M Bizi
email: m.bizi@brgm.fr

G Baudet

Contribution of static light scattering to the textural characterization of large aggregates

Keywords: Density, Floc size distribution, Fractal dimension, Kaolin, Light scattering, Obscuration, Porosity. _________________________________________________________________________________

The industrial processes of water clarification often imply flocs of millimetre length. The principal motivation of this work relates to the characterization of these large flocs with laser diffractometry, for which the authors propose particular experimental approaches. In addition, a reformulation of the various properties of the flocs accessible by laser diffractometry is presented, in particular for the determination of the size, density, porosity, volume fraction and fractal dimension. By way of illustration, these experimental and theoretical developments are applied to the characterization of flocs obtained by flocculation of a commercial kaolin. The size, fractal dimension and density of kaolin floc were examined under various flocculant concentrations. Measurements reveal important variations of the granulometric and textural properties of large size flocs in response to flocculation, opening ways of optimization for the associated industrial processes.

Introduction

Flocculation is the process by which disperse solid or microbial elementary units aggregate as flocs under the effects of a chemical reagent. The efficiency of the flocculation is assessed in terms of i) water quality, ii) post-processing state of the sediment obtained and iii) the swiftness of the physical and chemical process selected. For a given material and water, these three assessment criteria depend on the nature of the reagent and on the hydrodynamic conditions usedand accordingly on the texture of the floc produced.

Thus, water purification depends on the possibility of aggregating all the particles into flocs and on the sedimentation rate of the flocs that have been formed; the latter is a function of both their size and their density. The settling of the sediment is linked with the mechanical properties of the flocs and with their porosity. Furthermore, many investigations have made it possible to associate the fractal structure of the flocs with various physical and chemical properties such as decantation [1][2][3], growth [4] and diffusion [5]. Size, density, porosity and fractal dimension can thus be considered as representative of the overall flocculation efficiency.

Taking into account the fact that flocs are extremely fragile structures, they accordingly need to be characterised in terms of size, density, porosity and fractal dimension by means of methods that are direct and non-destructive. For practical reasons we propose to use laser scattering to cover, in terms of textural characterization, a range of aggregates linked with several types of industry. The sizes targeted are those of flocs produced industrially, ranging between 0.01 and 5 mm. In conformity with this objective, the study was subdivided into three parts. The first part develops the parameters of theoretical bases necessary to describe the texture of the flocs. The second part relates to the development of a system for the analysis of large size flocs using laser diffractometry. The third part, essentially experimental, proposes an application of the developments of the two preceding parts to the characterization of large flocs obtained by flocculation of a commercial kaolin.

Static light scattering characterization

Over the past 30 years, laser diffractometry has become the reference technique for determining size in fine-grained materials. The fundamental principles of this technique have been dealt with in detail in a number of reports or publications [START_REF] Baudet | [END_REF]8]. It presents a number of advantages over classical methods such as electron microscopy or X-ray absorption (Sedigraph). It is fast, reproducible, easy to use, and inexpensive and yields several types of textural information: size, shape coefficient of lamellar particles, external surface geometry [9], and the porosity, density, fractal dimension of the flocs [START_REF] Guan | Proceedings of the 26th Australasian Chemical Engineering Conference (Chemeca 98)[END_REF][START_REF] Amal | [END_REF][12]. Its main drawback is linked to the limitations, inherent to the Fraunhofer and Lorentz-Mie theories used to interpret the diffraction and diffusion patterns. As explained below, both these theories were designed for spherical particles. In addition, for the principles of Fraunhofer to be applied, the particles must be opaque and larger than 5 0 , or otherwise, for the Lorentz-Mie theory to be used, they must have well-known optical properties. As in all the other techniques, the size distributions are established accordingly to the model of the equivalent sphere. In the light of its specificities, laser diffractometry is complementary to the other techniques.

Size, porosity and density of the flocs obtained by laser diffractometry

The underlying principle behind laser diffractometry is the exploitation of the information contained in the light scattered by the particles that examined subsequent to their interaction with a TEM 00 -type electromagnetic plane wave. The amount of light scattered and the size of the angle of diffusion allow us to determine the size of the particles and their relative quantity. This data can be extracted by applying the Lorentz-Mie theory on the condition of respecting that certain hypotheses are satisfied and that the optical properties of the material being analysed are known. Thus the particles are supposed to be spherical, isotropic, homogenous and non-magnetic. In practice, the investigated materials are actually not suitable with this definition: they are neither spherical nor isotropic, and rarely their optical properties are known. In the field of flocculation/coagulation, the situation is even more complicated. As compared with a raw product, the flocs display an optical contrast with respect to the transport fluid that varies widely according to the amount of flocculant and the structure of the flocs. In this context, the Fraunhofer model, a special case of the Lorentz-Mie theory, must be called on to interpret the signals. It makes it possible to determine the size distribution of the particles, taken to be spherical and opaque, from photometric measurements. This model represents a good approximation for particles whose diameters are five times greater than the wavelength  0 of the incident beam. If the ratio diameter/wavelength is smaller than 5, the errors are liable to be large, and the distributions should be considered as relative value rather than absolute. However, when the flocculation of fine particles (<5 0 ) is concerned, the level of error decreases with increasing size and compactness (fractal dimension) of the flocs, which is true for the flocculation in the present study.

The Fraunhofer model, present on all laser particle size analysers (PSA"s), is based on the principle of light scattering [START_REF] Swithenbank | AIAA 14 th Aerospace science meeting[END_REF][START_REF] Van De Hulst | [END_REF]. In the case of the Mastersizer-S PSA used here, the helium-neon laser, with a wavelength of 0.632 µm, emits a beam that is broadened by means of an afocal optic system equipped with a spatial filter. This beam, 18 mm in diameter, passes through a liquid film of width ℓ crossing an analysis cell where the particles to be measured are dispersed. The particles, assumed to be opaque, diffract the light according to an angle inversely proportional to their diameter, and the diffraction pattern centred on the image of the source depends neither on position nor on particle motion. Each granulometric class centred on a diameter d i has its own diffraction pattern. If all the particles are of the same size, the resultant pattern is that of Airy, which appears as a succession of concentric rings. The size of these identical particles is deduced from that of these rings. However, when the material is polydisperse, the elementary diffraction patterns superimpose on each other in the focal plane, and the rings disappear. The size distribution is determined from the irradiance (diffracted energy) received by the detector head. For the PSA used here, the detector is composed of 42 silicon photodiodes arranged along concentric arcs. In the standard range that is usable in wet treatment (from 0.05 to 880 µm), all the photodiodes are called on for size measurement. On the other hand, for the 4.2 to 3480 µm, only the first 32 diodes are used. In both cases, each photodiode is allotted to a particle-size range. The mode of calculation of the size distribution is largely treated in the literature. It will not be included in this work. The result of the measurement analysis is a volume distribution characterised over the size limits of the optical configuration used. The distribution may be listed as a table of results, giving frequency and cumulative forms of distribution.

Moreover, the particle-measurement instrument is equipped with a central detector (0°) devoted to the measurement of obscuration i.e., attenuation of laser beam by the sample. This obscuration is deduced from measurement from intensity of the central beam I C by neglecting the diffusion in front of absorption. As indicated above, obscuration is a function of the optical trajectory ℓ and of the turbidity of the medium , which itself is a function of the concentration (or number of particles) and of the efficient extinction factor Q ext (the ratio between the energy flux drawn from the incident wave and the energy flux received by the geometric section of the particle). Through this factor, obscuration also depends on the size parameter  and on the complex refractive index of the medium n m in which the wave is propagating. The connection between Q ext and these parameters lies beyond the scope of this work.

0 1 I I Ob c   (1)    . exp 0    I I c Beer-Lambert law (2) i ext i i Q A N . .     (3)
The relations and approximations assigned to this factor are widely dealt with in the literature [15,16]. However, its limit tends towards 2 for large values of  (the field of application of Fraunhofer).

0 0 r . . 2     (4)
For a cloud of spherical, isotropic, homogenous, nonmagnetic and monodisperse particles, turbidity can be defined by [16]

ext S Q d C . . 2 3 2 . 3     (5)
which shows fairly clearly that, for a given optical trajectory, obscuration increases to a certain extent as the concentration increases. On the other hand, for a given concentration and optical trajectory, obscuration decreases when particle size increases.

In the case of the polydisperse spherical particles, the turbidity is computed from the relative volumes of the different size classes, V ri , and the volume concentration C/ρ, noted C v . The projected surface area of a size class with volume V i and diameter d i is given in the present case by the following relation:

i i i i d V A N . 2 3 .  (6)
The volume corresponding to a class i is written: beam volume, which is the cross-sectional area times the path length; V ri relative volume of particles in size band i per unit volume; V SB total volume of all solid scattering particles in the beam; ρ S density of particulate matter expressed as grams per cm 3 .

B SB i ri V V V V .  (7) so, ri B SB i V V V V .  and B SB i ri i i V V d V A N . . 2 3 .  (

Substituting for

i i A
N . its last expression in Eq. ( 3), the turbidity becomes

i ext i ri B SB Q d V V V . . . 2 3     (9)
The ratio

B SB V V represents the volume concentration, C V .
Combining Eqs. ( 2) and ( 9) allows the final expression of the volume concentration measured by laser light scattering to be established:

i i ext ri c B SB V d Q V I I V V C . 0 . 2 3 ln               (10)
This relation can be used to determine the volume concentration from a measurement of the transmittance I c /I 0 and the computed turbidity. However, it may prove not to be applicable for a number of reasons. Thus, the proportionality between obscuration and concentration is correctly verified only over a particular range of concentrations which ensures multiple scattering and practically non-existent mask effects. The rules for using this relationship will be detailed in Section 4.1.

However, textural characterization by the laser diffractometry of porous materials (aggregates or flocs) measuring C V makes it possible to determine the mean porosity and the effective volume-specific mass of these materials. The technique is fast, reproducible, statistically representative and relatively reliable in comparison with the classical indirect methods derived from the Stokes law. These classical methods consist in linking the fall rate of the flocculated particles and their diameter to the Stokes equation, corrected in terms of the Reynolds number and the shape factor of the particles. The diameters are often determined by image analysis. This correction must take into account the permeability and the shape of the flocs, which evolve with the physical and chemical and hydrodynamic conditions. Another worthy technique is the assessment of effective volume-specific mass from the measurement of the volume and the mass of the flocs using micro scales. Typically, these methods are time-consuming and costly.

In textural characterization, porosity is defined by

SB SR SB F V V V    (11)
where SB V is the volume of porous entities intercepted by the laser beam, corresponding to the sum of the real volume of the solid SR V and of the flocs porosity.

V B SB C V V .  and S B SR C V V  .  (12)
Therefore, the average porosity is defined according to the value

V C measured by PSA.   S V F C C 1      ( 13
)
The result is the following expression of the average density of porous materials such as flocs:

  F L F S F 1           ( 14
)
The porosity and the density obviously depend on the number of particles an aggregate contains. This number varies, increasing with increasing size of the aggregate R. It depends on the aggregate"s structure, and accordingly on its fractal dimension. These relationships are incorporated into the following equation

F D 0 0 r R k ) r ( n          ( 15
)
where D F average fractal dimension; n number of primary particles in an aggregate; k 0 fractal prefactor, which is a function of the average size of primary particle; r 0 radius of the primary particle (monodisperse); R radius of the aggregate.

This equation is defined over a size range varying between that of the elementary particle and that of the aggregate. From this relation derives any number of useful expressions linking to various properties of the aggregate with its fractal dimension. The porosity of the fractal aggregate, for instance, is a function of its size:

SB SB SR F V V r n V V r 0 ) ( 1 1 ) (       (16)
For spheres,

3 SB R 3 4 V   ( 17
)
3 0 0 r 3 4 V   ( 18
)
3 0 SB 0 R r V V        (19)
so :

3 D 0 0 F r R k 1 ) r (             (20)
The complement to the porosity is the solid volume fraction, that is,

3 0 0 1               F D F F r R k  (21)   3 D 0 0 L S L F F r R k                   (22)
This equation shows that floc density decreases with increasing floc size, roughly in accordance with a power-law relationship between density and size. It will be checked experimentally thereafter. The significance of the various symbols is deferred in the nomenclature to the end of this article.

Estimation of the mean fractal dimension of the flocs by laser diffractometry

Concerning methods for measuring fractal dimension, a distinction should be made between those relying on the analysis of the signal produced by an interaction between the matter and an acoustic or electromagnetic wave, and direct methods using visualisation. Among all these methods, only the light scattering technique will be presented here.

Light scattering plays an important role in the realm of textural characterization. The structural characteristics of objects, such as their size, roughness, shape and number, may be determined from diffusion curves.

The small-angle diffusion theory developed for X-rays diffractometry (DPAX) can be transposed in certain types of measurement to the scattering of neutrons or light. In all three cases, it is the contrast between the homogenous matrix and the diffusing objects that will induce an intensity diffused at small angles. This contrast will be of a diffusing nature according to the wave that is scattered. For X-rays, this contrast is caused by differences in the efficient section of the diffusion lengths; for light, it results from a variation in the refraction index. X-rays and neutrons are generally used to characterise structures smaller than one micrometer, and light, for structures on the order of one micrometer.

The intensity diffused by a group of aggregates depends on their textural variability: size and structure distributions and the nature of the objects. In the simple case corresponding to the Rayleigh-Gans-Debye (RDG) theoretical model, where the aggregate distribution in the solvent is statistically isotropic, the suspension is highly diluted so as to allow the aggregates to diffuse independently. The aggregates all have the same structure and are composed of the same basic units that verify the following optical conditions: 2|n sn m |≪1 and |n s -n m |≪1. The diffused intensity can be written

) ( ). ( . . ) ( q S q P C K q I A  (23)
where K A is a constant, which depends on the equipment setup and the contrast between solvent and particles. C is the particle concentration, P(q) the form factor of the particles, and S(q) the structure factor of the system. q is the amplitude of the scattering vector. It is a function of the wavelength of the incident beam, of the refractive index of dispersion medium and the scattering angle:

       2 sin . n . . 4 q 0 0    (24)
For fractal aggregates, it can be shown that [16][17][18] the total scattered intensity will exhibit a power law dependency on q; i.e.

For R g ≪q≪r 0 , S (q ) q

-D F and I (q)  K A .C.q -D F (25)
where R g is the radius gyration of the aggregate, r 0 is the primary particle radius and D F the mass fractal dimension. At length scales, approaching R g the q -DF dependence is modified by the edge of the aggregate and at small scales (approaching r 0 ), the non fractal nature of the constituent particles becomes apparent [START_REF] Guan | Proceedings of the 26th Australasian Chemical Engineering Conference (Chemeca 98)[END_REF].

In principle, the relationships presented above are adequate as a description of aggregates of monosized particles only. In the more realistic case where the primary particles are polydispersed, the theory can be extended by considering the aggregates as being made of different size classes of monosized particles and accounting for each size class and its interactions with other size classes separately [19]. Dimon et al. [20] have shown that the structure factor will not be affected by polydispersity effects. The work of Tence [21], Amal and Bushell [START_REF] Amal | [END_REF] shows that the fractal structure and the form of the cut-off function that describes the gross shape of the aggregates is unaffected by the details of the primary particle size distribution. It is consequently possible to determine the mean fractal dimension of the aggregates from the curve of log(I(q)) versus log(q). Over the interval [R g , r 0 ], the curve then displays a linear segment with a slope equal to -D F .

Material and methods

Material

The basic material used in this experiment is a commercial kaolin "Kaolin 7A", coming from the layer of Ploemeur in Morbihan in France. This material, generally employed for the coating of paper, was selected as a mineral load rather representative in term of morphogranulometry, texture and of mineralogy of the fine jets of mineral industry. From the point of view of its size distribution, this material is regarded as reference for validating the granulometric methodology of analysis of the flocs who were developed and for clearly highlighting the textural properties being able to be measured by laser diffractometry.

The preliminary characterization of this kaolin is given in Tables 1 and2. Mineralogy was determined by X-ray diffractometry. The particle-size distribution was measured by laser diffractometry according to the optical model of Mie (MALVERN MasterSizer S) and by attenuation of X-ray (SEDIGRAPH 5100). Specific surface area of rough material and its fraction lower than 2 µm was measured by adsorption of nitrogen according to the method BET [22] by using a Micromeritics TriStar 3000 multipoint adsorptometer.

Batch flocculation reactor

A flat-bottom baffled geometry was selected as the basis laboratory experiments. The geometry is given in Fig. 1a in dimensionless form. The vessel contained four regularly spaced baffles. Vessels with inner volume of 4.2 L were used during this work. The selected impeller was a two-blade radial flow turbine. Torque readouts from the mechanical stirrer were calibrated with water and a 50 wt% sucrose solution at 20°C. The resulting power curve is shown in Fig. 1b. The relation between the power number and the Reynolds number is given by the empirical relationship dealt with in detail in a number of reports or publications [START_REF] Allen | Powder Technology series Chapman and Hall[END_REF][START_REF] Baudet | [END_REF][8]:

 

Scattering experiment set-up

The range of analysis for wet treatment provided by different particle size analysers on the market barely exceeds 900 µm. In addition to analysing finely divided materials, this range is also adapted to characterising stabilised flocs that do not exceed this limit and that can withstand the shear forces generated by the pump when the suspension is circulated in close circuit. For non-stabilized flocs, the system must run in open circuit, where the product flowing through the pump does not return to the analysis cell. Moreover, and regardless of the mode of analysis, the use of a peristaltic pump is highly inadvisable. Its pulsation propagates all the way into the cell and generates shear and a poor circulation of the pulp. In certain areas of the cell the circulation is all but stopped. This phenomenon negatively affects the reliability of the measurements. It is therefore preferable to use an open circuit driven by gravity, with a constant flow rate and, if needed, to add a centrifugal pump at the outlet. In this context, it was necessary to develop an analysis system enabling large-sized fragile flocs to be characterisedfrom a few micrometers to 4 mm. To do so, alterations were made to the Malvern Mastersizer-S PSA. This instrument, which lends itself well to this development, possesses a long optical bench for dry treatment analyses with a 1000 mm lens making it possible to cover a range of 4.2 to 3480 µm. To convert it for wet treatment, an analysis cell having a 10 mm optical path was built by BRGM. It was inserted in open circuit between a 4.2 litre baffled feed reactor obeying similarity for the geometric parameters indicated in the preceding paragraph (Fig. 1) and the PSA"s centrifugal pump. The mixture is placed in suspension by means of the perforated impeller turning at 80 rpm (G=20 s -1

). The circulation takes place from bottom to top, with a flow rate of 1.8 l/min. For each analysis, the flocs retrieved in the flocculation reactor when stirring stops are placed gently in the water of the PSA reactor by means of a "ladle" of known capacity. However, despite all the precautions taken, the structure of the macro-flocs (1 to 5mm) that formed in the flocculation reactor several moments after stirring has stopped is not preserved in the PSA reactor due to impacts between primary flocs. This methodology makes it possible to characterise in a satisfactory manner the primary flocs constituted when stirring ended, as a function of the physical and chemical and hydrodynamic conditions.

Experimental

As a preliminary to the flocculation tests, the new cell was positioned, in terms of obscuration, with respect to the classical 0.5 and 2.4 mm cells. The suspension to circulate in it must be neither too weak, in order to obtain a statistically valid representation from a large enough number of grains, nor too strong, which would induce an optical distortion and errors in the textural parameters that are measured and, in particular, in the determination of the voluminal concentration. To respect these criteria, obscuration measurements as a function of concentration were performed for the three optical paths (0.5, 2.4 and 10 mm) on a quartz sample with a granularity range of 2 to 80 µm. The Beer-Lambert law was examined, and the critical obscurations were determined.

The flocculation of the kaolin was carried out in the reactor of flocculation indicated above. The concentration employed is 100 mg/L. The impeller velocity is fixed to 200 rpm during 15 s. The corresponding averaged velocity gradient and Reynolds number are respectively 545 s -1 and 24,000. Floc structure was examined in relation to the flocculant concentration (AN 934 MPM).

The values of the fractal dimensions are determined from the relationship log(I(q)) versus log(q) in the range R z ≪ q ≪ r s (R z is the maximum size of aggregates and r s is the scatterer radius), where the function is linear (Eq. ( 25)). Experimental observation showed that this dimension may have values ranging between 1.4 and 2.8 [23,24].

Results and discussions

Critical obscuration of the new cell

An examination of the volume concentration in relation to the concentration of the quartz suspension (Fig. 2) reveals the existence of a critical point corresponding to a critical obscuration above which the proportionality between C v and C (or Ob and C) is no longer respected. Any parameter measured or determined above this point presents certainly large errors. Multiple diffusion, mask effect and optical saturation occur frequently in this zone, and evolve very significantly in relation to the actual concentration. Below this point, the size and the particle volume concentration measured by the PSA are statistically accurate. The obscuration intervals usable by the 0.5, 2.4 and 10 mm cells are respectively 3 to 18%, 3 to 20% and 3 to 28%.

Preliminary characterization

The preliminary characterization of the kaolin 7A shows that:  This material is polydisperse. Its granulometric extent lies between 2 and 3 following the method of analysis employed.  It contains a very large colloidal fraction in mass and a number. The estimate of this fraction is given starting from the data of the "Sedigraph" and the projected area distribution of particles obtained by laser diffractometry.  In suspension, this material is very stable.

Flocculation of kaolin

The particle-size distributions in volume of the rough kaolin and the various tests of flocculation are given in superposition in Fig. 3. The raw kaolin curve consists of two populations centred approximately on 0.3 and 4.5 µm. The population density in volume of this latter largely exceeds that of the first population. For flocculated products and for the prevailing hydrodynamic conditions, the number of populations depends on the concentration in flocculant. For a quantification of less than 100 g/t (Fig. 3, E2 to E5), the populations are three in number. The first two, of very small amplitude, correspond to a residue of the two populations in the raw product. The third population results from the flocculation. The amplitude of the first two populations decreases, thereby contributing to increasing the third population"s amplitude as the flocculant concentration increases; it tends practically towards zero from 100 g/t on. Above this dosage, the distribution consists mainly of a single population, the centre of which shifts progressively to larger sizes as the concentration in flocculant increases up to an optimum dosage of 350 g/t. Beyond this value, the centre of the population remains constant. This stabilisation is probably linked to a saturation of the sites of flocculant adsorption in the mineral. The fractal dimension, also, stabilises around 2.6, indicating a state of extreme compactness. Above 100 g/t (Fig. 3, E6 to E12), the curves can be deduced from each other by simple translation. Furthermore, the distributions become increasingly tight. These properties implicitly point to a convergence towards a monomodal population composed of compact flocs with very similar degrees of compactness. The values of average mass fractal dimension evolve in this direction as shown on Fig. 4a. Fig. 4b, depicting the evolution of the average mass fractal dimension of mass determined by light scattering versus flocculant concentration, indicates the appearance of a floc structure that is increasingly compact. It changes from 1.2 ± 0.1, for 47 g/t of flocculant, to 2.2 ± 0.04, for 100 g/t. This range corresponds to flocs that have receptor sites still available and a structure up to 1.8 that is loose, and then increasingly compact from there on. It continues to increase up to 2.61 ± 0.03 for 340 g/t of flocculent. A further increase in quantification does not appear, at the scale of the test, to alter the internal organisation of the macro-flocs. The optimum condition in terms of concentration, determined by the intersection of two tangents, lies at 350 g/t for a D F value of 2.61. At the scale of the test, floc architecture stabilises between 340 and 800 g/t. The behaviour of the particle size distributions is in line with these observations. In a first approximation, the relationship between D F and DSIV (distribution spreading index in volume) is linear (Fig. 5a). Below 340 g/t, the fractal dimension increases when the spread of the DSIV distributions of the flocs decreases. Above this dosage, DSIV stabilises. This suggests the existence of an upper limit value for D F , with the saturation of the adsorption sites and the presence of an excess of flocculant beyond the concentration corresponding to D F MAX .

The analysis of the fractal behaviour in the space ln( F - L ) or ln(1- F ) as a function of ln(dmL/dmL 0 ) and for concentrations of flocculant between 47 and 800 g/t indicates the existence of two families of flocs (Fig. 5b). The first family, F1, corresponds to flocs formed by the aggregation of dense microflocs, the structure of which becomes less and less loose as the flocculant concentration increases. The places of inking are less and less free. The fractal dimension of this family displays a linear and fairly rapid increase. The second family, F2, reflects the existence of fairly compact macro-flocs. The mean fractal dimension of the two families together is 2. The range of concentrations used does not make it possible to demonstrate the zone where micro-flocs form, situated below 47 g/t.

An investigation of Eq. ( 22) or ( 20) also enables the determination of the mean fractal dimension for all the flocculation tests, irrespective of family (Fig. 5c). The value obtained in the present case is 2. Fig. 5c also shows that floc density decreases with in creasing floc size, roughly in accordance with a power-law relationship between density and size. Where CF is the concentration of flocculant in gram per ton.

Conclusion

This work shows that laser diffraction particle size analysis, as a very widespread analytical tool in industrial contexts, enables certain textural characteristics to be obtained and these latter are fairly suitable to explain the macroscopic properties of a physical and chemical phenomenon. In the realm of flocculation, as in quite a few others, the investigation of the influence of texture, determined by using this method, on the hydrodynamic behaviour of the matter makes it possible to optimise the industrial installation. To measure the thickness and the shape coefficient of lamellar particles, this technique has largely proven effective. For flocculated matter, the size, porosity and density of the flocs, as well as the volume fraction, can be obtained without restrictions due to their polydisperse nature.

For suspensions of flocs consisted of polydisperse fine particles centred on 1 µm and having a median diameter of about 0.5 µm, laser diffractometry using a wavelength of 0.632 µm is completely adapted and suitable to determine the fractal dimension of the flocs.

Aggregate density in the investigated systems decreased rapidly with increasing aggregate size. The density-size distributions can be used to obtain an accurate mass-size distribution for the flocs in an aggregated suspension.

Fig. 1 .

 1 Fig.1. Laboratory conditioning system. (a) Geometrical configuration of reactor; (b) Power curve ( e ±23).

Fig. 2 .

 2 Fig. 2. Evolution of the granulometer volume concentration as a function of the concentration of solid.

Fig.

  Fig. 3. Floc size distribution as a function of flocculant concentration after 15 s of stirring.

Fig. 4 .

 4 Fig. 4. Evolution of the average fractal dimension as a function of the relative floc size (a), and of the flocculant concentration (b).

Fig. 5 .

 5 Fig. 5. Floc texture as a function of flocculant concentration

Table 1

 1

	Granulometric results of the basic material
	Method	d10	d50	d90	dm	DSI	%	%
		(µm)	(µm) (µm) (µm)		at 1 µm at 2 µm
	PAD Laser Diff. 0.2	0.6	3.6	1.4	2.8	63.0	78.5
	Sedigraph	0.1	0.7	3.2	1.2	2.2	61.2	79.7

Note. Dx, diameter corresponding to x% of cumulative undersize (x=10, 50 or 90); dm, mean diameter; dmL, mean diameter measured by laser diffractometry; DSI, distribution spreading index (an indication of the extent of size distribution, DSI = (d90-d10)/2xd50); PAD Laser Diff., projected area diameter by laser diffractometry.

Table 2

 2

	Specific surface area and mineralogical composition
	Size Fraction	Wt	SSA	Kaolinite	Illite	Muscovite	Quartz
		(%)	(m²/g)	(%)	(%)	(%)	(%)
	-2 µm +2 µm a a	75 25	19 5	n.d. n.d.	n.d. n.d.	n.d. n.d.	n.d. n.d.
	Analysed head 100	15.5	91	5.3	3.4	0.6

Note. SSA, specific surface area; n.d., not determined.

a Size fractions separated by centrifugation

  3. Floc size distribution as a function of flocculant concentration after 15 s of stirring.

	Test	E1	E2	E3	E4	E5	E6	E7	E8	E9	E10	E11	E12
	CF(g/t) 0	23.2	47.2	72.2	98.2	125.4 154	211.5 343	482	629	795.4


The Rumanian case: the Iron Guard as Part of the fascist Network I thank the organizers for inviting me to talk on the topic of the width and the intensity of the Romanian participation to the fascist European network. This approach is not the one privileged by scholars, because their efforts in the case of the so-called "small fascisms" consisted in demonstrating the autonomy of home-grown Fascisms. In terms of network theory, it means privileging the nodes over the links. This approach incites first to a comparative, and not to a relational methodology. It is certainly indispensable to propose a generic definition of Fascism.

But the relational and transfer approaches will prove useful to evaluate some comparative theories in the view of the actors themselves: did they consider that ideological and structural commonalties could create international relationships?

The main point of my argumentation is the pre-eminence of the ideology over Realpolitik in Fascist international relations. Fascist States are not Westphalian States, they do not evolve in the so-called "international disorder" and do not obey only to rationality of interests, but also to ideology driven geopolitics.

I therefore propose a three level presentation:

-the first level is the plain transfer through direct contact with other kindred milieus;

-the second one is the active linking role of legionaries as go-between in the rapprochement between German national-socialists and Italian Fascists; -the third level is the interference of Fascist ideological cluster in the multi-level relations between States, parties and individuals.

I -

C/ Italian ineffective prestige

At the beginning of the twenties, in Romania as elsewhere in Europe, a lot of movements claimed to follow the Italian model, but with no much Italian support. Theodor Armon underpinned the Italian lack of interest towards the Romanian right until the German challenge. And even after 1933, its anti-Semitic stance placed it rather on the German side.

The Legionaries were represented in some Italian organs as the science and literature Institute called Europa Giovane, created in 1938 inside the National institute of Fascist culture, and whose honorary members were very different right wing personalities as Nicolae Iorga, Codreanu and Manoilescu, the specialist of corporatism, freshly elected on the Iron Guard's lists, but as an independent personality, also president of the CAUR in Romania 4 . Thus, the concrete links between the Iron Guard and the Fascist Great Powers were weak.

II -The Iron Guard's effective role in the European Fascist net

One important question is the consciousness about ideological similarity as a condition for a good relationship: the theoretical background of this problem is that the kind of nationalism developed by Fascism is not a traditional 19 th century one, framed in a country-State-people nationalism; thus the hostility among nationalisms are not the core of Fascist nationalism, and the ideological transnational commonalties and convergence do matter.

A first attempt of "international nationalism" is that of Msgr. Benigni, who had begun an activity of network building among the far right Europe grace to his Correspondance de Rome. He met Moţa during the anti-Semitic meeting organized by Gyula Gömbös in 19255 . Thus Moţa could display some support to the German thesis. Nevertheless, the motion was a compromise which Moţa asked his German counterpart to accept as a fair basis of reconciliation with the Italians. He also invited him to a certain "moderation" on the biological racism, excepted towards the Jews.

This network activity was conserved by Moţa

In his answer, Pottere complained that the Fascist movements would not recognize the importance of anti-Semitism in the palingenetic ideological formula: "Any national regeneration movement is condemned to death if it neglects the Jewish question." [START_REF] De | alias Pottere du 27 février 1935 à Moţa[END_REF] But he agreed with Moţa that the racial criterion must have been limited to the Jews: "Let's not forget that there is not a German or a Romanian racethere is only the Aryan race (divided among several nations) and the Jewish race." 11 In exchange of this noticeable service, Moţa's intended to underpin Iron Guard's importance and difference with the other far right movements, in order to justify its refusal to merge with them. So he refused to take part to the Welt-Dienst Congress of the 26 th of August gathering twenty countries, because the Romanian anti-Semitic movement was already represented by the old rival Cuza, whereas the Legionaries "envisaged as the only possibility a solution intimately linked to an action of moral rebirth of our people" 12 , illustrating what R.

Griffin calls the palingenetic ideological trend of Fascism.

Further correspondence confirmed this position, for example the absence of any member of the Iron Guard at the Nazi Party's Rally in September 1935 [START_REF] Lettre D'invitation De | alias Pottere du 27 août 1935 à Moţa[END_REF] .

Whatever the Legionaries' behavior towards the Welt-Dienst, the latter's role was on a descending slope as the difficult years had passed and the need of ideological solidarity vanished, replaced by the Realpolitik advantages of power. As Michael Hagemeister puts it: "The previous staffwho were, according to Adolf Eichmann, 'more or less dubious characters'were all fired. … The era of bizarre idiosyncratic conspiracy theorists was over; the time was ripe for pragmatic, professional practitioners of power." [START_REF] Hagemeister | Russian Émigrés in the Bern Trial of the "Protocols of the Elders of Zion[END_REF] Paradoxical and not so paradoxical is that at the same moment, Codreanu placed the international affairs and his pro-Axis stance on the forefront of his propaganda. Thus, secret relationships became useless as they were in the public domain and became one of the most important power lever in the competition between the King and the Legionaries for an international balance between the Western Democracies and the Fascist Axis. This division of roles functioned quite mechanically: in time of delicate or adverse situation for the Fascist Powers, Realpolitik would not work and ideology filled the gap.

Thus the impact of the Legionary underground network on the decision makers was rather weak but its influence existed certainly on the parties' apparatus vs State administration

III -The crossed-leveled relation:

preeminence of ideological kinship over the Realpolitik I will limit this section to some public declarations, mainly by Codreanu. I distinguish the comparative and the relationship sides of legionary international analyses.

A/ Where Codreanu goes comparative

Codreanu claimed in his main book, For my legionaries, that Legionarism, Fascism and National-Socialism were fundamentally kin movements: "I want to demonstrate that the nationalist movements and regimes in present Europe, as the Legionary movement, the Fascism, the National-Socialism, etc., are neither dictatorial nor democratic". 15 And two years later in a press conference: "I am against democracy, as I am against dictatorship. At morning's dawn arises another system, new, never met before. This is what I am for." 16 So the arguments in favor of this kinship are the popularity of the political renewal and, in fact, of the whole social system. This renewal is founded on the fertile stress between popular enthusiastic adhesion and authority principle, the adhesion being ensured by the deep and strong conviction that the authority is necessary in order to realize supra-human transfiguration in every field of social and political life. Such a virtuous circle is certainly nourished by concrete realizations in the domestic and international fields, directing society's aspirations towards the promise of improvement, of strength, of identification with the nevertheless unreachable charismatic leader.

So analyzing secret network is certainly useful, but more obvious evidence for kinship and intense relationships aspirations are very well known from public declarations.

B/ Codreanu and the promises of a European fascist collaboration

The legionaries' position on international relations converged with Germany's interests 17 but also with King Carol's and the whole Romanian right opinion about Romania's integration to the Franco-Soviet axis. Indeed, the support for soviet red army passage through the Romanian territory in order to converge with the French army against Berlin was scarce outside some narrow circles of the Romanian chief of diplomacy Titulescu. But if the King wanted good but distant relations with the Soviets, legionaries were progressively involved in crusade propaganda against the Franco-Soviet link.

Codreanu's circular letter dated 30 th of May 1936 18 was clearly hostile to the Romanian diplomacy. Geostrategic realistic reflexion was not absent in this judgment, with the risks of bolshevisation in case of passage of the Soviet army or of dismemberment by the Fascist powers in case of victory on the Franco-Soviet couple 19 . But radical ideological motivation belonged, however, to Codreanu and the far right. Titulescu was forced to resign at the end of August, but that changed nothing to the severe critics of Codreanu. In his open letter to the King and to the politicians dated 5 November 1936 20 , on an urgent and solemn tone, Codreanu reacted to shift of power of the year 1936 (Rhineland, Rome-Berlin Axis and League's sanctions against Italy).

He intended to create difficulties to the King and show the Axis powers who was their true support on the Romanian political stage and their most fitted counterpart. The multiscalar approach reveals an international radicalization of the head of the Iron Guard favorable to the Fascist regimes, which was not shared by all the Legionary Movement.

Codreanu then took an initiative articulating the two plans, interior and exterior: he decided the departure of seven high-level legionary executives, including his brother-in-law Moţa, for the Spanish front 21 accomplishing thus a transnational choice on the side of Fascist powers, in radical ideological opposition to international communism, but with very light network preparation.

If this event was not important for the central administrations of the great powers, the legations and the parties, at least the NSDAP, began to take into serious consideration the Iron Guard out of ideological motives. In March, the government and the king made it clear in Berlin that support to legionnaires could have serious consequences on the German-Romanian relations 23 . In spite of it, a dispatch from Wilhelm Fabricius, the German Minister in Bucharest, proved that he had understood what distinguished the Iron Guard of the rest of the far right whose emissaries succeeded in Berlin to apply for grants and moral support, while "the only ones who deserve the support and encouragement are just [...] the legionaries of the Iron Guard, who precisely because of their harshness of character and ideas, are subject to persecution, imprisoned and prosecuted without mercy." 24 2 points in the conclusion

The network looks rather weak:

-its range is limited, as the transfers naturally concerned mainly the elites: or, the importance of Fascist movements lies in the mass mobilization by national myths, thus the transfer of international ones like the Elders of Zion might have proved important for the elite, but it had to be transformed into a popular digest to have its range widened and adapted;

-its density is also low: only a few intellectuals were implied in the net and the node Moţa linked three other nodes -Action Française, Welt-Dienst and CAURwho ignored and even detested each other for Realpolitik reasons. Moreover, the linking node came from a small country whereas the separated nodes belonged to great powers;

-its sustainability is very unpredictable: we have seen that the ideological convergence during high international crisis drew the Fascists nodes close to each other, but this was not a firm rule.

Thus I propose to come back to the ideological kinship, which do not replace

Realpolitik relationships between States, but arises each time the Fascist regimes, movements or personalities are in danger. And danger was inherent to Fascism: after all, Mussolini had adopted the nietzschean "vivere pericolosamente".

Thus I propose to finish with two quotations, by Codreanu and by Hitler.

At this end of his trial, which he knew it could lead him to death, Codreanu was charged with "treason", "intrigue against the social order" and "crime of rebellion"25 . He rejected those accusations and referred to the commonalties of the Fascist movements:

"The accusation carried against me today by the final order, I have already encountered, and it is, it seems, always linked to these movements of moral and national rebirth on which those who hate them throw, with all the invective, all the charges in the world."26

The sentence "always linked to these movements" has meta-linguistic value for me, as the link does not lean on the relationships between movements, but rather the palingenetic ideology provides the link between the movements. Thus, Codreanu launches a subliminal threat to the court, reminding that if he was not Hitler's hireling, some day Hitler might also remember how Carol's regime had treated a kindred movement.

Precisely, less than two years later, Hitler contributed hugely to crush Carol's regime grace to the second Vienna Award, but on realisticand not ideologicalpurposes, because less than five months later, he also gave Antonescu a free hand to repress the Iron Guard, assimilated to the turbulent SA before Barbarossa. In spite of this realism displayed at the beginning of the war, Hitler warned Antonescu not to break with the popular support the legionaries could represent:

"From a historic point of view we can say, on the basis of a vast experience, that any regime has to lean on the people. The history showed that there where misses this foundation and the regime leans only on the strength, in the best case it does not survive the exceptional personality who established it."27 Thus, if Hitler took advantage of the repression of the Fascist movement in Romania in order to ensure Barbarossa, his long term political thought brought him back to a populist,

  The transfers: "Paris und Berlin als Lernort für die Legionäre" It will deal with the contacts of the two main legionary personalities, Codreanu and Moţa, with Maurras and the German radical Burschenschaften at the beginning of the Ruhr crisis. A/ The French connections proved more and more evanescent through the thirties Florin Ţurcanu, the specialist of Mircea Eliade's legionary youth, tried to demonstrate that Action Française had an important influence on the creation of the Legion of the Archangel Michael through Ion Moţa and his Romanian Action, a radical anti-Semitic counterpart of the prestigious French model. Moţa translated into Romanian The Protocols of the Elders of Zion in 1922, only one year after its publication in France by a member of the Action Française. So the transfer seems obvious here. His letters of the 1 st of April and 9 th of June 1925 to Maurras narrate the first trialsand acquittalsof the students members of the League of National-Christian Defense of Professor Cuza. They had plotted in October 1923 to assassinate political and Jewish personalities. Codreanu had also murdered in 1924 the Prefect of Police in Iaşi. However, at the end of 1925, when Moţa and Codreanu travelled to Grenoble to write their law thesis, their writings do not mention any relations with Maurras. Presumably, the radicalization of the youth section of the League began to separate maurrassian Cuza and Codreanu not only on the problem of violence, but also on the structure of the movementthe young leader wanted to create a mass movement permanently mobilizedand on the ideologyas Codreanu wanted to add to the monomaniac anti-Semitism of his aging mentor elements of a new affirmative ideology. All these converging choices would lead to the creation of the Legion in June 1927. A second manifestation of interest for Maurras reappeared at the beginning of 1934. The letter was addressed to Maurras by Vasile Marin, another organic intellectual of the Iron Guard: he intended to appease the Action Française about the accusations brought to the Iron Guard of having murdered Prime Minister Duca on Hitler's orders. True is that until Moţa's and Marin's death in Spain in January 1937, Hitler preferred Cuza's Party as a much more obedient partner, ready to realize Germany's aims of merging all the right parties in order to give Germany easier manipulative possibilities. But the Iron Guard resisted those attempts, certainly not in order to please French interests but to safeguard Legionary Movement's political independency. Thus, the centre France represented for the young Romanian nationalists at the beginning of the period faded away and the link lost much of its density during the thirties. B/ The German influence on Codreanu's organization and national ambitions ... ... seems important during a student's trip realized at the end of 1922 by Codreanu to the University of Berlin. In reality he would "study the German and Austrians students' organisation of the anti-Semitic activity" 1 . When he came back from revolutionary mood Germany after the beginning of the French occupation of the Ruhr, swastikas would flourish on the Romanian students' coats to mark the adepts and gather money to support the autonomy of the movement born in March 1923, the League of National-Christian Defense 2 . On the way back from Germany, he also met the students in Cernăuţi and Iaşi in order to propose "The transformation of the university student movement into a great national movement outside the university, because our struggle interested the whole nation." 3 His position was soon adopted and the influence of the German youth certainly had an impact on the vantage Codreanu took upon his intellectual Francophile comrades like Moţa, Marin or Polihroniade, formed in the entourage of the right wing Parisian salons of the French winner. After the Machtergreifung, Codreanu showed a friendly attitude, also intended to counteract the much more noisy and servile pro-Hitler demonstrations from Cuza. But Codreanu had understood the importance of the new German element in the European balance. Romanian diplomacy was preparing its integration into the Paris-Moscow axis in gestation since the arrival of Hitler and the democratic parties gave pledges to Paris in this sense. Codreanu gave a double answer, of independence and sympathy towards Germany.

  .

  The first expertise asked to Moţa was on the trial held in Bern about The Protocols of the Elders of Zion 6 . The defender of the Swiss anti-Semites was the Welt-Dienst of Erfurt, an organism financed by Goebbels since 1933 and intended to become an international propaganda office under the direction of the retired Oberstleutnant Ulrich Fleischhauer 7 .Moţa's correspondent wasGeorg de Pottere, a former Austro-Hungarian consul in Moscow, born in the Banat 8 , thus a former compatriot of Transylvanian Moţa and who knew well the Russian context of the anti-Semitic forgery of The Protocols. But the main role Moţa had to play was that of go-between for anti-Semitic National-Socialists and not yet anti-Semitic Italian Fascists after the Austrian crisis of July 1934. He was invited at the Congress of the Committees for the universality of Rome (CAUR) in Montreux in December 1934; it was intended to balance the German influence. The motion on the Jewish question he presented ended in an ambivalent statement: in the Italian line, "Congress declare[d] that the Jewish question [could not] lead to an universal campaign of hate against Jews", but the anti-Semites obtained recognition of the Jewish problem as that of "a state within the state" and an internationalist revolutionary minority, resulting in the decision to fight it 9 .

  . There, Moţa and Marin were killed near Madrid 22 , 17 Chiper, România şi Germania nazistă, … op. cit., p149. Voir aussi Traian Sandu : « La Roumanie sur l'axe Paris Moscou, 1933-1937 : sécurité européenne et coopération militaire », dans Bonneville-de Gayffier, Anne-Claire [dir.], Sécurité et coopération militaire en Europe, 1919-1955… op. cit., pp. 249-267 18 « Circulaire -politique extérieure », Codreanu, Circulări şi manifeste…, op. cit., pp74-75. 19 This classical reflexion may be found, inter allia, in the personal letter from Goga to the King of 14 July 1936, ANIC, CR, vol.7/1936, f.3-9 20 « Mémoire adressé à S.M. le Roi, aux hommes politiques et au pays », Codreanu, Circulări şi manifeste…, op. cit., pp97-101. 21 Lettre de Moţa à sa famille du 1 er décembre 1936, Testamentul lui Ion Moţa, Munich, éd. « Ion Mării », coll. Europa, pp21-24.

  For example, after the Vienna Award giving Northern Transylvania to Hungary, some historical Legionary leaders as Corneliu Georgescu or Radu Mironovici România şi Germania nazistă, … op. cit., p222. 24 « Informations au sujet d'un nouveau rapport de Fabricius », note n°30(621) du 8 mai 1937 de la DGP, ANIC, DGP, vol.17/1937, f.20-21, ici f.21.

	would risk a war against Germany; but when Barbarossa was launched, Legionaries fought
	well in spite of Antonescu's repression with Hitler's approval.

22

Circulaire du 15 janvier 1937, ibid., p118. Voir aussi Scurtu et al., op. cit., documents n°144 et 145, pp258-260.

23

Chiper,

Rapports de la Siguranţa des 7 et 17 novembre 1922, Scurtu et al., doc. n°24 et

25, pp256-257.

Ion Motza, Corrispondenza col Welt-Dienst[1934][1935][1936], Parme, All'insegna del Veltro, 1996 ; traduction roumaine : Corespondenţa cu Welt-Dienst, Munich, Ed. « Ion Mării », 2000, pp74-78, p10 et lettre de Moţa à Pottere du 5 février 1935, pp34-39, ici p38.

Nicault Catherine, « Le procès des protocoles des sages de sion, une tentative de riposte juive à l'antisémitisme dans les années 1930 », in Vingtième Siècle. Revue d'histoire n°53, janvier-mars 1997. pp. 68-84.

Voir la page que lui consacre Richard Alan Nelson sur Wikipedia [consulté le 22 avril 2010] : http://en.wikipedia.org/wiki/Ulrich_Fleischhauer

See the Ulrich Fleischhauer page on the German Wikipedia, consulted on the 18 th of June, 2012.

Note de la Direction générale de la Police du 21 janvier 1935, Scurtu et al., op. cit., doc. n°24, p81.

Corneliu Zelea Codreanu, Pentru legionari … op. cit., p311.

Corneliu Zelea Codreanu, Circulări şi manifeste 1927-1938 (Circulaires et manifestes 1927-1938), 5 e éd., Munich, coll. Europa, 1981, 294pp., conférence de presse du 29 novembre 1937, pp.220-223, ici p.222.

Ibid., p94.

Défense de Codreanu du 23 mai 1938, Scurtu et al., op. cit., pp98-112, ici p99.

Entrevue d'Obersalzburg du 14 janvier 1941, Antonescu-Hitler, Corespondenţă şi întîlniri inedite (1940-1944) (Antonescu-Hitler, correspondance et rencontres inédites (1940-1944)), édités par Ion Ardeleanu, Vasile Arimia et Ştefan Lache, Bucarest, Ed. Cozia, 1991, vol. I, 216p, p67.

anticonservative and transnational -the "vast experience" he invokeslegitimization of the regime. I thank you for your attention.