuations 1 HD downstream is a decade higher than that upstream. At 3 HD, the amplitude is reduced but still higher than that upstream. This increase in fluctuation is due to the presence of the circular spacer grid. In Fig. 9, the PSD of pressure fluctuations on the inner wall of the pipe shows that the amplitude of fluctuation is higher downstream compared to upstream. The fluctuations or amplitude of power decrease with frequency. Figure 10 shows an angular distribution of standard deviation of the pressure field on the inner wall. The deviation increases by 50% at 1 HD downstream. The symmetric distribution is due to the symmetry of the grid.

Conclusion

A mesh sensitivity analysis with structured grids was performed in an annular pipe using LES. Velocity profiles for 5 different meshes were compared with benchmark DNS, following which an acceptable grid resolution of the order of 10 (axial), 3 (azimuthal) and 1.3 (radial) in wall units was proposed. It was observed that the results are more sensitive to azimuthal resolution than axial resolution. Presence of a circular spacer grid in the pipe increased the fluctuation downstream of the grid as seen from the PSD plots of velocity and wall pressure. As future work, it would be interesting to repeat the same study with a square spacer grid. Also the grid resolutions in Table 2 could be improved to reach the one discussed in Sect. 2.1.

Fig. 1

 1 Fig. 1 Schematic diagram of the pipe

Fig. 3 a

 3 Fig. 3 a Axes, b C1 (Coarse), c C2 (Coarse), d F1 (Fine), e F2 (Fine), f UF (Ultra-fine)

Fig. 4 Fig. 5 Fig. 6 a

 456 Fig. 4 Two point correlation for streamwise velocity

Fig. 7

 7 Fig. 7 Annular pipe with circular grid

Fig. 8

 8 Fig. 8 PSD of instantaneous velocity

Fig. 9

 9 Fig. 9 PSD of pressure fluctuations on the inner wall

Table 1

 1 Grid resolution in wall units for 5 different cases Case Number of grid points (N r , N θ , N z )

			Δ + r	Δ + θ	Δ + z	Elements	CPU time
						(in millions)	(in hours)
	C1 (Coarse)	(25, 80, 120)	7.7	9.2	15.3	1.3	4140
	C2 (Coarse)	(25, 160, 120)	8.8	5.3	17.6	2.7	9315
	F1 (Fine)	(73, 160, 480)	1.3	5.1	2.4	33	74980
	F2 (Fine)	(73, 320, 240)	1.3	2.7	4.9	33	111780
	UF (Ultra-fine) (73, 640, 120)	1.3	1.3	9.6	33	74980

Table 2

 2

	Grid resolution
	Direction	Boundary	Grid resolution (in wall	Grid resolution (in meters)
			units)
	Radial	Inner wall	3.2	0.0003
		Outer wall	2.9	0.0003
		Circular grid	3.6	0.0003
	Azimuthal	Inner wall	2.8	0.00026
		Outer wall	5.4	0.00055
		Circular grid	4.8	0.0004
	Axial	Inner wall	12.9	0.0012
		Outer wall	11.7	0.0012
		Circular grid	14.5	0.0012