J Bongono

N Azema

A Johannet

P Gaudon

Determination of the characteristics of agglomerates in aqueous suspensions using nonlinear optimization

Keywords:

Measurement of characteristics of particles in suspensions without dilution has a practical interest in formulation, mineral processing, material sciences and environmental technologies. These characteristics are the size, shape, and surface properties of the primary particles, and also the size, structure and the number of primary particles in the agglomerates. In this work, the multiple light-scattering model through the optical analyzer, Turbiscan MA 2000 is used to determine the mean settling velocities of monodisperse glass beads and two polydisperse samples of powders, kaolin D and alumina, differing by their particle size distribution, their shape and their surface properties. Beyond the experimental validation of theoretical and empirical predictions, the nonlinear adjustment of experimental settling data gives the number of primary particles per agglomerate and the agglomerate size. These two characteristics lead to the determination of the fractal dimension of the agglomerates. The latter was found in the range of 2.5-2.7 for all suspensions examined. The calculation of permeability and spherical factor reveals the nonspherical impermeable agglomerates.

Introduction

Most of industrial processes involve suspensions as an intermediary of production, final products or as effluents. These suspensions are unstable and present various behaviors. Most of them are aqueous and concentrated. Their properties are dependent on primary particles, agglomerates and liquid medium characteristics which are localized at the microscopic, mesoscopic and macroscopic scales, respectively. The control of the behavior of these suspensions requires the establishment of the relationships between all the characteristics at all scales. The investigation methods vary due to the diversity of the suspensions. Each suspension seems to be specific and is considered as a particular case. Both light-scattering, monitoring and image analysis, devoted to the determination of the structural characteristics of agglomerates formed in suspensions have their limitations [START_REF] Bushell | On techniques for the measurement of the mass fractal dimension of agglomerates[END_REF]. Blakey and James [START_REF] Blakey | The viscous behavior and structure of aqueous suspensions of goethite[END_REF] show that the microscopic properties (e.g. surface charge of primary particles, their distance of separation, their size…) cannot estimate the effect of the structure on the macroscopic properties (e.g. viscosity, electrostatic stability…) of aqueous suspensions of goethite for some conditions. Determination of transversal parameters such as structural characteristic (e.g. mass fractal dimension, D f ) for all types of suspensions with a single method is a key point for rapid and accurate control of these media. Fractal dimension determines the structure of agglomerates and the suspension. This parameter is dependent on the microscopic properties of particles and liquid medium and it is well correlated with most of the usual macroscopic properties of suspension, justifying the increasing number of research concerning its determination over the last years.

In this work, we proposed an approach for the determination of the fractal dimension D f based on the measurement of the settling velocity and on the nonlinear optimization of the experimental settling data. The optimization of the parameters enabled the calculation ofD f . This paper includes the fundamentals on sedimentation process and particle velocity in Section 2. The settling data is recorded with the concentrate suspensions analyzer, Turbiscan MA 2000, the principle of which is presented in Section 3. The results including some hydrodynamic characteristics are presented in Section 4. Section 5 is devoted for the discussion.

Theoretical developments

Sedimentation process and particle velocity

As a suspension settles in a closed container, the concentration necessarily becomes non-uniform. A clear layer, devoid of particles, forms at the top and sediment at the bottom. In addition, concentration gradients can appear in the region above the sediment.

The processes which convert the homogenous suspension into a suspension with two separate regions, clear liquid and sediment can be described with the following:

∂ϕ ∂t + ∂f ϕ ð Þ ∂x = 0; ð1Þ
with 0 ≤ x ≤ h, t N 0 and where f(ϕ) = v p × ϕ is the flux function; v p , ϕ, x, t stand for particle velocity, particle volume fraction, height of the settling column and time, respectively. Eq. ( 1) is considered together with the initial condition

ϕ x; 0 ð Þ = 0 for x = h; ϕ 0 for 0 b x b h; ϕ max for x = 0 8 < :
where it is assumed that the function f(ϕ)satisfies

f ϕ ð Þ = 0 for ϕ ≤ 0 or ϕ ≥ ϕ max b 0 for 0 b ϕ b ϕ max &
The parameter ϕ max is the maximum solids concentration and h is the height of the sample in the settling column.

Kynch [START_REF] Kynch | A theory of sedimentation[END_REF] first formulated the theory of sedimentation process based on Eq. ( 1) for incompressible sediment. The basic assumption of this theory is that the particle velocity is a function of the local volume fraction of particle only, which for batch sedimentation in a close column is equivalent to state that v p = v p (ϕ).

Solving Eq. ( 1) by the method of characteristics [START_REF] Kynch | A theory of sedimentation[END_REF] gives the solid volume fraction ϕ at any point (x, t) for a given initial solid volume fraction ϕ 0 .

ϕ x; t ð Þ = ϕ 0 x-v p t ð2Þ
Eq. ( 2) can be constructed in the plane (x, t) [START_REF] Kynch | A theory of sedimentation[END_REF]. The characteristic curves are straight lines with slope v p (ϕ) and the value ϕ(x, t) remains constant along any characteristic line.

The validity of the theory of Kynch was proved in several papers but its major inconvenience is that the initial condition of the homogeneity of the suspension is difficult to meet experimentally.

The other manner is to construct a virial expansion valid to O(ϕ) by expressing the velocity of the ith particle through a pairwise additive approximation. The results enable exact calculations of the settling velocity v p (ϕ) in monodisperse suspensions at dilute solid volume fraction [START_REF] Batchelor | Sedimentation in a dilute dispersion of spheres[END_REF][START_REF] Glendinning | A pairwise additive description of sedimentation and diffusion in concentrated suspensions of hard spheres[END_REF][START_REF] O'brien | A method for the calculation of the effective transport properties of suspensions of interacting particles[END_REF] as given:

v p ϕ ð Þ v p;0 = 1-6; 55ϕ + O ϕ 2 ð3Þ
The extension of higher concentration for monodisperse hard sphere suspensions is given by Eq. (4) [START_REF] Richardson | Sedimentation and fluidization[END_REF] and Eq. ( 5) [START_REF] Mills | Settling of suspension of hard spheres[END_REF].

v p ϕ ð Þ v p;0 = 1-ϕ ð Þ n ð4Þ
v p ϕ ð Þ v p;0 = 1-ϕ 1 + kϕ 1-ϕ ð Þ 3 ð5Þ
where v p ϕ ð Þ v p;0
is the dimensionless settling velocity or settling rate, v p, 0 is the Stokes settling velocity, n in Eq. ( 4) and k in Eq. ( 5) are free parameters and stand for the angular dispersion of the fluid stream lines against the vertical direction.

If the sphere are cohesive, need is to take into account the aggregation during settling. Assuming that during sedimentation, agglomerates produced are monodisperse, Valverde et al. [START_REF] Valverde | The settling of fine cohesive powders[END_REF] modified Eqs. ( 4) and ( 5) and showed that the resulting Eqs. ( 6) and ( 7) are valid for settling of cohesive powder.

v p ϕ ð Þ v a = 1-ϕ ef n ð6Þ
v p ϕ ð Þ v a = 1-ϕ 1 + kϕ ef 1-ϕ ef ð Þ 3 ð7Þ
with the effective agglomerate volume fraction ϕ ef given by:

ϕ ef = ρ 0 N 4 3 πR 3 ð7aÞ
ρ 0 is the density of a particle which is the number of primary particles per unit volume of suspension. In Eq. ( 7),

v a = v p;0 N q ð7bÞ
is the settling velocity of an individual agglomerate, where q = R r is the normalized agglomerate radius and r is the primary particle radius.

The generalization to multimodal suspension is available in Ref. [START_REF] Russel | Colloidal Dispersion[END_REF] but the variation of the coefficients with separation renders the partial differential equation difficult to solve analytically in any general sense. The semi-analytical solutions are possible for small and large values of the Peclet number [START_REF] Batchelor | Sedimentation of a dilute polydisperse system of an interacting spheres. 2. Numerical results[END_REF]. Some further information is available in e.g. Ref. [START_REF] Davis | Sedimentation of noncolloidal particles at low Reynolds number[END_REF].

Eqs. ( 6) and [START_REF] Richardson | Sedimentation and fluidization[END_REF] enable the determination of the number of primary particle N per agglomerate and agglomerate radius R by a nonlinear curve fitting. The fitting parameters are the agglomerate radius R and the number of primary particles per agglomerateN. These parameters are related to the fractal dimension D f by Eq. ( 8) [START_REF] Dobbins | Absorption and scattering of light by polydisperse aggregates[END_REF]:

N = k 0 R g r D f ð8Þ
where k 0 is the fractal pre-factor and is about unity. R g is the radius of gyration. In Eq. ( 8), R g is normalized by the primary particles radius to insure the cross-attributive of the model.

Determination of hydrodynamic characteristics 2.2.1. Reynolds number

Most of the models used in this study assume that the flow is laminar. In order to evaluate this characteristic, we used Eq. ( 9)

R e;p = ρ l v a d s μ ð9Þ
where ρ l , v a , μ and d s are the liquid density, agglomerate velocity in dilute suspension, liquid dynamic viscosity and area equivalent diameter, respectively.

Drag coefficient and drag-corrective coefficient

The drag coefficients C D for each suspension were evaluated assuming the following three cases.

Case 1: Agglomerates are spherical, impermeable and the motion is Stokesian

C D = 24 Re ð10Þ
Case 2: Agglomerates are the spherical permeable particles

C D = 24 Re Ω perm ð11Þ
where Ω perm is the drag-corrective coefficient. According to Vanni [14], a good approximation for Ω perm (D f N 2) is

Ω perm = 2α 2 1-tanh α α À Á 2α 2 + 3 1-tanh α α À Á ð12Þ
with the permeability ratio α = R ffiffi p p , where R is the outer radius of the agglomerate. R is almost equal to the hydrodynamic radius R i = 1.04R H, i [START_REF] Gruy | Experimental study of small aggregate settling[END_REF]; p is the agglomerate permeability at the agglomerate surface for which uniform porosity is [14]

p = 2r 2 1 9ϕ L ϕ ð Þ E ð13Þ
where L(ϕ) and E are, respectively, the Happel function and the shielding factor:

L ϕ ð Þ = 3-4:5ϕ 1=3 + 4:5ϕ 5=3 -3ϕ 2 3 + 2ϕ 5=3 ; ð14Þ
E = 1-0:6e -10ϕ : ð15Þ
Case 3: Drag-corrective factor depends only on the uniformity S of the arrangement of the primary particles in the agglomerate and the fractal dimension D f .

C D = 24 Re Ω S ; ð16Þ
where

Ω S = S 1 D f ð17Þ
S is the structure factor [16] which can be determined by small angle laser scattering. It can be expressed as a function of the fractal dimension D f , the radius of gyration R g of the agglomerate, the primary particle radius r and the number N of the primary particles in the agglomerate.

S = N R g r -1 D f + 2 D f ! -1 2 e -D f ð18Þ
2.2.

Spherical factor of particles and Peclet number

The spherical factor ψ [START_REF] Gruy | Experimental study of small aggregate settling[END_REF] and the Peclet number are expressed respectively:

ψ = 0:065 e 1 0:843 Ω s ð19Þ Pe = 2rΔv p;0 D 0 ð20Þ
In Eq. ( 20), Δv p, 0 is the relative Stokes velocity of particle with radius r and D 0 is the diffusion coefficient.

Later, we will evaluate all the models listed above for all the suspensions used in this study. The goal is either to estimate the order of magnitude of these hydrodynamic characteristics for studied suspensions but also, to explain their behavior through their mesostructure.

Experimental

Materials: powders and suspensions

Three powders were used in our experiments: micro glass beads from Potters-Ballotini company (France), kaolin powder (type D) from Brazil and Alumina from Martinswerk (Germany). The three powders have distinct size distribution, shape, roughness and surface charge. Their main physicochemical and granular characteristics are reported in Table 1.

In order to control chemical entities in the medium and interfacial properties, dry powders of each material were dispersed in demineralized water which was obtained after crossing a double ion exchange column. The resulting suspension was stirred with a magnetic stirrer at a constant speed during 15 min. These conditions are sufficient to insure homogeneity. Part of this homogenized suspension was introduced in a (16 × 125 mm) borosilicate glass cylindrical tube and immediately analyzed in Turbiscan 2000. The sample height in the cell is ~43 ± 2 mm. Five scans were completed for all experiments and the time elapsed between scans was maintained at 1 minute. For all experiments, the mother-suspension was prepared with 8 vol% solids loading and unless otherwise stated, 3.5 vol% and 5.7 vol% were used for analysis.

Methods: turbiscan MA 2000

The fundamentals and principles of the Turbiscan MA 2000 device are well exposed, respectively, in Bru et al. [START_REF] Bru | Particle size and rapid stability analyses of concentrated dispersions: use of multiple light scattering technique ACS doc[END_REF] , Mengual et al. [START_REF] Mengual | multiple light scattering measurement for concentrated emulsion and suspension stability analysis[END_REF], and Snabre & Arhaliass's [START_REF] Snabre | Anisotropic scattering of light in random media: incoherent backscattered spotlight[END_REF] works. In this section, we restrict our attention to the operating principle Fig. 1. It consists to scan by a pulse near infrared light source (λ = 850 nm) a cylindrical cell containing the sample. Some of the photons undergo deviation and are scattered in all directions (scattered light). The others go through the sample without deviation (transmitted light). The backscattered light at 135°a nd the transmitted light at 0°are registered simultaneously, step by step, every 40 μm and convert into two spectra. An example of the backscattering light spectrum is shown in Fig. 2. The Y-axis corresponds to percentage of the backscattered light and the X-axis is the height of the settling cell. Every minute, a scan was performed along the cylindrical cell. The evolution of these signals allowed the determination the velocity of the upper interface (which corresponds to the mean settling velocity of particle v p ) in the way described in Section 4.1. At the bottom of the cell, the percentage of the backscattered light increased, allowing us to record the evolution of the lower interface (interface between the sediment and the bulk suspension). The evolution of both the upper interface and the lower interface depends on the characteristics of the primary particles, the agglomerates, and the suspending liquid.

Results

Settling analysis: measurement of the mean settling velocity

In Fig. 2, we represent an example of sedimentation profiles. At the top of the sedimentation column, the upper interface was located between the clear liquid and the bulk suspension. Its follow-up in function of time enabling the determination of the mean settling velocity. To calculate the mean settling velocity, we needed to evaluate the distance Δh t between every scans along the horizontal line H. See Fig. 2 for the position of line H. Then assuming the number of Reynolds Re b 1and the uniform movement of the upper interface, the mean settling velocity at time t can be expressed a:

v p = Δh t t ð21Þ
Experimental settling data were collected from the sedimentation profiles through the mean settling velocity given by Eq. [START_REF] Buscall | The settling of particles through Newtonian and non Newtonian media[END_REF]. These data were adjusted with the theoretical models (4), ( 5), [START_REF] O'brien | A method for the calculation of the effective transport properties of suspensions of interacting particles[END_REF], and [START_REF] Richardson | Sedimentation and fluidization[END_REF]. The results of the optimization for all materials were presented as the mean settling rate in function of particles volume fraction in Figs. 345. In these figures, it is clear that the particles settled initially at a constant velocity, but as the upper interface approach the bottom of settling column, the particles slowed down, indicating the formation of stresses carried by interparticle contacts. In the legends of graphs, Eqs. ( 4) and ( 6) correspond to the Richardson & Zaki models for hard spheres and the modified Richardson & Zaki models for cohesive particles respectively. Eqs. ( 5) and ( 7) correspond to the Mills & Snabre models for hard spheres and modified Mills & Snabre models for cohesive particles respectively. As we noticed it early, Eqs. ( 6) and ( 7) are the results of the modification of Eqs. ( 4) and ( 5) in order to adapt them for sedimentation of cohesive particles. Valverde and coworkers [START_REF] Valverde | The settling of fine cohesive powders[END_REF] are the authors of this adaptation.

The fitting parameters 4.2.1. Adjustment of noncohesive models

The only fitting parameters in Eqs. ( 4) and ( 5) were n and k, respectively. Thus, the adjustment of noncohesive models to the experimental data was straightforward. We were expecting that the values n = 5.6 [START_REF] Batchelor | Sedimentation in a dilute dispersion of spheres[END_REF] and k = 4.6 [START_REF] Mills | Settling of suspension of hard spheres[END_REF] established for noncohesive particles in the dilute limit would conform to the values of n and k corresponding to the experimental settling data of glass beads. For cohesive materials (Kaolin D and Alumina), the values of n and k are expected to be different.

Adjustment of cohesive models

In the cohesive models, the fitting parameters were n, k, R and N. The adjustment proceeded into two steps. The first step was to evaluate the free parameters n and k defined in Eqs. ( 6) and [START_REF] Richardson | Sedimentation and fluidization[END_REF] second step was the adjustment itself, i.e. to find the best parameters that are conform to the experimental data. Later, we will focus our development only on the determination of the parameter k. The determination of n following the same way, it final values will be given in Table 3.

Let us consider Eq. ( 7). For very diluted suspension of cohesive particles, the expansion to the first order of the right member of Eq. ( 7) on the agglomerate effective volume fraction ϕ ef gives:

v p v a = 1-kϕ ef ð22Þ
Eq. ( 22) is the linear approximation of Eq. ( 7). It is valid for all materials provided that the agglomerate effective volume fraction is close to zero. A statistical analysis of the mean value of ϕ ef for two small volumes of suspension in function of the number of primary particles allows the determination of ϕ ef that is physically appropriate for Eq. ( 9). Despite the fact that it is more accurate to calculate ϕ ef for each material in order to estimate k we assume that ϕ ef = 0.01 for all the systems studied. The main reason that supports this assumption is the fact that the variation of particles mean diameter does not exceed one order of magnitude for all the material investigated. The latter assumption allows us to calculate the parameter k from Eq. ( 22). We found the values of k = 26, 58, and 80 for glass beads, kaolin D and alumina suspensions, respectively. These values are one order of magnitude larger than the 4.6 value calculated for "large" monodisperse glass beads (r =350 μm) in the glycerine-water mixtures [START_REF] Hanratty | Fluidization and sedimentation of spherical particles[END_REF] or the 5.4 value obtained for polystyrene spheres with r =1.5 μm in 10 -3 M NaCl solution [START_REF] Buscall | The settling of particles through Newtonian and non Newtonian media[END_REF]. This remarkable value of k will be discussed later.

The fitting parameters R and N were obtained by nonlinear optimization. The optimization procedure is based on Matlab function "lsqcurvefit" which solves the nonlinear data fitting problems in least square sense. Details regarding the adjustment parameters (R and N) and the parameters that best fit the experimental settling data together with the fractal dimension D f are mentioned in Table 2. The initialization values of R and N were obtained by considering the linear approximation of Eq. ( 6) in the frame work of very dilute suspension (10 -3 -10 -2 particles volume fraction). Table 2 also includes the interval within which the best parameters were found. This interval was expressed in terms of lower and upper bounds. The lower bound for R and N was the "primary particles radius r" for each materials and "1 primary particle" respectively. The upper bound for R was the length of the linear agglomerate that consists of the upper bound of N i.e. the total number of primary particles.

Mean settling rate

Hydrodynamic characteristics

In Eq. ( 9), v a is given by the y-intercept at ϕ = 0 in the Figs. Drag coefficients C D were calculated for each suspension with different assumptions on agglomerate shape and permeability. We found that drag coefficients calculated using Eqs. ( 10)-( 15) and that calculated using Eqs. ( 16)-( 18) compare to each other with the relative error less than 6%. The drag-corrective factor was found about unity (Ω = 0.95) indicating that the agglomerates are almost impermeable. the obtained results expressed the influence of the external shape and the roughness of the body on the drag coefficient. We then calculated the spherical factor ψ using the corrective drag coefficient Ω S . Poor sphericity was obtained. It is about ψ = 0.2 for all agglomerates even for those composed of microspheres of noncohesive glass beads. This apparent contradiction will be discussed in Section 5. In order to determine which of the thermodynamic or the hydrodynamic forces was prevalent in examined suspensions, we calculated the Peclet number Pe using Eq. [START_REF] Hanratty | Fluidization and sedimentation of spherical particles[END_REF]. The obtained values of Pe indicate that hydrodynamic force was dominant in both suspensions. The hydrodynamic force is 1 to 2 orders of magnitude in kaolin D and alumina suspensions compared to that of glass beads suspensions. The values R e , C D , Ω, ψ and Pe are summarized in Table 3.

Discussion

Before developing this discussion, we should clarify the difference between agglomeration and aggregation, agglomerate and aggregate. The confusion is sometimes made in the use of these vocabulary. The key difference between agglomeration and aggregation processes is that the first one does not involve chemical reactions. The agglomeration process produces agglomerates and the process is entirely reversible because of the weakened nature of the connection (e.g. physicochemical interaction as van der Waals forces, hydrogen bond…) between primary particles inside the agglomerate. The aggregation process produces aggregates: the process is irreversible due to the strong nature of the connection (e.g. covalent chemical bond) between primary particles inside the aggregate. Moreover, the aggregation process is concerned with colloidal dispersion where the Brownian force is significant. In this study, we carefully avoided any chemical reaction between particles. The process involved then was the agglomeration and the objects produced are agglomerates.

In Table 2, the number of primary particles N in the agglomerate increases as the primary particle size decreases indicating that for the same time of sedimentation, aggregation intensifies for fine cohesive particles. This tendency was confirmed by the obtained values of Peclet number. In both suspensions, gravity and hydrodynamic forces were predominant but the Brownian forces were not eliminated since the values of Pe were not infinite. The smaller the value of Pe, the larger is the Brownian force. The latter in turn acts on small particles to favor collision and agglomeration. The obtained agglomerates were not spherical and impermeable with fractal dimension in the range of 2.5 b D f b 2.7. For other systems where primary particles aggregate, it has been established that such fractal dimension implies the diffusion limited particle-cluster aggregation (DLPCA). The DLPCA model of aggregation often occurs when the initial sample of suspension contains dissimilar (small and coarse) primary particles. That is the case in the systems considered in this study. By analogy with the aggregated systems, the mechanism of agglomeration could be described as follows: the small particles diffused in all directions as the Brownian forces acted on them. The coarse particles settled without diffusing. During the diffusion of small particles, they may collide with the coarse particles and some of them may stick onto them. The van der Waals forces act as the sticker when they get closer. The mechanism is called "diffusion limited particle-agglomerate agglomeration". According to the work of [START_REF] Auzerais | The resolution of shocks and the effects of compressible sediments on transient settling[END_REF], the Brownian forces (Pe = 850) smoothens the discontinuities at the interfaces. The interface becomes the interphase with a progressive gradient of concentration. In this work, we observed this progressive gradient of concentration at each interface instead of a sudden cut-off. The values of Pe obtained (Table 2) were in very good agreement with the experimental observations.

Gruy and Cugniet [START_REF] Gruy | Experimental study of small aggregate settling[END_REF] studied the hydrodynamics of the small aggregate. They found that porosity and permeability are properties without real meaning for the smallest aggregates (N b 11). They also indicate that for relatively large aggregates (30 b N b100, D f = 2.5) the effect of porosity on drag coefficient is negligible. These conclusions seems to be valid for very large agglomerate (N = 1,425, 5,396 or 136,270, with 2.5 b D f b 2.7) for which the corrective drag coefficient is very close to unity (Ω = 0.95).

The point that underpins the large value of k is the low sphericity of the agglomerate. The spherical factor ψ is found equal to 0.2 indicating definitely that the agglomerates have nonspherical shape. This sphericity factor is calculated using the structure factor S and the fractal dimension of agglomerate. The assumption made in Eq. ( 7) that the volume of agglomerate can be approximated by the volume of sphere is false regarding this result.

Low sphericity amplified the angular dispersion of the fluid stream lines against the sedimentation direction, and hence, increased the value of k. On the other hand, the microspheres of glass beads were not cohesive. How could they agglomerate? The complementary experiments consisting of watering and dewatering the microspheres in the environmental scanning electron microscopy shows the formation of a water bridge between two particles at a certain distance. But the resulting adhesion force is not enough to agglomerate the microspheres. Thus, we suggest that the effect of concentration can lead to the formation of the "weak agglomerate" during sedimentation. At 3.5% or 5.7% volume fraction of microspheres, the mass sedimentation occurred in the settling column implying that some groups of microspheres settled together.

However for k = 80, the fractal dimension of alumina agglomerates is estimated at about 3.5 using Eq. ( 7). This result did not correspond to any known theory of aggregation and brings two essential questions: the suitability of the model or/and the optical method used to study sedimentation reached its limits? For the first question, we showed that the assumption of the volume of agglomerate by the volume of sphere made the model inaccurate. The second question requires further developments.

Conclusion

We measured the settling velocity of macroscopic agglomerates consisting of a large number of primary particles in water. The Reynolds number was always small than 1. We show that the large agglomerates formed during sedimentation were dense and impermeable for 2.5 b D f b 2.7. The high value of free parameters was underpinned by the low sphericity of the agglomerates. The modified models were found in good agreement with the experimental data for approximately the same values of N and R except for the Alumina suspensions, where Eq. ( 7) failed. This failure was explained as a consequence of assuming that the volume of agglomerate can be approximated by the volume of sphere. The results concerning fractal dimensions of agglomerates suggested that the mecanism of agglomeration was a diffusion limited particle-agglomerate agglomeration. Particles mean settling velocity (m s-1 ) v p, 0 Individual primary particle settling velocity (m s-1 ) α Dispersion angle of liquid surrounding the particle against

Nomenclature

Fig. 1 .Fig. 2 .

 12 Fig. 1. Turbiscan operating principle.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Mean settling rate in function of solid volume fraction for glass beads in water.

  3-5 representing the mean settling velocity in function of particles volume fraction. Using area equivalent mean diameter, we found that the Reynolds number Re is in the range of [10 -04 -10 -02 ]. The range of Re obtained indicates that the laminar flow assumption is correct.

Fig. 5 .

 5 Fig. 5. Mean settling rate in function of solid volume fraction for alumina in water.

Table 1

 1 Main physicochemical characteristics properties of materials examined.

	Materials	Laser diffraction		External shape	Electrophores is mobility
		d mean (μm)	modes (μm)		(μm.cm/V.s)
	Glass beads	43.2	45	spherical	-0.2
	Kaolin D	13.8	0.3-2.3-26.1	agglomerates of small platelets	-3.7
	Alumina	3.8	2.7 -16.4	irregular agglomerates of small platelets	3.2

Table 2

 2 Detailed initialization of the optimization and the best adjustment parameters with the corresponding fractal dimension.

		Glass beads				Kaolin D				Alumina
		3.5%		5.7%		3.5%		5.7%		3.5%		5.7%
		R (μm)	N	R (μm)	N	R (μm)	N	R (μm)	N	R (μm)	N	R (μm)	N
	Initialization	164	5400	164	5400	164	5400	164	5400	164	5400	164	5400
	Lower bound	21.6	1	21.6	1	6.9	1	6.9	1	2.4	1	2.4	1
	Upper bound	2.3E + 10 3.8E + 09 2.3E + 10 3.8E + 09 2.3E + 10 3.8E + 09 2.3E + 10 3.8E + 09 2.3E + 10 3.8E + 09 2.3E + 10 3.8E + 09
	Best adjustment	Eq. (6) 364	1425	370	1393	173	5396	169	5400	160	136270	160	160670
		n = 13	n = 13	n = 13	n = 13	n = 9	n = 9	n = 11	n = 11	n = 5	n = 5	n = 5	n = 5
		Eq. (7) 353	1774	358	1724	164	6889	164	1077	100	1119700	100	1357300
		k = 26	k = 26	k = 26	k = 26	k = 18	k = 18	k = 21	k = 21	k = 80	k = 80	k = 80	k = 81
	Fractal dimension Eq. (6) 2.6		2.6		2.7		2.7		2.7		2.7
		Eq. (7) 2.7		2.7		2.8		2.8		3.5		3.6

Table 3

 3 Reynolds and Peclet numbers with the corresponding drag coefficients and the spherical factor of agglomerates.

		Reynolds number	Peclet number	Drag corrective coefficient Ω	Drag coefficients C D assuming that		Spherical
		Re Eq. (9)	Pe Eq. (20)	Eqs. (12)-(15)	Eqs. (17) and (18)	Spherical and impermeable	Spherical and permeable aggregates	Spherical and permeable	factor ψ Eq. (19)
							aggregates	Eqs. (11)-(15)		aggregates
				3.5%	5.7%		Eq. (10)	3.5%	5.7%	Eqs. (16)-(18)
	Glass beads	2.9E-03	2.6E + 05	0.8	0.9	1.0	8.3E + 03	7.0E + 03	7.5E + 03	7.9E + 03	0.2
	Kaolin D	8.1E-04	2.3E + 04	0.9	1.0	1.0	3.0E + 04	2.8E + 04	2.8E + 04	2.9E + 04	0.2
	Alumina	6.9E-04	5.3E + 03	0.9	0.9	1.0	3.5E + 04	3.1E + 04	3.2E + 04	3.4E + 04	0.2


Caroline Autier

Nathalie Azema
email: nathalie.azema@mines-ales.fr

Nathalie Az ´ema

Pascal Boustingorry

Using settling behaviour to study mesostructural organization of cement pastes and superplasticizer efficiency

Keywords:

published or not. The documents may come

Using settling behaviour to study mesostructural organization of cement pastes and superplasticizer efficiency

Introduction

Superplasticizers have been developed for decades in order to increase the workability of fresh concretes by dispersion of mineral particles composing concrete pastes. Many studies deal with the influence of the molecular structure of superplasticizers on their Mesostructural organization can be defined as the organization resulting of interactions between unit or agglomerated particles in an intermediate scale between unit particle one and the suspension. This relationship was studied by some authors with various mineral suspensions like kaolins or alumina. While some studies focused on the influence of the addition of dispersants or surface treatments on particles, others focused on the influence of the suspension solid volume fraction [START_REF] Vié | Study of suspension settling: a approach to determine suspension classification and particle interactions[END_REF][START_REF] Azéma | Sedimentation behavior study by three optical methods -granulometric and electrophoresis measurements, dispersion optical analyser[END_REF][14][START_REF] Burgos-Montes | Stability of concentrated suspensions of Al2O3-SiO2 measured by multiple light scattering[END_REF][START_REF] Lee | Preparation of stable dispersions of Ni nanoparticles using a polymeric dispersant in water[END_REF][START_REF] Dudašová | Study of asphaltenes adsorption onto different minerals and clays. Part 2. Particle characterization and suspension stability[END_REF][START_REF] Amiri | Influence of pH, high salinity and particle concentration on stability and rheological properties of aqueous suspensions of fumed silica[END_REF][START_REF] Balastre | Role of polyelectrolyte dispersant in the settling behaviour of barium sulphate suspension[END_REF][START_REF] Wiśniewska | Influences of polyacrylic acid adsorption and temperature on the alumina suspension stability[END_REF]. For this reason, the Turbiscan MA2000 from the Formulaction Company was used. This device was indeed developed to study nascent instability phenomena in concentrated suspensions allowing to take into account interparticle interactions present in the suspension [START_REF] Mengual | multiple light scattering measurement for concentrated emulsion and suspension instability analysis[END_REF][START_REF] Mengual | Characterisation of instability of concentrated dispersions by a new optical analyser: the TURBISCAN MA 1000[END_REF]. The coupling of this technique with other ones such as SEM or laser granulometry allows to provide information about mesostructural organization and hence interparticle interactions. The aim of this paper is to highlight the influence of mesostructural organization, in connection with organo-mineral interactions (occurring between the superplasticizer and cement particles) on the homogeneity and the stability of fresh cement pastes. This study is focused on Ordinary Portland Cement (OPC) pastes during the dormant period when the chemical reactivity slows down. In these conditions, the physicochemical phenomena are favoured over hydration reactions.

The stability and homogeneity of cement pastes over time as a function of the dosage of several PCE-based superplasticizers (PCE) were characterized using Turbiscan MA 2000 and laser granulometry. The influence of the molecular structure of the PCE on the destabilization phenomena and the stability range was highlighted. A Phase Separation Index (PSI) inspired by the works of Vié [START_REF] Vié | Study of suspension settling: a approach to determine suspension classification and particle interactions[END_REF] was defined to characterize the stability of the suspensions. The relationship with mesostructural organization was established through the correlation with the dispersion state characterized by laser granulometry.

The correlation with adsorption by Total Organic Carbon (TOC) measurements allowed showing the influence of organo-mineral interactions on larger scales. Indeed, the affinity of a PCE with the cement particles as a function its molecular structure was highlighted.

Materials and methods

Materials

A commercial Ordinary Portland Cement provided by Calcia, the characteristics of which are presented in Table 1, was chosen for the preparation of the paste. The cement composition was determined using X-ray fluorescence. The Na 2 O equiv. is low, so competitive adsorption with sulphate ion is low [START_REF] Yamada | Controlling of the adsorption and dispersing force of polycarboxylate-type superplasticizer by sulfate ion concentration in aqueous phase[END_REF]. The dormant period, determined by conductivity and calcium concentration measurement, lasts 3 h45 at 25 • C [START_REF] Maximilien | Study of the reactivity of clinkers by means of the conductometric test[END_REF]. The Blaine fineness and specific surface areas by laser granulometry show similar low values and slightly higher values than the B.E.T. specific surface area (factor 3), which characterizes the absence of porosity and few agglomeration phenomena on the dry powder.

Four PCEs provided by the CHRYSO Company (France) were studied and called A, B, C and D later in this paper. They are composed of a poly(methacrylic acid) backbone, responsible for adsorption, partially esterified with methoxy-terminated polyoxyethylene side-chains (PEO) responsible for steric repulsion. The chemical structure is shown in Fig. 1. The ester grafting ratio (m/n + m) increases from 10 to 40% through polymers A to D with a fixed PEO length (p) of 45 monomers. This series of polymers was chosen in order to study the influence of grafting ratio on the efficiency of PCE.

Pastes preparation

Cement suspensions were prepared by adding 200 g of cement powder to admixture solutions in deionized water (liquid chosen to control the water quality: pH, ionic conductivity, etc.) with water to cement ratio of 0.5 (including the amount of water provided by the admixture). Each polycarboxylate was tested through a dosage range up to 1% of dry active matter with respect to cement weight. The mixing equipment consisted in a twisted mixing anchor blade adapted to a Stuart, SS 30 mixer and a stainless steel beaker. The suspension was mixed at a speed of 185 rpm during 20 min before analysis that must be done during the 2 h of the dormant period (checked by conductivity and calcium concentration measurements).

For granulometric, suspension stability and Total Organic Carbon measurements, paste samples were first diluted in deionized water. This perturbation should modify ionic strength and solidsolution equilibrium of studied system, but it was neglected in a first approximation. As far as possible the dilution was the same (30% weight) for suspension stability and TOC analysis.

Characterization of the cement pastes by TOC and laser granulometry

The particle size distributions of the cement pastes were measured in deionized water using a LS 230 laser granulometer (Beckman Coulter). The optical model used was computed with a refractive index with a real part of 1.7 and an imaginary part of 1. The analysis time was fixed to 1 min. The particle size distributions obtained were expressed in a percent by volume and were normalized to 100%. The particle size distributions as a function of the height in the column were performed after 40 min of settling of the diluted paste.

The PCE adsorption was measured according to the depletion method. The quantity of consumed polymer was estimated by difference between the quantity of PCE introduced in the paste and the measured quantity of PCE remaining in pore solution. For that purpose, suspensions were diluted and let to settle in the same conditions as for the settling measurement. Then, the liquid phase at the top of the column was extracted and the pore solution was separated from the particles by filtration with a 0.2 m membrane filter and neutralized with concentrated hydrochloric acid. The quantity of remaining PCE was also determined by Total Organic Carbon (TOC) analysis using a commercial TOC-VCPN analyser (Shimadzu, Japan).

In the same way, solutions of PCE with the same dosages as in the pastes were analyzed and used as an initial concentration measurement. In order to eliminate the amount of organic carbon released by the cement (coming from grinding aids) the value of TOC of the unadmixtured paste was considered as background and subtracted from all measurements. The Turbiscan MA 2000 analyser from the Formulaction Company is designed to detect faster than naked eye nascent instability phenomena in concentrated dispersions (e.g. suspensions and emulsions). The ability to work in concentrated media (up to 20% volume to volume for suspensions) allows taking into account the interparticle interactions that may occur in the dispersion.

The principle of this technique is based on the detection of the light flux transmitted and backscattered as a function of the height in the dispersion column. The device is composed of a detection head which moves vertically with a step of 40 m along a cylindrical cell (15 mm diameter and 110 mm height) containing the sample. Two measurements at 0 • and 135 • from the incident beam ( = 850 nm) direction are performed and correspond respectively to the intensity of transmitted and backscattered light.

As shown in Eqs. ( 1) and (2), there is a relationship between the backscattered light intensity and the mesostructural parameters such as particle volume fraction and mean diameter [START_REF] Mengual | multiple light scattering measurement for concentrated emulsion and suspension instability analysis[END_REF][START_REF] Mengual | Characterisation of instability of concentrated dispersions by a new optical analyser: the TURBISCAN MA 1000[END_REF].

BS ≈ 1 √ * (1) * (˚, d) = 2d 3˚(1 -g)Q s ( 2
)
where BS is the intensity of the backscattered light (%); * is the photon transport length; d is the mean diameter of the particles;

Ф is the solid volume fraction; g is the asymmetry factor; and Q s is the scattering efficiency factor. The last two parameters are optical parameters from the Lorentz-Mie Theory.

Similarly, Eqs. ( 3) and ( 4) present another relationship between the percentage of transmitted light (T r ) and these parameters.

T r ≈ exp -r i (3) = * (1 -g) = 2d 3˚Q s (4)
where r i is the internal radius of the measurement cell. By evolution of the acquired profiles as a function of time it is then possible to detect particle size changes (through dispersion or agglomeration) or particle migration (sedimentation) as a function of the height in the sedimentation column.

Measurement parameters

The stability of the cement suspensions was studied at room temperature (25 • C) using a Turbiscan MA 2000. The analysis time lasted 40 min and the time elapsed between two profiles was 2 min.

Before analysis, the paste was previously diluted at 30% weight in deionized water and submitted to a moderate magnetic stirring during about a minute. After dilution, the solid volume fraction is 12%.

Results and discussion

Visual observations and granulometric characterizations of sedimentation columns

As a preliminary step, visual observations of some sedimentation columns allowed to describe settling behaviours as a function of the dosage of PCE incorporated (Fig. 2). These kinds of destabilization phenomena are called clarification, relating to concentrated suspensions [START_REF] Quemada | Energy of interaction in colloids and its implications in rheological modeling[END_REF][START_REF] Tadros | Correlation of viscoelastic properties of stable and flocculated suspensions with their interparticle interactions[END_REF][START_REF] Coussot | Rhéophysique des pâtes et des suspensions[END_REF]. In all columns two phases can be distinguished at 40 min of settling: a supernatant at the top and sediment at the bottom. Their formation kinetics and characteristics seem to be influenced by the PCE dosage. Indeed, two regimes are observed: at low dosages of PCE (0-0.05 wt.% with respect to cement weight) the supernatant is clear and separated from the sediment (which does not seem to reach its maximum packing yet) with a sharp boundary called "clarification front". Note that in the column containing 0.05% of PCE, the supernatant is hazier than in the unadmixtured column suggesting some colloidal particles dispersion by the PCE. Furthermore, the particle size distributions taken in the bulk of the sediment area, presented in Fig. 3a, are similar. This result shows the homogeneity of the sediment.

At higher dosages of PCE (0.1-1 wt.% with respect to cement weight) the supernatant is opaque and seems heterogeneous. This is confirmed by Fig. 3b which presents a gradient of size in the sedimentation column at 0.1% of PCE. Note that the sediment at 0.1% is thinner than the 0.05% one, and the sedimentation front is difficult to observe.

In order to differentiate these two cases of settling, the second one presenting an opaque supernatant will be called "sediment formation". The front delimiting an opaque supernatant and packed sediment will be called "sedimentation front". Let us point out that all these distinctions are made for analysis times of 40 min, when the settling may not be completely over.

These first observations allowed us to highlight two destabilization phenomena depending on the dosage of PCE within the conditions of duration and solid volume fraction used in the analysis: a destabilization phenomenon at low dosages related to the clarification of a supernatant, and another at high dosages related to the packed sediment formation. In order to develop a quantitative approach, a settling study was performed using the Turbiscan MA 2000 transmission or backscattering data. The influence of the molecular structure and the dosage of PCE on the suspension stability were also investigated as discussed in the next section.

Study of instability phenomena by Turbiscan MA 2000 3.2.1. Supernatant evolution using the transmission profiles

At low dosages, the transmission profiles resulting from the light passing through the suspension is used to characterize the clarification of the supernatant thus the influence of the PCE addition on suspension stability. As shown in Fig. 4 (case a) where the height of the sedimentation column is represented on the abscise axe, a clear supernatant is identified by a high value of transmission percentage up to 50-60%. In this case, two parameters may then characterize the clarification of the supernatant: the displacement of the clarification front and the transmission rate time evolution. Indeed, the release of unsettling particles by the PCE resulting from deagglomeration of (sub)micronic particles or hydrate precipitates [START_REF] Autier | Mesostructure evolution of cement pastes with addition of superplasticizers highlighted by dispersion indices[END_REF] may accordingly decrease the amount of transmitted light. However, when the supernatant is too opaque there is no transmitted light (case b) and the transmission profiles cannot be used.

Note that a stabilization of the suspension translates into a decrease of the displacement of clarification front and a high value of transmission percentage in the supernatant.

(a) Evolution of the clarification front As a first step, the evolution of the supernatant relative thickness as a function of the dosage of the PCEs tested is presented in Fig. 5. In all cases, a variable threshold time is observed indicating a delay before the onset of the clarification process. Later on, the evolution of the curve is linear up to a plateau corresponding to a significant slowdown of the phenomenon. Two parameters may then be extracted: the clarification threshold time and the kinetic of clarification corresponding to the initial slope of the curve.

The PCEs A and D present opposite behaviours; when the dosage of PCE A increases, the value of threshold time increases up to 25 min (at 0.1% of PCE) and the slope decreases continuously from 0.35 to 0 min -1 (at 0.25% of PCE), traducing a continuous slowdown of the clarification front evolution with dosage. In the case of the PCE D, both parameters present constant values whatever the dosage (the threshold time remaining constant at about 5 min and the slope at about 0.35 min -1 ). The PCE D does not seem to influence the clarification front evolution up to 0.25 wt.% above which there is no clarification anymore. The PCEs B and C present intermediate behaviours. Like the PCE D, they do not seem to affect settling up to a critical dosage (respectively 0.075% and 0.05%) beyond which, they abruptly present a PCE A-like regime, where threshold time increases and slope decreases when dosage increases.

(b) Turbidity of the supernatant

In order to quantify and compare turbidity of supernatants influenced by the presence of dispersed particles and/or precipitated hydrates, the evolution of light transmission in the supernatant as a function of the dosage of PCE was monitored over time. Note that this parameter is not widely used in the literature. The results are presented in Fig. 6.

Much like the previously observed trends, all curves present a threshold time corresponding to the delay before the clarification starts, the evolution of which depends on the molecular structure of the PCE. Then, the transmission signal increases up to a variable plateau where it remains steady until the end of the analysis time. According to Eqs. ( 3) and ( 4), this value depends on the mean diameter and solid volume fraction of unsettling particles remaining in the supernatant.

The previously observed slowdown of the supernatant relative thickness with the dosage of PCE A does not seem to be correlated to the percentage of transmitted light which remains at about 60% up to a dosage of 0.075%. This value, close to the pure water value (about 90%), corresponds to a very clear supernatant.

On the opposite, the increase of the PCE D dosage leads to a stable transmission values up to a dosage of 0.08% (at about 40% transmission which corresponds to a turbid supernatant). Then, these values decrease until there is no transmission (opaque supernatant at 0.25%).

When increasing the dosage of PCEs B and C the evolution of the transmission rate seems correlated to the supernatant relative thickness. To sum up our observations about the influence of the molecular structure of PCE, two opposite mechanisms define a range of behaviours:

• For low grafting ratio polymer, a gradual increase of clarification threshold time with the increase of PCE dosage associated to a thin clear supernatant (H sup. /H C < 10%).

• For highest grafting ratio polymer, on the opposite, a short constant clarification threshold time associated to an abundant cloudy supernatant.

The two intermediate polymers simply feature a combination of those extremes, following the grafting ratio value. Mesostructural organization was characterized by computing a dispersion index defined in a previous study [START_REF] Autier | Mesostructure evolution of cement pastes with addition of superplasticizers highlighted by dispersion indices[END_REF]. This index is based on the comparison of the particle size distributions of a unadmixtured reference paste with an admixtured paste. As shown in Fig. 7, the addition of superplasticizer causes a shift of the particle size distribution towards smaller diameters, defining intersection points, T D and T A (T for particle transfer, D for dispersion and A for agglomeration), which represent points of matter transfer between agglomerated and more dispersed populations.

The dispersion index is defined as follows:

I D (%) = As <TD -Aref <TD A 1 × 100 = A 2 A 1 × 100 = A 2 (5)
where -As <TD is the area lower than T D located under the curve of the sample, Aref <TD is the area lower than T D located under the curve of the reference, A 1 is the total area located under the curve of the reference (=100% because the curves are normalized), A 2 is the area located between the curve of the sample and the curve of the reference under the particle transfer point T D .

The evolution of the dispersion index as a function of the dosage of PCE is presented in Fig. 8.

The influence of the PCE A on the dispersion state of the paste clearly stands out. More precisely when its dosage increases, dispersion state of the paste seems to increase in the studied dosage range (an optimal dispersion state is not yet reached). Oppositely, the other PCEs present an optimal dispersion state at 0.08 wt.% and appear to be efficient molecules. These results may be compared to the stability behaviours previously highlighted. They show an optimum of stabilization at respectively 0.1% and 0.075% for the PCEs B and C according to the dosage of optimal dispersion state.

In the case of PCE D, stabilization presents a shift towards higher dosages when compared to PCEs B and C (at 0.25% -cf. Fig. 6), independently of an optimum dispersion state observed at 0.08 wt.% by laser granulometry study. These differences of results may originate from the agitation of sample during the particle size distribution measurement which may affect interparticular bonds and lead to the same dispersion state for PCEs B, C and D.

In order to quantify the maximum adsorption and affinity of the PCEs with cement surface in these analysis conditions (cf. point 2.2), the Langmuir isotherm was applied to PCE consumption measured by TOC analysis. This model, presented in Eq. ( 6), is based on three assumptions: monolayer coverage, adsorption site equivalence and independence.

Q = Q sat × KC 1 + KC ( 6
)
where Q is the amount adsorbed (mg/g); Q sat is the maximum adsorbed (mg/g); K (adsorption/desorption ratio) is a constant that characterize the affinity of the polymer with the surface (l/mg); C is the concentration remaining in solution (mg/l). Q sat and K values are obtained by Langmuir linearization i.e. by noticing that

Q = Q sat (1 + KC -1)/(1 + KC) = Q sat -Q sat / (1 + KC) = Q sat -1/K(Q/C).
Hence, Langmuir parameters may be determined by measuring the intercept and the negative reciprocal of the slope of the Q = f(Q/C) curve. The Langmuir isotherms of the PCEs tested are presented in Fig. 9.

In all cases, PCE adsorption increases with dosage up to a saturation plateau. The adsorption affinity somewhat measured by K increases with carboxylate group ratio in the molecular structure [START_REF] Zingg | Interaction of polycarboxylate-based superplasticizers with cements containing different C3A amounts[END_REF][START_REF] Zingg | Interaction of polycarboxylate-based superplasticizer with cement containing different C3A amounts[END_REF]. According to the isotherm, the PCE D does not seem to have reached the maximal adsorption (plateau) in the range explored whereas the others seem to have. As a general rule the maximum adsorption decreases when the grafting ratio increases which highlights the increasing self-hindrance induced by increasing POE amount.

The low adsorption of the PCE D on cement particles allows explaining its weak influence on the suspension stability up to 0.25%. On the opposite, although the PCE A is adsorbed in higher amounts, its relatively lower efficiency on the dispersion state correlates to its low efficiency on the stability which is probably due to its low grafting ratio leading to a poor steric repulsion. The PCEs B and C having intermediate grafting ratios present an intermediate adsorptive behaviour. Indeed, they seem to have a sufficient carboxylate ratio to adsorb onto cement and a sufficient ester grafting ratio to disperse efficiently. This optimized molecular structure allows stabilizing the suspension even at lower dosages. This optimum effect in the molecular structure is well known in the literature [START_REF] Shin | Effects of polycarboxylate-type superplasticizer on fluidity and hydration behavior of cement paste[END_REF][START_REF] Zingg | Adsorption of polyelectrolytes and its influence on the rheology, zeta potential, and microstructure of various cement and hydrate phases[END_REF][START_REF] Yamada | Controlling of the adsorption and dispersing force of polycarboxylate-type superplasticizer by sulfate ion concentration in aqueous phase[END_REF]. A Phase Separation Index, denoted PSI(clar.) is defined to quantify this instability phenomenon, instability increasing with the index value. This index combines supernatant volume and light transmission rate in order to characterize all clarification phenomena at a given settling time (20 min was chosen later in the work) according to Eq. ( 7):

PSI t (clar.) = H sup . H c × %Tr.(supernatant) (7)
where H sup ./H c represents the volume proportion corresponding to the clarification volume and %Tr.(supernatant) is related to the quantity and size of suspended particles in the supernatant. A stable suspension is defined by a PSI t (clar.) value equal to zero (%Tr = 0 and a minimum value of H sup. ). Note that in the literature, the transmission percentage is seldom used. Fig. 10 shows the evolution of the PSI 20 (Clar.) as a function of the dosage of the PCEs studied. Except for the lowest dosages, the PSI decreases continuously when PCE dosage (thus adsorption) increases as a result of the dispersing effect.

The suspension stability with PCE C appears at a lower dosage than the others (0.05 wt.%). While for PCE D stability occurs at a higher dosage (0.25 wt.%).

Sediment formation using the backscattering profiles

In order to obtain information on the stability of opaque settling suspensions, 135 • -backscattered light profiles were also processed. In this study, the profile time evolution is used to investigate the influence of PCE addition on the homogeneity and stability of opaque supernatants as well as the formation of sediments formed at high dosages. As shown in Fig. 11, stable and homogeneous opaque settling suspensions present steady backscattering values (about 40%) over time and column height (case a). So, there is no observable evolution of the particle size or volume fraction in the suspension during the analysis.

In the case of unstable suspensions (case b), two phenomena may be observed.

The first one located in the opaque supernatant area corresponds to the increase of the mean value of backscattered light over time. According to Eq. ( 1) presented in Section 2.4.1, this may be related to a decrease of mean particle size or/and a local increase of the particle volume fraction. A variation of the mean particle size is assumed here since the particle volume fraction is relatively low (12%) and its influence is therefore less significant [START_REF] Mengual | Characterisation of instability of concentrated dispersions by a new optical analyser: the TURBISCAN MA 1000[END_REF]. The second phenomenon corresponds to the formation of sediment characterized by two parameters: its relative thickness and the mean backscattering rate (the first 5 mm at the bottom of the analysis cell should be discarded since they correspond to a distortion induced by the vial glass bottom).

In a first step, the time evolution of the mean value of backscattered light in the opaque supernatant divided by the initial backscattering rate is presented in Fig. 12. Its evolution seems to depend neither on the dosage nor on the structure of the PCE. Indeed, almost all curves fall on a master curve and BS/BS 0 reaches an asymptotic value of about 1.4 after 40 min. Therefore, the time evolution of mean diameter and volume fraction in this area seems to depend neither on the dosage nor on the molecular structure of the PCE. The increase of the BS/BS 0 during the first 20 min corresponds to a decrease of the mean particle diameter induced by the settling of larger particles and probably by a dispersion phenomenon in these opaque suspensions.

In a second step, parameters characterizing the sediment formation were studied at 20 min when the phenomenon previously described has reached a steady state. Their evolutions are presented in Fig. 13.

Suspensions enter the sediment formation regime from critical dosages which are lower in the case of the PCEs B and C: respectively 0.12% and 0.08 wt.% whereas they are respectively 0.25% and 0.35% in the cases of the PCEs A and D. However, the sediment formation kinetics and the backscattering rate in the sediment seem unaffected by the dosage and the molecular structure of the PCE (for all these formulations H sed /H c is about 40-50%). Similarly, the value of the backscattering rate is approximately equal in all characterized sediments (30-40%).

The sediment formation regime is then characterized by critical dosages being a non monotonous function of the grafting ratio but neither the settling kinetics nor the compacity of the sediment are affected.

Under these conditions, the Phase Dispersion Index presented in Eq. ( 4) and defined by Vié et al. in a previous study should be constant [START_REF] Vié | Study of suspension settling: a approach to determine suspension classification and particle interactions[END_REF]. This index integrating the latter parameters is defined as follows and its dosage dependence at 20 min is presented in Fig. 14:

PSI t (sed.) = H sed. H c × %BS(sed.) (8)
Note that in the same way as for the clarification phenomenon, the molecular structure of PCE influences the onset of the instability phenomenon at high dosage. The PCEs B and C present similar trends as they induce sediment formation at lower dosages (respectively 0.12 and 0.08 wt.%) than the two others (0.25% for A and 0.35% for D). In comparison with dispersion indices displayed in Fig. 8, the dispersion indices with PCEs B and C present no evolution between 0.1% and 1% which explains why no change in the PSI 20 (sed.) is observed. In the case of the PCE D, the increase of the dispersion index in this range explains the increase of the PSI 20 (sed.). In the case of PCE A, although dispersion degree increases, stability decreases in this range.

Most efficient dosage ranges as a function of the molecular structure of the PCE

As shown previously and schematized in Fig. 15, the two destabilization phenomena occur at different dosage ranges and do not correspond to the same physicochemical phenomenon. All PCEs tested present same trend: first, they tend to stabilize the clarification phenomenon when dosage increases up to a most efficient range corresponding to the optimal stabilization of the suspension. The width of the most efficient range of dosage also depends on the molecular structure of the PCE. Beyond this regime, a second step of destabilization occurs with the sediment formation. The latter phenomenon is independent on the molecular structure and the PCE dosage.

In order to quantify the variations of stability of cement pastes as a function of the dosage and molecular structure of PCE, a global Phase Separation Index, defined as the sum of the previous PSIs, is defined: PSI t = PSI t (clar.) + PSI t (sed.)

The PSIs evolutions as a function of PCEs dosage are presented in Fig. 16. The PCEs B and C which have intermediate ester grafting ratios show similar values and induce narrower stability ranges than the other PCEs at lower dosages. The PCE A with the lowest grafting ratio confers a wider stability range at higher dosages. Then PCE D induces the widest stability range but for higher dosages.

From these observations it may be inferred that the molecular structure of the PCE influences the width and the dosage limits of the stability range through the interplay between the adsorbed amount and the intrinsic steric repulsion. The non-monotonic evolution of the PSI as a function of the ester grafting ratio highlights an optimum effect of the molecular structure of the PCE. This non-monotonous effect of the structure may be explained by the following reasons.

According to Flatt et al. [START_REF] Flatt | Conformation of adsorbed comb copolymer dispersants[END_REF] adsorbed comb polymers take a conformation described as a chain of hemispheric blobs the thickness of which is given by the blob radius:

R AC ≈ P 7/10 N -1/10 ( 10
)
where P is the graft length expressed in monomer number (constant in our study) and N is the number of backbone repeating units containing one graft, i.e. the reciprocal of the grafting ratio. The adsorbed layer thickness, taken as an estimate of the range of steric repulsive forces, is then expected to increase as the grafting ratio raised to the power of 1/10.

On the opposite it was shown that increasing the grafting ratio at a constant graft length decreases the affinity for the substrate [START_REF] Zingg | Interaction of polycarboxylate-based superplasticizers with cements containing different C3A amounts[END_REF][START_REF] Zingg | Interaction of polycarboxylate-based superplasticizer with cement containing different C3A amounts[END_REF], which we confirm in our study (see the K values in Fig. 9).

We conclude that grafting ratio has an opposite influence on the affinity on the one hand and on the steric repulsion range on the other hand.

At low grafting ratios the polymer features then a high affinity for the cement surface but the grafts are too few along the backbone to form a sufficiently thick repulsive layer. Thus it requires a high adsorbed amount of polymer (i.e. a high dosage) to reach a density of grafts on the surface sufficient for triggering sedimentation. This is the case of PCE A with high-dosage sedimentation transitions.

On the opposite, at high grafting ratios each polymer forms a thicker repulsive object but the affinity is so weak that it requires high dosages before obtaining a sufficient surface coverage. PCE D seems to behave this way with once again high-dosage sedimentation transitions. PCEs A and D would feature then a similar behaviour (high transition dosages), but for very different reasons.

Between these two extremes there exists a domain where affinity and layer thickness are balanced in such a way that dosage efficiency is maximum, which seems to be the case for PCEs B and C as they show the lowest transition dosages.

Conclusions

The relationship between organo-mineral interaction, mesostructural organization, stability and homogeneity of suspensions was highlighted. For that purpose, the stability was characterized using Turbiscan MA 2000. Two destabilization regimes were highlighted: the first one occurring at lower dosages consists in a clarification of the supernatant which tends to disappear with increasing the dosage of PCE. The suspension then enters an intermediate stable dispersion state. The second destabilization corresponds to the sediment formation regime which consists in a packing of the sediment occurring at even higher dosages. A Phase Separation Index (PSI) taking into account these two destabilization phenomena was defined in order to quantify the stability of suspensions. This index was compared with the dispersion index characterizing the dispersion state of particles and with the adsorption isotherms. In this way, the macroscopic behaviour was related to mesostructural organization of the paste. The influence of PCE structure and affinity with mineral surface on the dispersion state was also highlighted.

More precisely, as the grafting ratio increases, adsorption affinity decreases and intrinsic steric repulsion increases. At a low grafting ratio, adsorption is quite high for a given dosage, but the adsorbed layer features too weak a repulsion efficiency (PCE A case). At a high grafting ratio the adsorbed layer is thicker but adsorption affinity is too weak (PCE D case). There exists an intermediate regime where steric repulsion and adsorption are more evenly balanced so that dispersion efficiency is maximal.

Fig. 1 .

 1 Fig. 1. Molecular structure of the PCEs tested.

2. 4 .

 4 Multiple light scattering analysis by Turbiscan MA 2000 2.4.1. Theoretical basis

Fig. 2 .

 2 Fig. 2. Visual observations of sedimentation columns in function of dosage of PCE after 40 min of settling.

Fig. 3 .

 3 Fig. 3. Particle size distributions at several heights in the column with (a) 0.05%; (b) 0.1% of PCE C.

Fig. 4 .

 4 Fig. 4. Transmitted light of diluted pastes admixtured with (a) 0.05%; (b) 0.1% of PCE C.

Fig. 5 .

 5 Fig. 5. Evolution of the relative supernatant thickness as a function of the dosage of PCEs A, B, C, D.

( c )Fig. 6 .

 c6 Fig. 6. Evolution of the percentage of transmission over time function of the dosage of PCEs A, B, C, D.

Fig. 7 .

 7 Fig. 7. Evolution of the particle size distribution by addition of superplasticizer [26].

Fig. 8 .

 8 Fig. 8. Evolution of the dispersion index as a function of the dosage of PCEs A, B, C, D.

Fig. 9 .

 9 Fig. 9. Langmuir isotherms of the PCEs tested.

Fig. 10 .

 10 Fig. 10. Evolution of the PSI20 (clar.) as a function of the dosage of PCEs A, B, C, D.

Fig. 11 .

 11 Fig. 11. Backscattered light in (a) homogeneous and stable settling suspension (0.05% PCE A) and (b) heterogeneous and unstable settling suspension (0.5% PCE A).

Fig. 12 .

 12 Fig. 12. Evolution of some relative backscattering in opaque supernatants over time.

Fig. 13 .

 13 Fig. 13. Evolution of (a) relative height of sediment; (b) relative BS value of sediment, at 20 min, as a function of the dosage of PCEs A, B, C, D.

Fig. 14 .

 14 Fig. 14. PSI20 (sed.) as a function of the dosage of PCEs A, B, C, D.

Fig. 15 .

 15 Fig. 15. Schematic representation of the destabilization phenomena as a function of the dosage of PCE.

Fig. 16 .

 16 Fig. 16. Evolution of the PSI20 as a function of the dosage of PCEs A, B, C, D.

Table 1

 1 Characteristics of the cement used.

	Chemical characteristics	Value
	Na2O equivalent	0.35%
	Oxides	%
	Al2O3	4.7
	Fe2O3	2.8
	SiO2	19.4
	CaO	65.8
	SO3	5.1
	Surface characteristics	Value
	B.E.T. specific surface area	1.1 m 2 /g
	Blaine specific surface	0.4 m 2 /g
	Specific surface area by granulometry
	• Deionized water	0.3 m 2 /g
	• Dry way	0.4 m 2 /g
	Dormant period
	• By conductivity (25 • C)	3 h45

Acknowledgement

The authors wish to thank Mr. Claude VALENTIN (Ciments Calcia -Italcementi Group) for having provide the cements used in the project.


Marine Le Dudal

Léa Huguet

Joëlle Perez

Sophie Vandermeersch

Elise Bouderlique

Ellie Tang

Carole Martori

Nicole Chemaly

Rima Nabbout

Jean-Philippe Haymann

Marine Le Dudal

Jean- Philippe Haymann

Vincent Frochot

Laurent Baud

Georges Deschênes

Michel Daudon

Emmanuel Letavernier
email: emmanuel.letavernier@aphp.fr

Stiripentol protects against calcium oxalate nephrolithiasis and ethylene glycol poisoning

Keywords: Stiripentol decreases urinary oxalate Stiripentol, Oxalate, Kidney, Nephrolithiasis, Ethylene glycol, Primary hyperoxaluria Conflict

Introduction

Urine oxalate excretion is low (normal value <0.5 mmol/day in human) but its affinity for calcium ions make it a major promoter of calcium oxalate crystals and kidney stones formation. [START_REF] Khan | Kidney stones[END_REF] Calcium oxalate precipitation in kidney tubules is particularly fateful when resulting from acute intoxication by ethylene glycol or from genetic disorders. [START_REF] Kruse | Methanol and ethylene glycol intoxication[END_REF][START_REF] Cochat | Primary hyperoxaluria[END_REF] Actually, primary hyperoxaluria is a rare but severe genetic enzymatic defect increasing glyoxylate and oxalate hepatic production; oxalate precipitates in kidney tubules, leading to end-stage kidney disease and poor prognosis in young patients.

Oxalate is produced in the liver from glyoxylate transformation by lactate dehydrogenase (LDH) type 5 isoenzyme and excreted in urine, with little biological control. [START_REF] Holmes | Glyoxylate synthesis, and its modulation and influence on oxalate synthesis[END_REF] To date, there is no drug reducing oxalate production by liver. In 2015, Sada et al. demonstrated that Stiripentol, an antiepileptic drug, targets lactate production by LDH-5 isoenzymes in neurons in vitro. [START_REF] Sada | Epilepsy treatment. Targeting LDH enzymes with a stiripentol analog to treat epilepsy[END_REF] We hypothesized that this drug could also inhibit hepatic LDH-5 isoenzymes and oxalate production by liver, and thereby decrease urinary oxalate excretion. Stiripentol is a safe drug that has been used for years in addition to other antiepileptic drugs to target seizures in Dravet syndrome, a rare form of epilepsy affecting young children. [START_REF] Verrotti | Pharmacological considerations in the use of stiripentol for the treatment of epilepsy[END_REF]

Results and Discussion

To investigate whether Stiripentol could decrease hepatic oxalate production, hepatocytes (HepG2 cells) were grown in vitro in hydroxyproline-enriched cell culture medium (Figure 1A). [START_REF] Baker | Glycolate and glyoxylate metabolism in HepG2 cells[END_REF] The exposure of hepatocytes to Stiripentol concentrations at "therapeutic" levels (5 to 100 µg/mL) resulted in a dose dependent and significant decrease in oxalate production (* p= 0.03, n=4 experiments, Figure 1A). As a matter of comparison, recommended dose of Stiripentol in Dravet syndrome is usually 1000-3000 mg/day in children, giving serum levels of 4-22 µg/mL. [START_REF] Farwell | Stiripentol in atypical absence seizures in children: an open trial[END_REF] As the drug has high first pass metabolism in liver, it may even be hypothesized that relatively low doses of Stiripentol could inhibit hepatic LDH activity efficiently without significant inhibition of systemic LDH-5 isoenzymes. To confirm the implication of LDH-5 isoenzyme, we performed SiRNA experiments targeting LDH-A mRNA (sub-unit of LDH-5). SiRNA suppressed 60 to 70 % of LDH-A mRNA and decreased significantly oxalate production. The addition of 10 µg/mL Stiripentol to SiRNA decreased mildly oxalate production by HepG2 cells, suggesting that most of oxalate synthesis was actually due to LDH-5 isoenzyme activity (Figure 1B).

We next analysed whether Stiripentol would also be efficient to reduce urine oxalate excretion in vivo. Six rats received orally 200 mg/Kg/day Stiripentol during 48 hours. Urine oxalate/creatinine excretion decreased slightly but significantly from 0.16±0.01 mmol/mmol before treatment to 0.11±0.01 mmol/mmol (* p=0.002). After a 4 days wash-out period, urine oxalate excretion was similar to baseline values (Figure 1C).

Ethylene glycol is present in anti-freeze and is a frequent cause of poisoning, causing more than 5000 intoxications in USA each year. [START_REF] Kruse | Methanol and ethylene glycol intoxication[END_REF] Its toxicity depends mainly of its transformation into oxalic acid by liver, which precipitates as calcium oxalate in kidneys promoting acute renal failure and acidosis. Ethylene glycol is first metabolized to glycolaldehyde by the enzyme alcohol dehydrogenase, and then undergoes oxidation to glycolate, glyoxylate, and at last oxalate. To date, the specific treatment of ethylene glycol poisoning is fomepizole or 4methylpyrazole, a competitive inhibitor of alcohol dehydrogenase in the liver. [START_REF] Brent | Fomepizole for the treatment of ethylene glycol poisoning. Methylpyrazole for Toxic Alcohols Study Group[END_REF] The use of Stiripentol as a therapy against ethylene glycol intoxication would be of interest since acting downstream of the metabolic pathway, and could therefore be still efficient after relatively long period following intoxication, even when high amounts of glycolaldehyde have already been produced. Six rats were exposed to ethylene glycol alone and six rats received both ethylene glycol and Stiripentol at 300 mg/kg at the same time (and Stiripentol in drinking water during the next 2 days). Animals were sacrificed 2 days later. Animals exposed to ethylene glycol alone were oliguric, but a small amount of urine has been collected at the time of the sacrifice to perform urine crystals analysis. Crystalluria revealed a large number of calcium oxalate monohydrate (COM) crystals in both groups and to a lesser extent calcium oxalate dihydrate crystals (COD) but the mean crystalline volume was 20 times less in animals receiving Stiripentol (9467±2259µ3/mm3 versus 201766±95023 µ3/mm3, p=0.004, Figure 2A-B). The kidneys of rats exposed to ethylene glycol alone were pale and voluminous with a mean weight at 1.31±0.11 grams whereas kidneys from animals receiving Stiripentol in addition had a usual red/brown aspect and normal weight at 0.85±0.02 grams (Figure 2C, *p=0.004). Stiripentol protected rats against ethylene-glycol-induced renal failure (mean serum creatinine 78.2±9.6 µmol/L versus 297.1±74.4 µmol/L, p=0.002, Figure 2G).

The other biological features are depicted in table I, evidencing that animals receiving Stiripentol had a trend toward lower metabolic acidosis (less decreased bicarbonate serum levels), and a significantly lower serum anion gap, the consequence of lower circulating oxalate levels in this context of ethylene glycol poisoning. The morphometric analysis of kidney tissues confirmed that Stiripentol decreased significantly calcium oxalate crystals deposition in kidneys (Figure 2D-F, p=0.002). These deposits were stained by Yasue coloration (revealing calcium oxalate crystals) and the analysis of kidney tissue by Fourier transform infrared spectroscopy (FTIR) confirmed that crystalline deposits in renal tubules were made of calcium oxalate monohydrate exclusively (Figure 2H-I).

Blocking oxalate synthesis could be particularly of interest in primary hyperoxaluria, a genetic enzymatic defect resulting from a mutation of AGXT, GRHPR or HOGA1 genes, increasing glyoxylate hepatic production which is finally transformed into oxalate by LDH-5. [START_REF] Cochat | Primary hyperoxaluria[END_REF] Oxalate precipitates in renal tubules, leading to end-stage kidney disease in children and young adults with high morbidity and mortality, often requiring a combined liver-kidney allograft. [START_REF] Bergstralh | Transplantation outcomes in primary hyperoxaluria[END_REF] There is currently no drug decreasing oxalate production by liver with the exception of pyridoxine which may lower urine oxalate excretion in some cases of type I hyperoxaluria. [START_REF] Cochat | Primary hyperoxaluria[END_REF] Sixteen Sprague Dawley rats received hydroxyproline and calcium in drinking water during 16 days. This classic animal model of hyperoxaluria induces oxalate nephropathy by increasing hepatic oxalate production as the result of mitochondrial hydroxyproline metabolism. [START_REF] Khan | Modeling of hyperoxaluric calcium oxalate nephrolithiasis: experimental induction of hyperoxaluria by hydroxy-L-proline[END_REF] The oxalate nephropathy is characterized by calcium oxalate intratubular crystal deposits similar to those observed in primary hyperoxaluria. [START_REF] Khan | Modeling of hyperoxaluric calcium oxalate nephrolithiasis: experimental induction of hyperoxaluria by hydroxy-L-proline[END_REF] Eight of these rats received Stiripentol orally by gavage, once a day during 16 days.

Urine oxalate excretion increased in both groups after exposure to hydroxyproline but urine oxalate was significantly lower in animals receiving Stiripentol in addition to hydroxyproline and calcium (Figure 3A, p=0.33 at day 2, p=0.10 at day 4, *p=0.0002 at day 8, *p=0.0019 at day 11, *p=0.0002 at day 15). In parallel, urine glycolate excretion increased in both groups but significantly more in rats exposed to Stiripentol (at day 2 and 8), suggesting that Stiripentol actually inhibits the transformation of glyoxylate into oxalate (Supplementary Figure 1). Crystalluria revealed the presence of calcium oxalate crystals in both groups but the mean crystalline volume was significantly lower in animals treated by Stiripentol (Figure 3B, p= 0.15 at day 4, *p=0.015 at day 8, p=0.08 at day 11, *p=0.007 at day 15). Animals were sacrificed after 16 days exposure to hydroxyproline. FTIR analysis revealed the presence of sparse deposits of calcium oxalate monohydrate crystals in renal tubules and kidney morphometric analysis demonstrated that Stiripentol decreased significantly calcium oxalate deposits in kidney tissues (Figure 3C-E µmol/L, estimated glomerular filtration rate 88 mL/min/1.73m²) but she was exhausted by recurrent colic nephritis (about once a month), repeated urological procedures and pyelonephritis. Urine oxalate/creatinine ratio was about 0.18-0.20 mmol/mmol. Her brother, affected by the same disease, had a rapid decrease in renal function and was treated with combined liver-kidney transplantation. Considering the evolution of the disease, in accordance with medical team and after parental agreement, Stiripentol was introduced at half-dose (25 mg/kg/day) and urine oxalate excretion decreased rapidly (Figure 4B). A further decrease in urine oxalate excretion has been observed when Stiripentol therapy was increased at 50 mg/kg/day (urine oxalate/creatinine ratio: 0.068 mmol/mmol), without identified side effect (Figure 4B). These results bring new hope to treat children affected by primary hyperoxaluria, a disease characterized by high morbidity due to renal failure and systemic deposits of calcium oxalate in the body, and high mortality. The genetic defect may be cured by liver transplant, but this disabling therapy is usually performed as a combined liver-kidney allograft when end-stage renal disease occurs. The main adverse events related to Stiripentol in Dravet patients are nutrition disorders (anorexia, loss of appetite, weight loss), neurological disorders (drowsiness, hyperexcitability) and in some rare cases neutropenia. Most of side-effects disappear when the dose of comedication is decreased (carbamazepine and clobazepam).

Actually, Stiripentol interacts with several P450 cytochromes. Fortunately, children affected by primary hyperoxaluria are not supposed to receive other drugs than pyridoxine and potassium citrate.

In summary, Stiripentol, a potent LDH-5 enzyme inhibitor, limits oxalate production by human hepatocytes in vitro and in rats in vivo, at "therapeutic" levels. Oral administration of Stiripentol protects rats against ethylene glycol poisoning and oxalate nephropathy.

Considering the safety profile of this drug and preliminary results in children, it brings a new hope to prevent the renal and systemic consequences of primary hyperoxaluria, a disease associated to a dramatic morbidity and mortality, and to treat ethylene glycol poisoning, deserving clinical studies.

Methods

Cell culture.

HepG2 cells, an hepatoma human cell line (Sigma Aldrich, France), were grown in DMEM medium (Gibco, Invitrogen, Cergy-Pontoise, France) supplemented with 10% fetal bovine serum (Gibco), 1% glutamine, 4.5 g/L glucose and penicillin/streptomycin (Gibco, 5µl/ml). HepG2 cells medium was supplemented with 10 mM hydroxyproline to induce oxalate production as previously described and to various concentrations of Stiripentol (5-100 µg/mL) during 24 hours. [START_REF] Baker | Glycolate and glyoxylate metabolism in HepG2 cells[END_REF] To modulate LDH-A expression, HEpG2 cells were transfected with small interfering RNA (siRNA) targeting LDH-A human gene, 4 siRNAs for Entrez gene 3939: SI02663535 (FlexiTube siRNA Functionally verified, SI00300622 (FlexiTube siRNA Functionally verified), SI04949616 (FlexiTube siRNA), SI04949609 (FlexiTube siRNA) or positive (silencing)-control siRNA Mm/Hs_MAPK1 control siRNA (SI03650318; both from QIAGEN). Briefly, HepG2 cells were seeded in a 100 mm Petri dishes at a density of 4 10 6 cells/ Petri dish in 10 ml DMEM and 10% FBS and directly transfected with 5nM siRNA through the use of 40 µl HiPerFect transfection reagent (QIAGEN). 24h after transfection, cells were stimulated for 24 h, with hydroxyproline (10 mM), with or without Stiripentol (10µg/ml). Cells were then lysed in RLT, and RNA was isolated with an EZ-10 Spin Column Kit (Proteogenix) and reverse transcribed with a First-Strand cDNA Synthesis Kit (Thermo Scientific). cDNA was amplified on a Light Cycler 480 system (Roche) using SYBR Green (Roche) and specific primers for LDHA (5'-TCTCTGTAGCAGATTTGGCAGA-3' and 5'-AAGACATCATCCTTTATTCCGTAAA-3'), MAPK1 (5'-TCTGCACCGTGACCTCAA-3' and 5'-GCCAGGCCAAAGTCACAG-3') and GAPDH (5'-TCCACTGGCGTCTTCACC-3' and 5'-GGCAGAGATGATGACCCTTTT-3') as house-keeping gene.

Animals.

Effect of Stiripentol on urine oxalate excretion

Six weeks old Sprague-Dawley male rats were purchased from Harlan Laboratories (France). All efforts were performed to reduce animal suffering. They were housed in similar conditions (3 rats/cage) with a 12-h dark/light cycle and fed ad libitum on standard rat chow.

Rats received Stiripentol (Biocodex, France) orally at 200 mg/Kg twice by gavage and urine samples were collected before treatment, 48 hours after treatment initiation and after a washout period.

Ethylene glycol intoxication protocol

Six 8-weeks old Sprague-Dawley male rats ("control" group) received ethylene glycol by gavage (Batch # SHBG0526V, Sigma Aldrich, France) at 6g/Kg once. Six rats ("Stiripentol" group) received ethylene glycol orally at 6g/Kg and Stiripentol at 300mg/Kg by gavage at the same time. Rats in the "Stiripentol" group had a free access to water containing Stiripentol at 4g/L whereas rats from the control group had a free access to water without Stiripentol. All animals were sacrificed 48 hours later.

Biological samples and Biochemistry.

Ethylene glycol intoxication protocol.

A sample of urine has been collected before protocol and at the time of the sacrifice in the acute model of ethylene glycol poisoning to assess crystalluria. A blood serum sample has been collected before protocol and at the time of the sacrifice. The blood samples have been analyzed for creatinine by enzymatic assay, bicarbonate, sodium, chloride and potassium to assess renal function and acidosis, on an iSYS analyzer from Immunodiagnostic Systems and an ABL815 from Radiometer.

Oxalate nephropathy protocol

Urine has been collected before the protocol and at days 2,4,8,11 and 15 during 24 hours in metabolic cages with free access to water (enriched in calcium and hydroxyproline), to assess urine oxalate excretion. Fresh urine has been collected after spontaneous voiding to perform crystalluria before the protocol and at days 4,8,11 and 15, immediately before 24-hr urine collection. The number, size and type of crystals have been analyzed by trained technicians to measure the mean crystalline volume. [START_REF] Daudon | Serial crystalluria determination and the risk of recurrence in calcium stone formers[END_REF] Blood (1 mL) has been collected at the time of the sacrifice to measure renal function.

Oxalate urinary excretion in humans

A single urine sample has been collected in patients affected by Dravet syndrome, in Necker Hospital (Paris) after parental information and written consent, ethical committee authorization N° ID-RCB 2016-A01032-49. Urine oxalate excretion in patients affected by cystinuria was obtained from Tenon hospital (Paris) database (CNIL declaration number 1709404 v0), this dosage is routinely performed in all kidney stone formers. Urine oxalate excretion in the patient affected by primary hyperoxaluria has been collected prospectively before and after Stiripentol therapy.

Creatinine has been analyzed by enzymatic methods (blood) and Jaffe method (urine) on an iSYS analyzer from Immunodiagnostic Systems. Oxalate and glycolate urine levels have been measured by ion chromatography (Dionex ICS-3000).

Histology, Yasue staining and morphometry

Kidney tissues were fixed in AFA and formalin and embedded in paraffin. Four-µm tissue sections have been performed and stained by Yasue procedure to reveal tissue calcifications.

A morphometric analysis of calcified tissue surface has been performed with the Image J software (NIH) on 5 photographs at 200x magnification by using polarized light to reveal crystalline deposits.

µFTIR spectroscopy

Microcalcification phases were characterized using µFourier Transform InfraRed spectrometry. Four micrometer tissue sections were deposited on low emission microscope slides (MirrIR, Keveley Technologies, Tienta Sciences, Indianapolis). FT-IR hyperspectral images were recorded with a Spectrum spotlight 400 FT-IR imaging system (Perkin Elmer 1 . The spectra were recorded in the 4000-700 cm -1 mid-InfraRed range. Each spectral image, covering a substantial part of the tissue, consisted of about 30,000 spectra.

Study approval

Animal studies: a specific authorization has been obtained from ministry and local ethical committee (N° #5110 2016042012069009 v2).

Human studies: ethical committee authorization N° ID-RCB 2016-A01032-49. Crystalline deposits were stained by Yasue coloration evidencing their calcic nature (Figure 2H) and Fourier transform infrared spectroscopy (FTIR) revealed the exclusive presence of COM among tubular deposits (Figure 2I). Data are expressed as mean± SEM. Mann-Whitney and Kruskall Wallis with Dunn's multiple comparison tests were used to compare the different groups.

  p= 0.004). Renal function was less altered in animals receiving Stiripentol (figure 3F, p= 0.028). To assess whether Stiripentol would reduce efficiently oxalate synthesis in humans, urine oxalate excretion was assessed in children affected by Dravet syndrome requiring Stiripentol treatment (n=8, median age 6 years) and in children of similar age affected by cystinuria, kidney-stone formers whose stones are not due to oxalate (control group, n=40, median age 7.5 years). Urine oxalate excretion was significantly decreased in patients affected by Dravet syndrome, suggesting that Stiripentol lowers urine oxalate excretion, even when urine oxalate concentrations stands within normal range (p=0.002, Figure 4A). A 17-yrs old girl affected by severe type I hyperoxaluria (homozygous AGXT mutation c.349-350 insG) received Stiripentol to reduce urine oxalate excretion in Robert Debré Hospital (Paris). Renal function was still normal in the absence of acute episode (serum creatinine 65

3 .

 3 Oxalate nephropathy protocol. Sixteen 8-weeks old Sprague-Dawley male rats had a free access to water containing 2g/l calcium (calcium chloride) and 20 g/L hydroxyproline (Batch 090289, Interchim SA, France) during 16 days. Eight of them received Stiripentol at 300 mg/kg by daily gavage, during 16 days. Environmental enrichment was routinely performed. All animal procedures of the laboratory are performed in accordance with the European Union Guidelines for the Care and Use of laboratory animals and with local Institutional Animal Care and Use Committees ("comité d'éthique en experimentation Charles Darwin C2EA-05") guidelines.

Statistical analyses .

 analyses Data are expressed as mean± SEM (Figures) and mean± SD (Tables). Mann-Whitney and Kruskall Wallis with Dunn's multiple comparison tests were used to compare the different groups, with the exception of serum parameters compared with t-tests (assuming gaussian distribution), by using Prism and Statview softwares. The level of significance was set to < 0.05.

Figure 1 :

 1 Figure 1: Inhibition of oxalate synthesis by Stiripentol in vitro and in vivo. HepG2 cells were grown in a hydroxyproline-enriched medium to produce oxalate (red bars). Oxalate synthesis (mM) was reduced in a dose-dependent manner when Stiripentol was added to the medium (Figure 1A *: p=0.03, n=4 experiments). SiRNA targeting LDH-5 subunits reduced significantly oxalate synthesis and the addition of 10µg/mL Stiripentol to SiRNA reduced mildly oxalate synthesis, suggesting that oxalate synthesis is mostly performed by LDH-5 (Figure 1B *: p=0.03 vs control, n=4 experiments). Stiripentol given orally during 2 days reduced significantly urine oxalate excretion (mmol/mmol: mmol oxalate/mmol creatinine, Figure 1 C *: p=0.002, n= 6 animals). After wash-out, urine oxalate excretion was restored. Data are expressed as mean± SEM. Mann-Whitney tests were used to compare the different groups.

Figure 2 :

 2 Figure 2: Stiripentol protects against ethylene glycol intoxication. Representative crystalluria evidencing the presence of calcium oxalate monohydrate crystals (COM, black arrow) and to a lesser extent calcium oxalate dihydrate crystals (COD, white arrow) in urine (Figure 2A). Mean crystalline volume in urine was significantly lower in animals receiving Stiripentol in addition to ethylene glycol (EG + Stiripentol: ■) than in animals receiving ethylene glycol alone (EG: •) (Figure 2B *:p=0.004, n= 6 animals/group). The weight of kidneys from rats exposed to ethylene glycol only was increased when compared to kidneys from rats treated by Stiripentol (Figure 2C, *p=0.004, n=6). Kidney crystalline accumulation was prevented by Stiripentol (Figures 2D-F, *p=0.002, n=6) Stiripentol protected rats against ethylene-glycol-induced renal failure (p=0.002, Figure 2G, n=6).

Figure 3 :

 3 Figure 3: Stiripentol protects against calcium oxalate nephropathy. Urine oxalate excretion (indexed to creatinine, mmol/mmol) was increased by hydroxyproline (HP)-enriched diet and the daily administration of Stiripentol (red bars) protected partly against hyperoxaluria (Figure 3A, p=0.33 at day 2, p=0.10 at day 4, *p=0.0002 at day 8, *p=0.0019 at day 11, *p=0.0002 at day 15, n=8 animals/group) and reduced urine crystalline volume (Figure 3B, p= 0.15 at day 4, *p=0.015 at day 8, p=0.08 at day 11, *p=0.007 at day 15, n=8 animals/group). Kidney crystal deposits were reduced by Stiripentol (HP + Stiripentol: ■, HP: •) (Figures 3C-E *: p=0.004, n=8 animals/group). Stiripentol protected rats against hydroxyproline-induced renal failure (Figure 3F, *: p= 0.028, n=8 animals/group). Data are expressed as mean± SEM. Mann-Whitney and Kruskall Wallis with Dunn's multiple comparison tests were used to compare the different groups

Figure 4 :Supplementary Figure 1 :

 41 Figure 4: Stiripentol decreases urine oxalate excretion in humans. Urine oxalate excretion (indexed to creatinine, mmol/mmol) was lower in children affected by Dravet syndrome and treated with Stiripentol than in controls, i.e. children affected by cystinuria (Figure 4A, p= 0.002; Dravet + Stiripentol: ■, n=40; Controls: •, n=8). Mann-Whitney test was used to compare the two groups.Urine oxalate excretion (indexed to creatinine, mmol/mmol) has been measured before and after Stiripentol therapy (25 mg/Kg/day and 50 mg/Kg/day) in a young girl affected by primary hyperoxaluria type I.

Table Table I: serum parameters after ethylene glycol intoxication

 Table

	Serum parameters
		EG	EG+ Stiripentol	p value
	Creatinine µmol/L	297.1±166.3 78.1±21.4	0.009
	Bicarbonate mmol/L	17.7±4.15	20.8±5.6	0.15
	Potassium mmol/L	6.5±2.4	4.8±1.3	0.07
	Sodium mmol/L	137.6±4.7	147.4±3.7	<0.001
	Chloride mmol/L	93±7.9	107.6±9.3	<0.001
	Serum Anion Gap mmol/L	33.5±11.1	23.7±12.2	0.04
	Serum parameters at day 2 after ethylene glycol intoxication (n=6 animals/group). Results are
	Data are expressed as mean± SD. Student t-test (assuming gaussian distribution of biological
	values) were performed. EG= ethylene glycol

Acknowledgements

The authors thank prof. Albert Bensman for his precious help in preparing the final version of the manuscript.This work has been supported by the Agence Nationale de la Recherche (ANR-13-JSV1-0010-01), the Académie Nationale de Médecine (Nestlé-Waters award), Convergence-UPMC CVG1205 and CORDDIM-2013-COD130042.