Jafar Al-Muhammad
email: almuhammadj@gmail.com

Séverine Tomas

Nassim Ait-Mouheb

Muriel Amielh

Fabien Anselmet

Fluid Flow

Keywords: Drippers, Labyrinth micro-channel, Micro-PIV, RSM model, Vortex identification

The labyrinth-channel is largely used in dripper systems. The baffles play an important role to generate the head losses and induce the flow regulation on the drip irrigation network. But they also develop vorticity regions where the velocity is low or zero. These vorticity regions promote the deposition of particles or other biochemical development causing dripper clogging. The flow in the dripper labyrinth-channel must be described to analyze dripper clogging sensibility which drastically reduces its performance. This characterization is performed experimentally using the micro-particle-image-velocimetry (Micro -PIV) method, and numerically using the RSM Simulation. In this study, Micro-PIV experiments allow to analyze the flow in ten-pattern repeating baffles which reproduce the micro-irrigation dripper. The cross section is equal to 1 mm 2 and the inlet Reynolds number varies from 345 to 690. The present study first introduces a global analysis of the flow through the mean velocity modulus, the Reynolds stresses u 02 , v 02 and u 0 v 0 and the turbulence Reynolds number. Then, results for the mean strain rate and the mean spanwise vorticity are presented and discussed. Next, advanced methods of vortex detection are introduced and analyzed to better distinguish the vortex zones and to determine the vortex sizes. Furthermore, the numerical model is used to validate and analyze in a more detailed way the experimental results obtained by Micro-PIV.

Introduction

Drip irrigation is a technique characterized by low-velocity water flows. Water drops near the plants through drippers. This type of irrigation improves efficiency by reducing evaporation, drift, runoff and deep percolation losses when compared with the other techniques such as sprinkler irrigation. In this technique, drippers are the most important and critical components (Karmeli, 1977 [20]). Drippers generate low flow rates between 0.5 and 8 [l.h 1 ] for pressure between 50 and 400 kPa (Goldberg et al., 1976 [15]). Dripper flow rate increases with static pressure in a lateral pipe according to a power-law (Karmeli, 1977 [20]): q = k d P x , where q is the dripper flow rate [l.h 1 ], k d the proportionality coefficient that characterizes each dripper, P the working pressure head at the dripper [Pa] and x the dripper discharge exponent. The value of this exponent depends on dripper conception. This relationship determines the dripper performance. Indeed, manufacturers try to design drippers whose flow rate is not directly dependent on the pressure head (x < 0.5). To reach this goal, they introduce some elements in the dripper such as a labyrinth-channel which generates local pressure head losses. Drippers can be divided into two categories: pressure compensating and non-pressure compensating drippers. Pressure compensating drippers are provided with a membrane by which the flow control is achieved. This category provides the same amount of water all the way down the slope. Non-pressure compensating drippers use long tortuous channels which provide greater durability and longevity along with clogging resistance and low maintenance thanks to the absence of moving parts.

The labyrinth-channel section is in the order of 1 [mm 2 ], so baffles are likely to be clogged by physical particles not captured by the filtering system. As a result, the irrigation uniformity is perturbed and the investigation cost is increased (Pitts et al., 1990 [31]) due to maintenance needs and durability decrease. Some studies have been performed to analyze the dripper clogging and performance. They indicate that clogging occurs in low-velocity vortex regions as it was experimentally found [START_REF] Zhang | Numerical investigation of the clogging mechanism in labyrinth channel of the emitter[END_REF] [START_REF] Zhang | Numerical investigation of the clogging mechanism in labyrinth channel of the emitter[END_REF]; [START_REF] Wei | Flow behaviour analysis and experimental investigation for emitter micro-channels[END_REF] [START_REF] Wei | Flow behaviour analysis and experimental investigation for emitter micro-channels[END_REF];

Ait-Mouheb et al. 2019 [START_REF] Ait-Mouheb | Impact of hydrodynamics on clay particle deposition and biofilm development in a labyrinth-channel dripper[END_REF]). When designing drippers, clogging can be prevented or at least significantly reduced by decreasing, as much as possible, the vortex size. Thus, anti-clogging properties and consequently drip irrigation efficiency are strongly related to hydraulic performance. The flow characterization inside the labyrinth-channel is difficult to examine by experimental methods due to the small size and intricacy of drippers (Zhang et al., 2007 [38]).

Therefore, numerical modeling is also helpful to study the flow in the labyrinth-channel. Several numerical studies emphasize that dripper performances are related to hydraulic conditions (Berkowitz, 2001 [6]; [START_REF] Li | CFD and digital particle tracking to assess flow characteristics in the labyrinth flow path of a drip irrigation emitter[END_REF] [START_REF] Li | CFD and digital particle tracking to assess flow characteristics in the labyrinth flow path of a drip irrigation emitter[END_REF]; Palau et al. 2004 [START_REF] Palau Salvador | Hydraulic flow behavior through an in-line emitter labyrinth using CFD techniques[END_REF]). From these studies, one can also infer that the choice of a numerical model is not fixed. Indeed, the standard, RNG (Re-Normalisation Group) and realizable k e models as well as the RSM model (Reynolds Stress Model) were used without clear justifications.

A few experimental studies have been performed to analyze the labyrinth-channel and to compare with the modeling.

The particle image velocimetry (PIV) was used by Li et al. (2008 [27]) to assess flow characteristics in the labyrinth flow path. Then, Li et al. (2008 [27]) compared experimental results with numerical ones obtained with the k e model as turbulence model. The Micro-PIV technique was also used by Wei et al. (2012 [34]) to visualize the water flow with suspended sand particles inside the labyrinth-channel under the pressure range 40-150 [kPa] on two geometries. They used the RNG k e model to perform simulations and conclude that Computational Fluid Dynamics (CFD) simulation results show reasonable agreement with their experimental results on the basis of the curve for the pressure-discharge relationship. Particle Tracking Velocimetry (PTV) was employed by Yu et al. (2017 [37]). Three However, a recent study performed by Al-Muhammad et al. (2018 [4]) has shown that the flow in the labyrinthchannel is anisotropic (i.e the turbulence is different in the three spatial directions (Pope, 2000 [32]). Therefore, models that assume isotropic turbulence should not be selected anymore to model such a flow. But, the standard k-e model and its variants (k-e RNG, k-e realizable) do not take into account the flow anisotropy (Al-Muhammad et al., 2016 [START_REF] Al-Muhammad | Modeling a weak turbulent flow in a narrow and wavy channel: case of micro-irrigation[END_REF]). That is why, in the present study, a more complex model such as RSM is considered to simulate properly this flow as an equation is solved for each of the Reynolds stresses. Also, we propose to overcome the difficulty of experimental measurements for a geometry such as the labyrinth-channel by an advanced optical technology. This consists in performing Micro-PIV experiments (Al-Muhammad et al., 2018 [START_REF] Al-Muhammad | Micro-PIV characterization of the flow in a milli-labyrinthchannel used in drip irrigation[END_REF]). As far as we know, it was the first time that such a Micro-PIV technique was developed to determine with high accuracy, compared to the other studies in the irrigation domain, the mean and fluctuating velocity fields inside the labyrinth-channel constituting irrigation drippers. Herein, these experimental results will be compared with RSM simulations to analyze the flow within the labyrinth-channel. Firstly, the velocity fields and profiles are presented along the labyrinth-channel, and then, the turbulence properties of the flow are presented and discussed. Next, a detailed analysis based on the definition of the vorticity is introduced. Finally, advanced methods such as the l 2 and Q-criteria are used to detect and characterize the vortex zones in the labyrinth-channel flow. Such an analysis is also important for passive micro-mixer subsystems where mixing enhancement is a crucial issue (Capretto et al., 2011 [7]).

Materials and methods

Case study

The dripper chosen is an integrated one with non-uniform section which produces a turbulent flow. This dripper is that most widespread in drip irrigation. It is displayed in Fig. 1. The dripper is composed of 60 baffles (labyrinthchannel units). Each three baffle pattern composes the basic unit which is repeated 20 times. This is the dripper least sensitive to clogging (see Al-Muhammad 2016 [START_REF] Al-Muhammad | Flow in millimetric-channel: numerical and experimental study[END_REF] for more details). A detailed geometry in 2D, with all dimensions, of the presently studied labyrinth-channel is shown in Fig. 2. All the dimensions are presented in table 1. For Micro-PIV, it is exactly the ten-pattern channel that is studied. For RSM simulations, only three baffles are considered, as the flow is then developed (Al-Muhammad et al., 2018 [START_REF] Al-Muhammad | Micro-PIV characterization of the flow in a milli-labyrinthchannel used in drip irrigation[END_REF]). Experiments have been performed with three flow rates 24 [ml.min

mm F=15mm

Re `= r • |u| inlet • D h µ , (1)
where µ is the dynamic fluid viscosity [kg.m 1 .s 1 ], r is the fluid density [kg.m 3 ], |u| inlet is the bulk velocity at the inlet, defined by the equation: |u| inlet = q/(d inlet ⇥ d depth ), with d inlet the inlet width and D h the hydraulic diameter.

Experimental method

The The measurement uncertainty strongly depends on both the particle-image diameter d t and the uncertainty in locating the image centroid represented by c. d t is defined as:

d t = q (M.d p ) 2 + d 2 diff ( 2
)
and

d diff = 2.44 f # l (M + 1) (3)
In the present experiments, f # =2.8, with wavelength l = 532 nm, the image magnification M = 7.7 and d p = 1µm.

When replacing in Eq.2, we find d t = 32.55µm. As it is found by Prasad et al. (1992 [33]) if a particle image diameter is resolved by 3-4 pixels, the location of a particle-image correlation peak can be determined to within 1/10 th the particle-image diameter. The measurement uncertainty is then of d x ⇡ d t /10M which gives an error of about 0.42µm. Next, the effects of the local velocity gradients is studied by Westerweel (2008 [36]). In some study, this effect can be ignored when the variation a of the local particle-image displacement is small with respect to d t . i. The random error s Dx is proportional to the width d D of the displacement-correlation peak, and for a simple shear it is approximately given by:

s Dx c d t r 1 + 2 3 a 2 /d 2 t ( 4
)
with c = 0.05 7 (Westerweel, 2008 [36]). In the present study,

d t = 32.55µm, L = 34.4µm, |∂ u/∂ x| = 3745 s 1
for Re `= 690 which give : s Dx = 1.46 205 µm. From the instantaneous velocity fields obtained by Micro-PIV, the velocity modulus |u|, the velocity fluctuations about the mean (u 0 and v 0 ) are derived and calculated.

|u| = p u 2 + v 2 (5)
This formulae can be applicable for the mean velocity (u) instead of instantaneous velocity (u) to find |u|, and

u 0 = u u (6)
and

v 0 = v v (7)
Several statistical quantities are calculated from ensembles of instantaneous velocity fields containing the mean x and y velocity components (u and v), the second-order moments of the fluctuating velocities u 02 , v 02 and u 0 v 0 and the mean velocity modulus |u|. These statistical quantities serve to calculate the convergence residues. While the final statistical quantities which serve to plot and calculate the velocity fields and vectors are calculated from:

u j (x, y) = 1 N v N v  k=1 u j k (x, y) (8) j=1,2 |u(x, y)| = 1 N v N v  k=1 |u k (x, y)| ( 9
)
where k is the running image number, N v is the number of valid images (around 700 in our case) which is different from the total number of images N (750).

The second-order moments of velocity fluctuations are defined as:

u 0 i v 0 j (x, y) = 1 N v N v  k=1 ⇣ u i k (x, y) u i (x, y) ⌘ ⇥ ⇣ u j k (x, y) u j (x, y) ⌘ (10)
i and j=1,2.

The second-order moments of fluctuating velocities residues are calculated by the formula:

R u 0 i u 0 j Nv =  1 N v N v  k=1 u 0 i k u 0 j k 1 N v 1 N v  k=2 u 0 i k 1 u 0 j k 1 2  1 N v N v  k=1 u 0 i k u 0 j k 2 , (11)
where : i, j = 1, 2 and for (x,y).

These residue values are globally about 10 7 for the u and v velocities and 10 6 for the second-order moments of fluctuating velocities u 02 and v 02 . For u 0 v 0 , the residues can not decrease lower than 10 5 because the denominators of the residue formula are generally closer to 0 (about 10 4 ) (see Al-Muhammad et al. ( 2018) [START_REF] Al-Muhammad | Micro-PIV characterization of the flow in a milli-labyrinthchannel used in drip irrigation[END_REF] for more details).

Turbulence model for the fluid flow

In this study, incompressible steady-state flow is assumed. Buoyancy and gravity are not taken into account. For a turbulent flow, the fluid motion can be described by the mean continuity equation, mean momentum equation, the exact transport equation for the Reynolds stress tensor, the turbulent kinetic energy (k) equation and the turbulent dissipation e equation. For the mean velocity field, the continuity and Navier-Stokes equations write:

∂ u i ∂ x i = 0 , (12)
r ∂ ∂ x j (u i u j ) = ∂ p ∂ x i + ∂ ∂ x j  µ ✓ ∂ u i ∂ x j + ∂ u j ∂ x i ◆ + ∂ ∂ x j h ru 0 i u 0 j i , (13)
where i and j are indices denoting Cartesian coordinate directions, u i and u j are the mean velocities [m.s 1 ], p is the mean pressure [Pa], and u 0 i and u 0 j are the velocity fluctuations [m.s 1 ]. The additional term, the Reynolds stress tensor, R i j = ru 0 i u 0 j , needs to be modeled. The Reynolds Stress Transport Model, (RSM-LRR) derived by Launder et al. (1975 [25]), is chosen herein to simulate the flow in the labyrinth-channel. This model closes the Reynoldsaveraged Navier-Stokes equations by solving additional transport equations for the Reynolds stresses R i j , together with an equation for the dissipation rate e.

Since the RSM can account for the effects of streamline curvature, swirl, rotation and rapid changes in strain rate, it has greater potential to give accurate predictions for complex flows such as that for the labyrinth-channel. The symbolic form of the exact transport equations for the Reynolds stress tensor ru 0 i u 0 j may be written as follows:

C i j |{z} Convection = D T,i j | {z } Turbulent diffusion + D L,i j | {z } Molecular diffusion + P i j |{z} Stress production + f i j |{z}
Pressure strain e i j |{z} Dissipation [START_REF] Gibson | Ground effects on pressure fluctuations in the atmospheric boundary layer[END_REF] The terms that do not require modeling are C i j , D L,i j and P i j . While, the other terms, D T,i j , f i j and e i j need to be modeled to close the equations. The turbulent diffusion D T,i j is usually modeled using a scalar turbulent diffusivity µ t (Lien and Leschziner, 1994 [START_REF] Lien | Assessment of turbulence-transport models including non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step[END_REF]). The modeling of pressure-strain term, f i j , is composed from several terms (Chou, 1945 [9]), and is modeled on the basis of the proposals of Gibson and Launder (1978 [14]), Fu et al. (1987 [12]) and Launder (1989 [24]).

Dissipation terms are obtained with the usual assumption that:

e i j = 2 3 red i j (15)
The value of e is obtained by solving the following modeled equation:

∂ ∂ x i (reu i ) = ∂ ∂ x j ✓ µ + µ t s e ◆ ∂ e ∂ x j + 1 2 C e1 G k e k C e2 r e 2 k ( 16
)
where s e = 1.00, C e1 = 1.44 and C e2 = 1.92. G k = µ t S 2 represents the production of turbulent kinetic energy, with µ t the turbulent viscosity defined as

µ t = rC µ k 2
e with C µ = 0.09, and S the modulus of the mean rate-of-strain tensor, which is defined as S =

q 2S i j S i j (S i j = 1 2 ( ∂ u i ∂ x j + ∂ u j ∂ x i )).

Numerical approach and boundary conditions

The study is performed using the commercial computational fluid dynamics software ANSYS/Fluent V14. Simulations are performed in three dimensions (3D). The mesh is generated and its quality is examined. A prism with quadrilateral base mesh type is adopted. The skewness, based on the deviation from a normalized equilateral angle, is around 0.56 which states that mesh quality is acceptable. The independence of the results to the meshing has been verified (see Al-Muhammad (2016 [START_REF] Al-Muhammad | Flow in millimetric-channel: numerical and experimental study[END_REF]) for more details). The mesh is constructed to satisfy y + < 5 (where y denotes here the distance to the wall of the first mesh point, normalized by the friction velocity and the kinematic viscosity).

Enhanced wall treatment is used to model the near wall region. When using enhanced wall treatment as the near-wall treatment, zero flux wall boundary conditions to the Reynolds stress equations are applied. The RSM model requires boundary conditions for turbulence quantities (k and e) and individual Reynolds stresses ru 0 i u 0 j . k and e can be input directly or derived from the turbulence intensity and a characteristic length. This last method is chosen; low turbulence intensity (5%) with a hydraulic diameter D h = 1.17 [mm] (see table 1) are chosen for the specification method. The turbulent kinetic energy (k) and turbulent intensity are, then, selected for Reynolds-Stress Specification method.

To solve the pressure-velocity coupling and to interpolate face pressure, we choose respectively the SIMPLE and STANDARD methods which are robust and valid for a large flow range. Third-order MUSCL discretization is selected to solve the momentum, R i j and dissipation rate equations because this method is accurate and adapted for all mesh types. Least Squares Cell-Based is the method used to calculate gradients. This method calculates gradient values using adjacent surface cells. Its accuracy is higher than the Green-Gauss Cell-Base method and its cost is lower than the Green-Gauss Node-Based method both available in ANSYS/Fluent. As a majority of the results discussed in section 4 are based upon the differential quantities, it is necessary to present in detail the schemes of gradient calculation.

The Least Squares Cell-Based method approximates the gradient at the center of each cell using the least squares approximation. The derivatives in each cell are assumed to change linearly along the separating distances of all the neighboring cells. In Fig. 3 the change in cell values between cell C 0 and C i along the vector ri can be expressed as (User's guide ANSYS/Fluent 14.0):

(-f ) (c 0 ) • Dr i = (f ci f c 0 ) (17)
when applying Eq.17 for all cell surrounding the cell c 0 , we obtain the following system :

[J](-f ) (c 0 ) = D(f ) (18)
Where [J] is the coefficient matrix which depends purely on geometry.

Then, Eq.18 can be solved by decomposing the coefficient matrix using the Gram-Schmidt process [START_REF] Anderson | An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids[END_REF]. This decomposition yields a matrix of weights for each cell w i0 . Therefore, the gradient at the cell center can then be computed by multiplying the weight factors by the difference vector,

-(f j ) (c 0 ) = N Â i=0 w j i0 (f ci f c 0 ) (19)
where j= 1, 2, 3; N is the number of neighboring cells; and w j the weighting factors of neighboring cells. The gradient schemes are presented in detail by Mishriky and Walsh (2017) [START_REF] Mishriky | Towards understanding the influence of gradient reconstruction methods on unstructured flow simulations[END_REF]. Re `= 690 respectively (Fig. 5). The estimation error can be related to the effects of the local velocity gradients which depends strongly on c (Eq.4). The parameter c depends on several parameters among it the seeding particles number in the interrogation window (Westerweel, 2000 [35]). This number is not well controlled in the vortex zone when the micro-PIV experiments are performed in view of the geometry complexity. Re `= 690 by 5% in comparison with the experimental values. However, an important difference is remarked in the vortex zone, characterized by low flow velocity, where the model under-estimates the mean velocity modulus with 75% in comparison with the experimental values. Indeed, the form of the vortex zone is slightly changed. Numerically, the vortex zone center is closer to the wall with a weak velocity value in comparison with Micro-PIV data. However, the mean velocity modulus does not allow to determine precisely the vortex zone and mainstream flow, therefore, a specific analysis is conducted in section 4.

Flow characteristics of labyrinth-channel dripper

Reynolds stresses

The objective of this paragraph is to study and to compare experimentally and numerically, the Reynolds stresses u 02 , v 02 and u 0 v 0 . The experimental Reynolds stresses are presented and discussed by Al-Muhammad et al. (2018 [4]).

The Reynolds stress profiles are presented in Fig. 6 and Fig. 7 for Reynolds numbers 345 and 690 respectively. [START_REF] Lee | Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulent[END_REF] show that, with the assumption that the small-scale contributions to the fluctuating velocity variances do not depend on the Reynolds number, some universal corrections can be applied.

This procedure was developed for canonical flat plate turbulent boundary layers at quite large Reynolds numbers Re t (where Re t is computed with the boundary layer thickness and the friction velocity), Re t = [900 2600], and for quite large interrogation windows (Dx + ' Dy + > 20). In our case, the interrogation window size is Dx = Dy = 34.4µm, corresponding to Dx + = Dy + ' 3.5, which is likely to induce negligible attenuation effects according to the figure 8 presented in Lee et al. ( 2016) [START_REF] Lee | Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulent[END_REF]. In addition, our configuration is far from a canonical turbulent boundary layer due to the labyrinth geometry and the Reynolds numbers are small (Re t = [60 85]). Therefore, no correction to account for the effect of the interrogation window size was applied in the present study. There are some differences between the micro-PIV and the RSM results for v 02 in the transition between the mainstream flow and the swirl zone (y/d 2 = 0.4 0.7). The transition between theses two regions is not captured by RSM model. Numerical

Reynolds stresses profiles are plotted in Fig. 8 for Re `= 690. The numerical results indicate that the Reynolds stress w 02 is smaller than v 02 , and the ratios w 02 /v 02 are about 10% and 60% in the mainstream flow and the recirculation region respectively, while the Reynolds stress u 02 is higher in the mainstream zone by a ratio 60% and smaller in the recirculation zone by a ratio w 02 /u 02 of 25%.

Normalized Reynolds stresses increase when the Reynolds number increases since turbulence increases. The ratios of u 02 , v 02 and u 0 v 0 for the two Reynolds numbers (Re `= 690 to Re `= 345), are about 20%, 30% and 35% in the mainstream flow Fig. 6 and Fig. 7. The turbulence Reynolds number is weak at the entrance and in the major part of the first baffle, and significantly larger, with an almost developed behavior, from the second baffle. The turbulence Reynolds number is then rather large in the vicinity of the teeth and impacted corners and much smaller in between and in the regions where k is small. It is important to compare in a quantitative way the Re t values for the two Reynolds numbers.

The profiles of Re t /Re `are plotted along the line 3 and presented in Fig. 10. They are almost identical, even though Re t /Re `for Re `= 345 is slightly larger than for Re `= 690 in the mainstream region (y/d 2 = 0.62 0.8). However, as expected, close to the walls, the ratio decreases to 0 as Re t is zero at the walls. Therefore, the turbulence Reynolds number Re t has the same order of magnitude as the global Reynolds number Re `. A detailed analysis of the terms constituting this ratio allows to understand this finding :

Re t Re `= k e k |u| 2 inlet |u| inlet d inlet . ( 21
)
The ratio k/e is a time scale (noted t L ). This time scale is larger at the inlet than inside the baffles because the flow is almost laminar at the inlet Re t ⇠ 0, Fig.

t p = d 2 p r p 18µ (22)
we find that t p = 0.37 ⇥ 10 3 3.7 [ms]. Whereas the sedimentation velocity is equal to:

U g = d 2 p (r p r) 18µ g ( 23
)
where g is the acceleration due to gravity [m.s 2 ], and d p is the diameter of the particle [m]. We find U g = 1.5 ⇥ [START_REF] Yu | The mechanism of emitter clogging analyzed by CFD-DEM simulation and PTV experiment[END_REF]) . Inside the labyrinth-channel unit, the larger k/e, the larger the mixing time occurs in the vortex zone center. This value is associated with the lower velocity magnitude which plays an important role in the capture of particles. However, the vortex center is less influential if the particles diameter is small and thus t p is very small (Yu et al., 2017 [37]). Indeed, dripper clogging is worse when the physical particles are not isolated and accompanied by other causes of clogging such as the formation of biofilm (Gamri et al., 2015 [13]).

Vortex detection and analysis

The study of the flow velocity shows that the flow inside the baffles is composed of a mainstream flow and a vortex zone. This vortex zone was first observed when considering the streamlines of velocity fields (Fig. 4). In order to identify swirling and shearing motion zones, a specific analysis is performed in this section to define with more accuracy these two zones.

Strain rate and vorticity

The deformation rate of the fluid is an important property. The deformation tensor describes how fluid elements deform as a result of fluid motion. This deformation (or velocity gradient) tensor is represented by D i j = Ou i, j (where O is the nabla operator) and defined by :

D i j = Ou i, j = ∂ u i ∂ x j = 0 B B B B @ ∂ u ∂ x ∂ u ∂ y ∂ u ∂ z ∂ v ∂ x ∂ v ∂ y ∂ v ∂ z ∂ w ∂ x ∂ w ∂ y ∂ w ∂ z 1 C C C C A . ( 24
)
As this is a second order tensor it can be decomposed into a symmetric and an anti-symmetric part. Applying this to the Jacobian matrix J = (-u) T , with symmetric and anti-symmetric components, S and W respectively, D i j = S i j +W i j :

S = 1 2 Ou + Ou T = 1 2 0 B B B B B B @ 2 ∂ u ∂ x ∂ u ∂ y + ∂ v ∂ x ∂ u ∂ z + ∂ w ∂ x ∂ v ∂ x + ∂ u ∂ y 2 ∂ v ∂ y ∂ v ∂ z + ∂ w ∂ y ∂ w ∂ x + ∂ u ∂ z ∂ w ∂ y + ∂ v ∂ z 2 ∂ w ∂ z 1 C C C C C C A ; (25)
W = 1 2 Ou Ou T = 1 2 0 B B B B B B @ 0 ∂ u ∂ y ∂ v ∂ x ∂ u ∂ z ∂ w ∂ x ∂ v ∂ x ∂ u ∂ y 0 ∂ v ∂ z ∂ w ∂ y ∂ w ∂ x ∂ u ∂ z ∂ w ∂ y ∂ v ∂ z 0 1 C C C C C C A . ( 26
)
The diagonal components of the strain rate tensor S ( ∂ u ∂ x , ∂ v ∂ y and ∂ w ∂ z ) are the extensional strain rates. Note that ∂ u ∂ x > 0 for an elongating body and ∂ u ∂ x < 0 for a shortening body. The strain rate due to shearing in the x-y plane is defined in the components of the strain rate tensor as:

S xy = 1 2 ✓ ∂ u ∂ y + ∂ v ∂ x ◆ . (27)
Vorticity ! w is a vector field defined as the curl (rotational) of the flow velocity ! u vector. Its definition can be expressed by:

! w = O ⇥ ! u . (28)
Therefore :

w z = ∂ v ∂ x ∂ u ∂ y . (29)
The mean strain rate S xy and vorticity w z are calculated from Eq.27 and Eq.29 (with the variables u and v replaced by u and v). Then, they are normalized by (|u| inlet /d inlet ) for both Reynolds numbers for the third baffle in both the Micro-PIV experiments and the RSM modeling. For experimental data, the second-order centred difference scheme is used to calculate the derivatives. This scheme is chosen according to the study by [START_REF] Foucaut | Some considerations on the accuracy and frequency response of some derivative filters applied to PIV vector fields[END_REF] [START_REF] Foucaut | Some considerations on the accuracy and frequency response of some derivative filters applied to PIV vector fields[END_REF] which concludes that a second-order centred difference scheme is the most efficient way to obtain good accuracy of the derivatives. Fig. 12 shows an example of the quadratical mesh used to treat Micro-PIV data by a Matlab code. The velocity derivatives are therefore computed as:

∂ v i ∂ x = 1 2Dx (v i+1 v i 1 ) (30)
∂ u j ∂ y = 1 2Dy u j+1 u j 1 (31)
where Dx = Dx i = Dx i+1 = Dx i 1 and Dy = Dy i = Dy i+1 = Dy i 1 since all the cells are square for experimental data with spatial resolution of 34.4 ⇥ 34.4µm.

i-1, j+1 i-1, j i , j i, j+1 i+1, j i+1, j+1 i, j-1 i-1, j-1 i+1, j-1 x i x i+1 x i-1 y j y j+1 y j-1
Figure 12. A quadrilateral mesh used in micro-PIV treatment by Matlab code extracted from Mishriky and Walsh (2017) [START_REF] Mishriky | Towards understanding the influence of gradient reconstruction methods on unstructured flow simulations[END_REF].

One can conclude (Fig. 13 to Fig. 16) 1 that the mean strain rate as well as the mean vorticity values are not much influenced by the Reynolds number when comparing the normalized fields for these two Reynolds numbers. The numerical results are rather close to those obtained experimentally. The observed results have a difference of about 10% along the line 3, except in the zones y/d 2 = 0.35 0.55 and y/d 2 = 0.55 0.65 on which a gap of 47% and 150% is observed for w z and S xy respectively. The last huge value is due to the fact that the sign of S xy is changed over this zone (y/d 2 = 0.55 -0.65) experimentally when numerically it keeps positive values. w z has a large value for the flow in the separation zone (red zone, Fig. 15), with a positive value for the bottom tooth and a negative value for the top tooth. Regarding the same zone in the fields of mean strain rate, one finds that the strain rate is also maximum in this zone. As a result of this, the mean vorticity could be used directly to identify vortices. But a problem associated with this method is that vorticity cannot distinguish between swirling motions and shearing motions (Kida et al., 1998 [22]). In addition, contrary to what is usually found for vortex zones, the normalized mean vorticity values in these zones are close to zero, as the variation of mean velocity occurs over a quite long distance (from y/d 2 = 0 to y/d 2 = 0.55, Fig. 5). In order to be more quantitative, the numerical and experimental data must be analyzed by advanced methods.

There are several methods to identify coherent turbulent structures (eddies) in a quantitative way. There is so far no universal accepted method to identify a coherent structure (Haller, 2005 [17]; Green et al., 2007 [16]). Many of these methods involve the mean velocity gradient tensor (Chakraborty et al., 2005 [8]; Green et al., 2007 [16]).

The characteristic equation is the equation which is solved to find matrix eigenvalues l , also called the characteristic polynomial. For a general matrix Z, the characteristic equation in variable l is defined by det(Z l I) = 0. The characteristic equation for the tensor -u is then given by:

l 3 + Pl 2 + Ql + R = 0 , (32)
where P, Q and R are the three invariants of the mean velocity gradient tensor.

l 2 -criterion. A symmetric tensor A is defined as follows:

A = S 2 + W 2 . ( 33
)
A is considered to determine if there is a local pressure minimum that entails a vortex. A vortex is defined as "a connected region with two negative eigenvalues of A" (Jeong and Hussain, 1995 [19]). Since A is symmetric, it has real eigenvalues only. Thus, its two eigenvalues (l 1 and l 2 ) are also real for a two-dimensional flow, and by ordering the eigenvalues l 1  l 2  l 3 the definition becomes equivalent to requiring that l 2 < 0. The local minimum of l 2 corresponds to a vortex core. If the value of l 2 is positive, the shear motion only exists and the vortex motion disappears in the local flow field. This is called the Lambda-2 (l 2 ) vortex criterion.

Q-criterion. One other commonly mentioned method is the Q-criterion (Green et al., 2007 [16]), where Q is defined as:

Q = 1 2 kWk 2 kSk 2 ; ( 34
)
The Q-criterion defines a vortex as a " connected fluid region with a positive second invariant of -u ". Coherent eddies are then defined as regions of the flow with positive values of Q and lower pressure than the immediate surroundings (Chakraborty et al., 2005 [8]), these can easily be visualized as isosurfaces. Looking at the definition of the second invariant, we can see that Q represents the local balance between shear strain rate and vorticity magnitude, defining vortices as areas where the vorticity magnitude is greater than the magnitude of rate-of-strain (Hunt et al., 1988 [18],

Vàclav Kolàr, 2007 [23]).

Eq.34 is developed to implement the parameter Q in Fluent software and to process it under Matlab for Micro-PIV experiments. Q can be written, in 2D and 3D, as follows:

Q = 1 2 ✓ ∂ u ∂ x ◆ 2 + ✓ ∂ v ∂ y ◆ 2 ! ✓ ∂ u ∂ y ∂ v ∂ x ◆ in 2D ; (35)
and ). The drawback of the Eulerian methods is that they are not independent from the reference frame, i.e. they are not objective. As Green et al. (2007 [16]) also point out, this method requires the user to effectively choose the thresholds discretionally (as Q > 0 may be changed to a higher value for instance in order to visualize more easily the vortex). The experimental Q-criterion fields obtained with Eq.35 are plotted in Fig. 19 and in Fig. 20 for the lower and larger Reynolds numbers respectively. The Q-criterion fields obtained likewise with Eq.35 are plotted in Fig. 21 and Fig. 22 for the RSM model. The Q-criterion helps to separate and distinguish between the vortex zone and the shear motion

Q = 1 2 ✓ ∂ u ∂ x ◆ 2 + ✓ ∂ v ∂ y ◆ 2 + ✓ ∂ w ∂ z ◆ 2 ! ✓ ∂ u ∂ y ∂ v ∂ x + ∂ u ∂ z ∂ w ∂ x + ∂ v ∂ z ∂ w ∂ y ◆ in 3D . ( 36

Conclusion

The present paper analyzes the flow in a baffle-fitted labyrinth-channel constituting irrigation drippers thanks to Micro-PIV and RSM modeling. The detection and the characterization of the vortex zone in a milli-labyrinth-channel are presented and detailed in this paper. The main conclusions are as follows:

-9 -8.5 -8 -7.5 -7 -6. • The ratio k/e can be used as variable to estimate the time delay between the two laser pulses within a pair since it determines the mixing time. This time is short in the vortex zone and long at the inlet.

• Advanced methods, the Q and l criteria, which serve to detect the vorticity and to deeper analyze the vortex zones, were implemented. Q and l 2 methods show that the vortex intensity is largest in the separation zone where the large vorticity values result from the change of flow direction. The vorticity values are larger in this zone than in the vortex region where vorticity remains rather weak. The Q criterion allows to distinguish between the shear motion and vortex zones. As a conclusion, just downstream the baffle, there is, as expected, a vortex region but of weak intensity in comparison with the mainstream flow, where the strong vorticity value is generated by the flow direction change.

• The RSM model, globally, can be considered as a reliable model to predict and characterize the flow in the labyrinth-channel. The results obtained by RSM model are in good agreement with the experimental results, a difference about of 5% in the mean velocity prediction, in the mainstream flow. The size and the position of vortex zone are similar to the experimental results. However, a difference gap of about 75% is observed in the estimation of the mean velocity.

These experimental results will be compared with 2D-3C Micro-PIV measurements from future work, on the same prototype with additional Reynolds number values. Data issuing from such experiments would allow to confirm the present numerical results concerning the third velocity component. Next, detecting the vortex zones, which are the main responsible of clogging problems in drip irrigation systems, and analyzing them in a quantitative way, in function of the third direction, is one of the main objectives of future work based on Micro-PIV data. Finally, these analyses and results will be used as a basis for studying two-phase flow by injecting particles. Moreover, having a precise and comprehensive aspect on the clogging topology and formation mechanism is essential to optimize an anti-clogging dripper.

  clay particle diameters were studied: 65, 100 and 150 [µm]. They employed CFD-DEM (Discrete Element Method) to perform the numerical work. The unsteady Standard k e model was used as turbulence model. Nevertheless, only the velocity (of the liquid or the solid phase) and the position of sedimentation regions were analyzed.

Figure 1 .

 1 Figure 1. Industrial dripper geometry.

Figure 2 .

 2 Figure 2. Ten baffle labyrinth-channel used in micro-PIV present experiments. Only the three first baffles are used to perform RSM modeling. The inlet and outlet conditions are the same in the experimental and numerical studies. The blue-colored line and rectangles R 2 and R 3 represent the zones where the results will be analyzed. The line 3 coordinates are x = 8.5 [mm], y = 0 2.80 [mm], and z = 0.575 [mm].

  e. a ⌧ d t , a = M Du Dt where Dt is the exposure time delay, and Du represents the local variation of the velocity field, i.e., |Du| ⇠ |∂ u/∂ x| • L where L is a typical dimension of the interrogation window size.

Figure 3 .

 3 Figure 3. Cell Centroid Evaluation, extracted from User's guide ANSYS/Fluent 14.0.

3. 1 .

 1 Mean velocity modulus fieldMean velocity modulus fields obtained experimentally by the Micro-PIV technique and numerically by the RSM model are compared in Fig.4where streamlines colored by mean velocity modulus are plotted for Re `= 690. The blue-colored zone, in the mean velocity fields, allows having a global overview on the vortex zone formed inside the labyrinth-channel flow. This vortex zone is characterized by low-velocity values. The RSM model predicts approximately the same vortex zone form as Micro-PIV does, even if the vortex center is not exactly at the same position and velocity magnitude is greater for the Micro-PIV results : 1.65 and 1.55 times greater at y/d 2 = 0.1 for Re `= 345 and

Figure 4 .Figure 5 .

 45 Figure 4. Velocity streamlines in the rectangle 2 (see fig.2) for Re `= 690.

4 (c) u 0 v 0 Figure 6 . 4 (c) u 0 v 0 Figure 7 .

 406407 Figure 6. Normalized Reynolds stress profiles along the line 3 for Re `= 345.

Figure 8 .Figure 9 .

 89 Figure 8. Normalized Reynolds stresses profiles along the line 3, RSM model for Re `= 690.

Figure 10 .

 10 Figure 10. Ratio of turbulence Reynolds number Re t to Reynolds number Re `along the line 3 for the RSM model in 3D.

9 . 2 inlet

 92 In addition, this time scale is also relatively larger in the vortex zone than in the mainstream flow. The smaller the mixing time is, the more agitated and turbulent the flow is. The time scale increases when the Reynolds number decreases. The term |u| inlet d inlet has the magnitude order of 10 3 [s 1 ], while k |u| has the magnitude order of 1 and k/e is in the order of 10 3 [ms] (see Fig. 11). The ratio k/e is presented in Fig.11 for Re `= 345 and Re `= 690 for the RSM model in 3D. It is important to compare the values of k/e in the vortex region to the characteristic time of clay particles t k . In general, the clay particles diameter is in the order of d p = 2 200 [µm]. Mean clay density is about r p = 1700 [kg.m 3 ]. When replacing these values in the equation:

10 6 1 . 5 ⇥

 15 10 2 [m.s 1 ]. Therefore, the dripper clogging is rather related to the flow hydrodynamics, low velocity and low turbulence kinetic energy k, as obtained at the inlet section and in the first vortex zone, which is also noticed by the works of Ait-Mouheb et al. (2019 [1]), and Yu et al. (2017

Figure 11 .

 11 Figure 11. Ratio k/e, [ms] for RSM model in 3D.

Figure 13 .Figure 14 .Figure 15 .

 131415 Figure 13. Normalized mean strain rate fields S xy /(|u| inlet /d inlet ), Micro-PIV.

Figure 16 .

 16 Figure 16. Normalized mean vorticity fields w z /(|u| inlet /d inlet ), RSM model.

) 4 . 2 . 2 .Figure 17 .

 42217 Figure 17. Normalized l 2 criterion, Micro-PIV.

Figure 18 .

 18 Figure 18. Normalized l 2 criterion, RSM model in 3D.

Figure 19 .Figure 20 .

 1920 Figure 19. Normalized Q criterion -Mean rate of strain (Q > 0) and vorticity (Q < 0) regions-for Re `= 345, Micro-PIV.

  zone. It appears that intensities vary linearly with the Reynolds number, while the size and position of the vortex zone vary very slightly with Re `. The Q-criterion confirms what is found by the l 2 criterion: the size and position of the region near the baffle teeth and that in which vortex occurs depend very little on the Reynolds number in the range of Reynolds numbers studied. Nevertheless, the limitations of these vortex zones are somewhat inaccurate since the Q values are very low. Therefore, the ratio of Q in 3D to Q in 2D is calculated numerically. This ratio allows determining with high accuracy the vortex regions. The Q-criterion is calculated in 2D and in 3D on the 3D geometry by Eq.[START_REF] Westerweel | Theoretical analysis of the measurement precision in particle image velocimetry[END_REF] andEq.36 respectively. The fields presented in Fig.21and Fig.22are for the 3D equation. In Fig.23, the ratio of Q 3D /Q 2D is calculated and shown. This figure points out the limitations of the vortex zone where small positive values in 3D become small negative values in 2D when the third component is eliminated (as with Micro-PIV data).

Figure 21 .

 21 Figure 21. Normalized Q criterion -Mean rate of strain (Q > 0) and vorticity (Q < 0) regions-for Re `= 345, RSM model in 3D.

Figure 22 .

 22 Figure 22. Normalized Q criterion -Mean rate of strain (Q > 0) and vorticity (Q < 0) regions-for Re `= 690, RSM model in 3D.

Figure 23

 23 Figure 23. Q 3D Q 2D calculated on the 3D geometry, RSM model.

1 ] (1.44 [l.h 1 ]), 36 [ml.min 1 ] (2.16 [l.h 1 ]), and 48 [ml.min 1 ] (2.88 [l.h 1 ]), where the minimum and maximum flow rates are chosen symmetrically around 2.16Table 1 .

 1 The presently studied labyrinth-channel dimensions. ] which corresponds to the nominal flow rate of such a dripper. These flow rates correspond to Reynolds numbers Re `of 345, 510 and 690. Re `is defined as

	[l.h 1
	Inlet width	d inlet	1.20 mm
	Outlet width	d outlet	1.40 mm
	Depth	d depth	1.15 mm
		d 1	1.35 mm
		d 2	2.80 mm
		d 3	1.35 mm
		D 1	10.00 mm
	Unit length	D 2	3.24 mm
	Hydraulic diameter Angle	D h a	1.17 mm 33 o

As the field of view is =

2.2 mm ⇥ 2.2 mm for d p = 1[µm], it is difficult to visualize an entire baffle. This is why the baffle is presented by juxtaposition of two fields of view. The deviated results, at y=1.5 mm, are due to the line which separates these two fields.

Acknowledgements

This work has been funded by the seventh Framework Programme FP7-KBBE-2012-6:Water4Crops and the Aleppo University in partnership with the laboratories IRSTEA (Institut national de Recherche en Sciences et Technologies pour l'Environnement et l'Agriculture) and IRPHE (Institut de Recherche sur les Phénomènes Hors Equilibre). The authors are grateful to Jean-Jacques Lasserre from Dantec Dynamics company.


Julia Immoor
email: julia.immoor@uni-bayreuth.de

Hauke Marquardt

Lowell M Miyagi

S Speziale

Sébastien Merkel

I Schwark

A Ehnes

Hanns-Peter Liermann

H.- P Liermann

An improved

Introduction

Understanding the physical and rheological properties of materials at simultaneous high pressures and temperatures is of key importance in Earth science as well as materials sciences.

The rheological properties of Earth's mantle materials, for example, govern large-scale mantle convection [START_REF] Kohlstedt | Properties of Rocks and Minerals -Constitutive Equations, Rheological Behavior, and Viscosity of Rocks[END_REF][START_REF] Tsujino | [END_REF][3][4] . In addition, Crystallographic Preferred Orientation (CPO) caused by the alignment of mantle minerals during deformation, leads to seismic anisotropy, providing a means to link seismic observations to mantle flow [5][6][7][8][9][10][11][12][13] . Several techniques have been developed in the past to study the rheology of materials under high pressure and temperature, but achievable pressures are mostly limited to those typical of the crust and upper mantle 3,14- 18 .

Deformation experiments at deep lower mantle pressures are almost exclusively performed in diamond-anvil cells in combination with synchrotron-based in-situ X-ray diffraction in a radial geometry (Fig. 1A,B). By employing radial diffraction geometry, lattice strains and deviatoric stress as well as evolution of CPO can be derived from analysis of in situ diffraction images. Radial X-ray diffraction in DACs has been widely employed in Earth as well as materials sciences, but high-pressure experiments have been mostly limited to room temperature [19][20][21][22][23][24][25] . Early high-temperature employed a laser-heated DAC, but data analysis and interpretation is challenging due to temperature gradients in the sample 26,27 . Liermann et al., (2009) 28 developed a resistive-heated DAC, which was tested up to 36 GPa and 1100 K while performing in-situ radial X-ray diffraction. The use of a resistive-heating setup reduces temperature gradients and provides more homogeneous heating of the entire sample chamber. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Here, we present a modified resistive-heated-radial-X-ray-diffraction-diamond-anvil-cell (RH-rXRD-DAC) (Fig. 2A,B) and report on its performance during in-situ radial X-ray diffraction experiments at simultaneous high pressure and high temperature on several This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Piston: 13: Kapton, which supports a cubic boron nitride gasket or amorphous boron epoxy gasket (14) with powder sample in the sample chamber (15). polycrystalline samples. The main improvement as compared to the setup described by Liermann et al. (2009) is the development and implementation of a water-cooled vacuum chamber (Fig. 3A,B) that also enables cooling of the piston of the Mao Bell type DAC. This modification decreases heating and thermal expansion of the piston of the Mao Bell DAC but allows the cylinder to heat up, thus reducing friction between the piston and the cylinder during compression at high temperatures. The use of a vacuum chamber prevents the oxidation of the cell, the Molybdenum rods and the diamonds at very high temperatures. We This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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Experimental Method

In radial X-ray diffraction experiments, the incoming X-ray beam is oriented perpendicular to the compression direction, i.e. the axis of the diamond anvils (Fig. 1A,C: 1). This setup provides the possibility to study the lattice strains, resulting from the effect of differential stress, together with the CPO of powder samples 19 . A pressure-transmitting medium is not used. This enhances the development of differential stress and texture. In order for X-rays to reach the sample chamber in the radial diffraction geometry, X-ray transparent gaskets are required. Here, we used either X-ray transparent amorphous boron epoxy + kapton 29 or cubic boron nitride (cBN) epoxy 27 13, 14) to reach high pressures 30 . The culet sizes of the employed diamonds were 200 µm or 300 µm (Fig. 2C: 12). The setup of the graphite heater is similar on the piston and cylinder side of the DAC (Fig. 2C). Diamonds are glued on tungsten carbide seats that are truncated at the side to increase the opening angle for diffracted X-rays (Fig. 2: 5). The seats are insulated from the graphite by a ceramic ring (Fig. 2: 4) fixed to the seat with OMEGABOND 500 liquid. The gaps between the ceramic plates and the diamonds are filled with ceramic glue (Resbond 989). The heads of the molybdenum rods end in horizontal strips with a small step at the end. A piece of graphite foil connects the molybdenum rods (Fig. 2A During the experiment, the temperature of the sample can be increased/decreased by varying an analog I/O signal from 0-10 V using the beamline control system. This proportionally adjusts the power of the DC power supply from 0-1800 W (0-8 V and 0-220 A) 31 . Pressure is changed remotely using a gas membrane device that is operated by the membrane pressure controller APD200 from Sanchez Technology 27,28,32 .

For high-pressure and high-temperature experiments, the RH-rXRD-DAC is placed in a newly-designed water-cooled vacuum chamber that serves to both cool the DAC and to prevent oxidation of the DAC, the molybdenum electrodes, the diamond anvils and the graphite heater (Fig. 3A,B). The piston of the DAC is indirectly cooled through a steel pin This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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that is connected to the base of the vacuum chamber, which is water-cooled. The differential cooling between the piston and the cylinder reduces the friction between the two parts of the DAC and enables a smoother pressure increase as compared to the previous experimental setup 27,28 . During the experiment the vacuum in the chamber can be as good as 5 x 10 -3 mbar.

Note that, due to connections between the pump and the cell chamber, vacuum levels around the diamond anvil cells may not be as efficient. Nevertheless, the achieved vacuum is sufficient to perform experiments with minimal oxidation of the heating elements.

Results and discussion

The new setup has been tested during different experimental campaigns at the ECB P02.2 at PETRA III, DESY (Hamburg, Germany). Diffraction images were collected with a XRD 1621 flat panel detector from Perkin Elmer. In the following, we will describe some selected experiments in order to illustrate the capability of the new setup for Earth and materials science research. We report on the deformation of polycrystalline samples of ferropericlase ((Mg0.8Fe0.2)O), the in-situ synthesis and deformation of cubic Ca-Pv (CaSiO3), experiments performed on a two-phase mixture of bridgmanite (MgSiO3) and ferropericlase, synthesized from a mixture of enstatite glass + ferropericlase in the resistive-heated DAC, as well as the high-temperature compression of tantalum carbide (TaC0.99), an ultra-high temperature ceramic material.

In-situ deformation of ferropericlase

Ferropericlase is the second most abundant mineral in Earth's lower mantle. It may play a key role in mantle dynamics since it is rheologically weaker than bridgmanite, the dominant lower mantle phase. Furthermore, it shows a pronounced elastic anisotropy, making it one of the candidates to explain seismic shear wave polarization anisotropy in the lower mantle 33 . This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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However, previous deformation studies at pressures of the lower mantle were limited to room temperature due to experimental complexity 19,[21][22][23]34,35 . In Immoor et al. (2018), we used the described setup to measure the deformation of ferropericlase to 62 GPa at 1400 K as well as to higher pressures but lower temperature. In our 1400 K run, the pressure of the sample was increased up to 40 GPa at room temperature and afterwards heated up to 1400 K. During heating, the pressure of the sample dropped to below 20 GPa. We increased the pressure again and reached 62 GPa when diamond failure stopped the experiment. During compression, we collected high quality diffraction images of ferropericlase. Based on these results, we were able to monitor the evolution of CPO in ferropericlase and confirm a change of slip system activity at high temperature as predicted by computations 10 .

In-situ synthesis and deformation of cubic CaSiO3

CaSiO3 perovskite is expected to be an important mineral in Earth's transition zone and lower mantle, where it is the third most abundant phase for a pyrolytic mantle composition 36 . In a deeply subducted oceanic slab, CaSiO3 perovskite may account for up to 25 Vol.% of the transformed basaltic crust 37 and will affect the bulk rheological properties of the lithospheric slab. According to a recent computational study 38 , the shear wave anisotropy of CaSiO3 perovskite is about 15-30% at conditions of the lower mantle. A strong CPO of CaSiO3 perovskite may, therefore, contribute to seismic anisotropy observations, in particular in the shallow lower mantle or lowermost transition zone, where the elastic anisotropy is strongest.

A previous CaSiO3 perovskite study has been limited to 49 GPa at ambient conditions 23 . At these conditions, however, CaSiO3 perovskite forms a pseudo cubic structure and the exact nature of the distortion is still under debate [39][40][41][42] . Whereas at temperatures typical for the lower mantle, the structure is cubic (Pm3m) [40][41][42][43] and may show a different rheological behavior.

CaSiO3 perovskite can be experimentally synthesized from CaSiO3 wollastonite at pressures

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. of about 20 GPa and temperature of about 1300 K 44 , but is not quenchable to ambient conditions. This implies that studies of the physical properties of CaSiO3 perovskite need to be performed in-situ and in the same pressure device where it has been synthesized.

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Using the improved RH-rXRD-DAC, we were able to synthesize CaSiO3 perovskite and performed several successful deformation experiments reaching temperatures of up to 1500 K at pressures of 45 GPa (Immoor et al. in prep.). The starting material was amorphous CaSiO3 mixed with platinum powder as pressure standard. Figure 4 shows two diffraction images collected during a compression experiment that reached a final pressure of 40 GPa at 1300 K. Cubic CaSiO3 perovskite was synthesized after increasing the temperature to 1300 K at which point the pressure dropped from 33 GPa to 27 GPa as a result of the phase transition (Fig. 4B). The collected diffraction patterns show smooth diffraction rings, indicating a relatively small and homogeneous grain size of the synthesized cubic CaSiO3 perovskite. The large pressure drop at the transition also caused strain heterogeneity in Pt finely mixed with the sample (see Pt peaks asymmetry in Fig. 4B). In both panel (A) and (B) the diffraction lines of diamond are masked in the integration and absent in the diffraction patterns.

Synthesis of Bridgmanite and Ferropericlase

The deformation behavior of multiphase rock assemblies might substantially differ from the behavior of single-phase assemblies, particularly if the phases show large differences in rheological properties 35,[45][46][47][48] . The lower mantle can be modeled as a two-phase mixture of bridgmanite and ferropericlase, two phases that show large differences in plastic strength and viscosity 3,5,22 . Because of this large contrast in rheological strength, it is difficult to predict mantle properties, including viscosity and seismic anisotropy, from single-phase measurements. There have been few deformation experiments on analogues 49,50 , as well as on a true two-phase lower mantle mixture at pressures and temperature of the very top of the lower mantle using a rational Drickamer apparatus 3 . Here, we used the improved RH-rXRD-DAC to synthesize a bridgmanite and ferropericlase assembly (Fig. 5A,B) from an enstatite glass powder mixed with ferropericlase, and applied deviatoric stress to the two-phase mixture at high temperatures (Fig. 5C). In one successful run, we first increased the pressure at 1600 K. Afterwards the pressure in the sample decreased while increasing the temperature continuously to 1900 K. A peak splitting of ferropericlase was observed, likely as a result of pressure gradients in the sample chamber, followed by the appearance of the typical diffraction ring triplet of the new phase bridgmanite. Bridgmanite grew while the pressure continued to decrease when the thermocouples stopped working. During a subsequent This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Ferropericlase was used as pressure calibrant. decrease of voltage and therefore presumably of temperature (based on power-temperature relation; see Fig. 6), the pressure in the sample chamber increased again to 35 GPa leading to deformation of the sample (Fig. 5C).

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Compression of tantalum carbide (TaC0.99 )

Carbides are characterized by high mechanical and thermal stability and play an important role in industrial applications, where they are used, for example, as coatings for abrasive tools. Many experimental and computational studies have been conducted on tantalum carbide (see references in 51 ). However, no experiments have been performed to study the behavior of this phase under simultaneous high pressure, high temperature and deviatoric stress. We performed two successful experimental deformation runs on tantalum carbide (TaC0.99) and constrained the pressure-volume-temperature equation of state 51 . The starting material was This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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TaC0.99 powder and the pressure was determined by a thin piece of Au foil (less than 5 µm) using the EOS published in Fei et al. (2007). In the first run, we started heating when the pressure reached 2 GPa, we increased the temperature to 673 K, and measured X-ray diffraction up to a final pressure of 33 GPa along the 673 K isotherm. In the second run, we increased temperature at a pressure of 2 GPa up to 1073 K, and we collected X-ray diffraction images up to a final pressure of ~38 GPa along an isothermal path. The data collected under non-hydrostatic conditions were used to constrain the quasi-hydrostatic high temperature EOS by extracting the hydrostatic unit-cell parameter from the x-ray diffraction data 53 . In addition these data can be used to determine the strength and activity of the slip systems of TaC0.99 at simultaneous high-pressure and -temperature (Speziale et al. in prep.).

Challenges and solutions

In several experimental runs the DAC jammed during high-temperature experiments leading to discrete pressure jumps as opposed to smooth increases of pressure. Because of their brittleness the ceramic gaskets were not able to buffer these pressure jumps resulting in failure of the diamond anvils. The reason for our difficulties to smoothly increase pressure at very high temperatures could be the expansion of both the piston and the cylinder of the Mao Bell DAC leading to increased friction between both parts. However, at moderately high temperatures, up to 1400 K, the differential cooling was effective such that a smooth pressure increase is generally possible. For higher temperature experiments the indirect piston cooling is still insufficient, and needs to be improved in order to reduce the thermal expansion of the piston and thus the friction.

Using the water-cooled vacuum chamber, temperatures up to 1900 K have been reached in the RH-rXRD-DAC, but no pressure increase was possible. Generally, both thermocouples This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. recorded stable temperatures during the experiments, with a reproducible dependence of temperature on power (Fig. 6).

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In a few runs, the difference in temperature reading between the two thermocouples was very large (the maximum difference observed was 400 K). In these cases higher temperature values were recorded by the thermocouple situated between the graphite sheets. Large differences in temperature reading usually occurred when one of the thermocouples, i.e. the one at the tip of the diamond was placed too far from the culet of the diamond.

Conclusion

We have presented an improved experimental setup for radial X-ray diffraction measurements based on a graphite-heated Mao Bell type diamond-anvil cell contained in a water-cooled This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Temperature and pressure in the diamond-anvil cell are controlled remotely during the experiment. Several successful experiments studies were performed by using the improved setup on a variety of Earth materials (ferropericlase, calcium perovskite, a two-phase bridgmanite-ferropericlase mixture) and tantalum carbide in order to show the capabilities of the resistive-heated-radial-X-ray-diffraction-diamond-anvil-cell. A major priority is currently This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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Figure 1 :

 1 Figure 1: (A) angle-dispersive high-pressure radial X-ray diffraction in a DAC (modified after

Figure 2 :

 2 Figure 2: Experimental setup of a resistive-heated DAC (modified after 10 ). (A) 3D CAD

  DOI:10.1063/1.5143293 discuss applications of the improved setup for studying the deformation behavior of major materials expected in Earth's lower mantle as well as tantalum carbide.

Figure 3 :

 3 Figure 3: (A) 3D CAD model of the vacuum chamber. (B) Photograph of the vacuum

  (10:1 Epotech 353ND) + kapton gaskets (Fig. 1: 8, 9; Fig. 2C: This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI:10.1063/1.5143293

  Fig.2C: 1a) and serves as heating element surrounding the diamond-anvils. A space is carved

  DOI:10.1063/1.5143293

Figure 4 :

 4 Figure 4: Synthesis of cubic calcium perovskite. The pressure was calculated from the

Figure 5 :

 5 Figure 5: Synthesis of bridgmanite (blue) + ferropericlase (red). Green arrows indicate the

  DOI:10.1063/1.5143293

Figure 6 :

 6 Figure 6: Power -Temperature curves of different experiments. The temperature is read using

  DOI:10.1063/1.5143293 vacuum chamber. The setup is available for users at the Extreme Conditions Beamline P02.2 at DESY, Hamburg and allows for reaching temperatures of up to 1900 K at high pressures (Fig.7).

Figure 7 :

 7 Figure 7: Maximum pressure-temperature-conditions reached in experiments on

16A

  DOI:10.1063/1.5143293 the search for a better gasket material which combines mechanical strength and hightemperature stability. Planet. Inter. 216, 91 (2013).This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI:10.1063/1This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI:10.1063/1the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI:10.1063/1This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI:10.1063/1This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI:10.1063/1This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE ASDOI:10.1063/1.5143293 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI:10.1063/1.5143293

Acknowledgements

This research was supported through the projects "GeoMaX" funded under the Emmy-

Program of the German Science Foundation (MA4534/3-1) as well as grant MA4534/4-1. HM acknowledges support from the Bavarian Academy of Sciences. LM acknowledges support from the US Department of Energy, National Nuclear Security Administration, through the Capital-DOE Alliance Center (DE-NA0003858) and NSF (EAR-1344579 and EAR-1654687). SM acknowledges support from the Institut Universitaire de France and the program PNP of CNRS/INSU. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III and we would like to thank K. Glazyrin for assistance in using Beamline P02.2. Part of the research leading to this result has been supported by the project CALIPSO plus under the Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI:10.1063/1.5143293


Robin Cremer
email: r-cremer@chru-lille.fr

Alexandra Binoche

Odile Noizet

Catherine Fourier

Stéphane Leteurtre

Grégoire Moutel

Francis Leclerc

Are the GFRUP's recommendations for withholding or withdrawing treatments in critically ill children applicable? Results of a two-year survey

Keywords: withdrawing treatments, guideline adherence, intensive care unit, ethics, child

come

Are the GFRUP's recommendations for withholding or

withdrawing treatments in critically ill children applicable? Results of a two-year survey.

Objective: to evaluate feasibility of the GFRUP's guidelines for limitation of treatments in PICU. Design: two-year prospective survey. Settings: 12-bed French PICU at a university hospital.

Patients were included when limitation of treatments was anticipated. Results: among 967 admitted children, 55 were included, with a two-day median delay. They were younger than others (24 months vs. 60), had higher PRISM score (14 vs. 4), higher POPC score at admission (2 vs. 1) -all p<0.002.

Thirty-four died (50% of deaths). A limitation decision was made without meeting for 7 children who all died: 6 do-not-resuscitate orders (DNRO), 1 withholding decision. Decision-making meetings were organized for 31 children, and led to 12 DNRO (6 deaths, 6 survivals), 4 withholding (1 death, 3 survivals), 14 withdrawing (14 deaths), and 1 continuing decision (survival). After limitation, 21 children died (31% of deaths), and 10 survived (POPC 4). Thirteen procedures were interrupted because of death and 11 because of "clinical improvement" (POPC 4). Parents' opinion was obtained after 4 family conferences (for a total of 110 min), 3 days after inclusion. The 1 st meeting was planned for 6 days after inclusion, held on the 7 th day; 80% of parents were immediately informed of the decision, which was implemented 0.5 day after. Conclusions: GFRUP's procedure was applicable in most cases. The main difficulties were anticipating the correct date for the meeting and involving nurses in the procedure. Children for whom the procedure was interrupted because of "clinical improvement" and who survived in poor condition without a formal decision pointed out the need for medical criteria for questioning, which should systematically lead to a formal decision-making process.

In developed countries more than 70% of children die in hospital, mainly in paediatric intensive care units (PICU). [START_REF] Van Der Wal | Circumstances of dying in hospitalized children[END_REF][START_REF] Mccallum | How children die in hospital[END_REF] Forgoing life-sustaining treatment decisions are made for 30 to 40% of dying children. [3 [4] [START_REF] Devictor | Forgoing life-sustaining treatments in children: a comparison between Northern and Southern European pediatric intensive care units[END_REF] Although formal English-language guidelines for withholding or withdrawing treatment in critically ill children are available since the nineties, French-language recommendations were lacking until recently. [START_REF] Aap | American Academy of Pediatrics Committee on Bioethics: Guidelines on foregoing life-sustaining medical treatment[END_REF][START_REF] Aap | Ethics and the care of critically ill infants and children. American Academy of Pediatrics Committee on Bioethics[END_REF][START_REF] Truog | Recommendations for end-of-life care in the intensive care unit: The Ethics Committee of the Society of Critical Care Medicine[END_REF] Because of this lack, and because several studies have demonstrated that French-speaking intensive care units did not follow US guidelines [START_REF] Pochard | French intensivists do not apply American recommendations regarding decisions to forgo life-sustaining therapy[END_REF], the French-speaking group of intensive care organized a workshop, including PICU nurses and physicians, parents, palliative care specialists, philosophers, and persons that had conducted ethics research. This group worked from 1999 to 2000 and its conclusions were published in July 2002 as a book that was disseminated to all French PICUs. [START_REF] Gfrup | Limitations et arrêts des traitements en réanimation pédiatrique[END_REF] Recently, French paediatric guidelines were derived directly from this text and validated by the Ethics Commission of the French Paediatric Society; the proposed procedure is summarized in table 1. [START_REF] Hubert | Limitations et arrêts des traitements actifs en réanimation pediatrique: recommandations du GFRUP[END_REF] Contrary to English language guidelines that regard parents as the most appropriate bearers of decisional authority, French guidelines are more physician centred, recommending that parents choose their level of involvement, without shifting the weight of responsibility for the decision on them.

The purpose of this study was to evaluate the feasibility of the procedure, to record related medical and paramedical time utilization, and to point out ethical problems that could be implied by the procedure itself.

Table 1:

The five steps of the procedure proposed by the French speaking group of intensive care physicians [START_REF] Hubert | Limitations et arrêts des traitements actifs en réanimation pediatrique: recommandations du GFRUP[END_REF].

1.

Questioning about the appropriateness of the treatments -Questioning about the appropriateness the treatments is part of the role of all categories of caregivers. Routinely, it consists of choosing the treatments that give the greatest proportion of medical benefits in comparison to harms.

-When the questioning is expressed by the child or his/her parents, caregivers must inform the physicians so it can be taken in account.

-Physicians must give true information to both parents and paramedical staff, and must encourage and arrange for team questioning during routine staff meetings.

2.

Organizing a special decision-making meeting -Medical reasoning implicitly assumes that the best interests of the child are ensured by medical knowledge. When medical reasoning alone is not able to respond to questioning, physicians must organize a special decision-making meeting in order to take into account factors other than medical.

-This meeting must be anticipated, scheduled and announced in order to permit all caregivers in charge of the child to be present.

Explanation of the decision

-A decision must be made at a special decision-making meeting that must be exclusively devoted to the problem.

-A medical analysis of the situation must be the first step undertaken at the special meeting.

-Following the medical analysis, it may appear that the problem was falsely deemed ethical, and that medical reasoning is able to respond to the questioning. It may also appear that some medical elements were lacking and that the meeting must be rescheduled.

-If the ethical conflict is validated, non medical factors must be taken into account in decision making. It consists of human factors (acceptability of the treatments by the child or his/her parents, quality of life, etc.), and sociocultural factors (ethical and deontological principles, risks of litigation, etc.).

-An authentic debate is proposed for resolving ethical conflicts. All treatment options, from maximal therapy to palliative care must be considered and their consequences must be appreciated.

-Principles of ethics of communication must be respected during the discussion, all arguments must be taken into account, and opportunities for speaking should be fairly managed.

Decision making

-Because debating requires that all caregivers are used as decision-making agents, collegiality is a necessary condition for decision making, but it does not ensure the quality of the decision by itself.

-Collegiality must be considered as a help for the physician making the decision, but it must not shift the weight of the decision onto paramedical staff.

-If there is a consensus, decision to limit life supporting treatments, a modality must be chosen. Decisions could include a do-not-resuscitate order in case of cardiac arrest, withholding new therapies, or withdrawing current therapies.

5

Implementing the decision -A decision must be announced to the child, parents and paramedical staff.

-Time must be given to parents to accept or contest the decision and they must be asked if they want to be present at the bedside when the decision is implemented.

Patients and methods

This prospective study was carried out from September 2002 to August 2004 in a 12 bed

French tertiary PICU at a university hospital. All children that were consecutively admitted during this period were included. A specific paper file was completed during the PICU stay as soon as one member of the medical staff anticipated that an ethics discussion could be necessary. This population was defined as "question raising children".

Results

Between September 2002 and August 2004, 967 children were admitted (7877 days of stay), and 68 died (7%). Median age was 58 months (1-565), PRISM score was 5 (0-52), and length of stay was 3 days (1-575). Discussion on limitation of treatments was considered as necessary in 55 children (5%), with a median two-day delay after admission (0-173). Length of stay of the question-raising children was 14 days (1-178); prevalence of ethical questioning was 8.4 per 100 PICU days of stay.

Characteristics of question-raising children

Significantly, the 55 question-raising children were younger than the others , had a higher PRISM score, higher POPC score at admission, and higher POPC score at discharge . Among them, 34 (59%) died, which represented 50% of all deaths. The 21 question-raising children who survived were younger, had a higher PRISM score and a higher POPC score at discharge than the 878 non question-raising survivors. The POPC score at admission was not different. These data are given in table 2. Among the 55 question-raising children (45%) had chronic disease before admission. Main

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organ failures at admission were: neurological (49%), respiratory (27%), cardiovascular (22%), and digestive (2%). Organ failures leading to questioning were: neurological (83%), cardiovascular (9%), and respiratory (7%). [START_REF] Pollack | Pediatric risk of mortality (PRISM) score[END_REF] 31 (0 -52) 17 (0 -52) p<0.001 POPC at admission [START_REF] Fiser | Assessing the outcome of pediatric intensive care[END_REF] 1 (1 -5) 3 (1 -5) p=0.047 PRISM: Paediatric Risk of Mortality -POPC: Paediatric Overall Performance Category.

Decision-making procedure

The decision-making procedure was interrupted without a formal treatment decision for 24 of the 55 question-raising children, and completed for 31 children, leading in to 12 do-not-resuscitate orders (DNRO), 4 withholding decisions, 14 withdrawing, and 1 decision to continue treatments.

Twenty-one children died after a limitation decision (31% of total deaths). These data are detailed in figure 1. Age, PRISM and POPC scores at admission for the 11 children for whom the decisionmaking procedure was interrupted due to clinical improvement were not different from those for whom the procedure was completed.

In the population for whom the procedure was completed, the median delay for initiating the process was two days after admission. The median delay for obtaining mothers' opinion was 3 days after inclusion and 4 days for fathers (not statistically significant). The first special decision-making meeting was planned 6 days after inclusion, held on the 7 th day after inclusion, and parents were informed of the decision on the same day. There was a positive correlation between the delay of expression of parents' opinions and the date of the first special decision-making meeting (p=0,008). These data are summarized in table 3.

Table 3: dates, delay and time utilisation for decision making procedures

Period before decision

As recommended in the guidelines, a senior expert was asked to give an opinion on prognosis in 25 children, including the 24 for whom the procedure was completed.

During the study, 180 preliminary family conferences were carried out to discuss the possible limitation of treatments, which represented 5131 minutes of medical time. In the population in whom the procedure was completed, there was a median of 4 family conferences and the total duration was 110 minutes (table 3). A nurse was present during 31 family conferences, including 22 for children for whom the procedure was completed. The referring resident was present during 42 family conferences, including 25 for children for whom the procedure was completed.

Thirty-seven mothers expressed wishes, including 23 in the population for whom the procedure was completed. Thirty-three fathers expressed wishes, including 18 in the population for

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whom the procedure was completed. Details of these wishes are given in table 4. a : in this group (except one case), poor prognosis and futility of treatments were simultaneously presented, during a single family conference, because of emergency situation. b : because of the absence of one of the parents at the family conference.

Special decision-making meetings

Thirty-two special decision-making meetings were organized for 24 children: one in 15 patients, two in 7 patients, and three in 1 patient. The duration was 30 minutes (30-110), number of physicians and nursing staff members were 6 (3 -12) and 2 (0-3), respectively. Nurses had worked a median of 4 days at the patient's bedside (0-30). Three special decision-making meetings were organized without any nursing staff member and 9 with a nurse who was at the patient's bedside for the first time. The PICU chief (or his representative) was present at all special decision-making meetings. Parents were informed that there would be a special decision-making meeting in 14 cases, they knew the date in 1, and they were not formally informed in 17.

During the 24 first special decision-making meetings, there were 2 decisions to continue all treatments, 9 DNRO and 12 decisions to limit treatments. During the seven second special decisionmaking meetings, one decision to continue treatments was changed into DNRO, one DNRO was confirmed, and five decisions to continue treatments were changed into a decision to withhold/withdraw the treatments. During the single third special decision-making meeting, the decision of withholding treatments was changed into withdrawing. Final decisions are given on figure was less than one day, lower than reported in South-European countries. This result, supports the hypothesis that formalising the procedure leads to the better preparation of parents for a decision. [START_REF] Devictor | Toward an ethics of communication among countries[END_REF] In our study, the 30% proportion of deaths following a decision to forgo life-sustaining treatments remained close to the 30% proportion reported among South-European countries, and lower than the 47% proportion reported among Northern countries. [START_REF] Devictor | Forgoing life-sustaining treatments in children: a comparison between Northern and Southern European pediatric intensive care units[END_REF] It was also comparable to the proportion reported by two recent studies from countries with a predominant Latin culture. [START_REF] Althabe | Dying in the intensive care unit: collaborative multicenter study about forgoing life-sustaining treatment in Argentine pediatric intensive care units[END_REF][START_REF] Kipper | Evolution of the medical practices and modes of death on pediatric intensive care units in southern Brazil[END_REF] It remains lower than the 53% proportion reported by Burns in a recent prospective study from the USA. [START_REF] Burns | End-of-life care in the pediatric intensive care unit after the forgoing of life-sustaining treatment[END_REF] Moreover, in our study as in Devictor's study of a South-European country group, causes of ethical questioning were largely dominated by neurological failure, whereas respiratory failure dominated in North-European countries. This remaining congruence with data reported from other Latin countries leads us to hypothesise that the implementation of a formal procedure does not change the incidence of ethical questioning or the ethical principles on which the resolution of ethical conflicts are based.

In a previous 4-month study carried out in 33 French PICUs, 80% of decisions were made at a decision-making meeting, a nurse was present in 50% of cases and parents in 6%. [START_REF] Devictor | Forgoing life-sustaining treatments: how the decision is made in French pediatric intensive care units[END_REF] Parents' wishes were known in 72% of cases, 10% of the parents knew that a decision-making meeting would be organised, and decisions were presented to parents in less than 19% of cases. [START_REF] Devictor | Forgoing life-sustaining treatments: how the decision is made in French pediatric intensive care units[END_REF] The paper was accompanied by an editorial entitled "the parents should not be excluded from the decisions of limitation". [START_REF] Hoehn | Parents should not be excluded from decisions to forgo lifesustaining treatments![END_REF] In our study, data about parents' wishes before the decision and their reactions after it was presented (table 4) showed that physicians did not search for informed consent, but for the absence of opposition. The guidelines recommend giving parents the choice of their level of involvement in the procedure, which represents a dual ethical purpose of recording their wishes without shifting the weight of decision onto them. Conceivably, the absence of informed consent may classify these decisions as a form of malpractice, but GFRUP's guidelines claimed that the right of parents to full autonomy does not exclude their right not to take part in decision-making. The positive correlation between the dates of the expression of parents' wishes and dates of decision indicated that parents' autonomy was taken into account. It appears that the GFRUP's guidelines remain more physician-centred (paternalistic?) than policy expectations would suggest for the USA, but in a recent qualitative study, Carnevale et al. have demonstrated that French parents agreed that life-support decisions should be made by physicians. [START_REF] Carnevale | The moral experience of parents regarding[END_REF] Recently, the French law about patients' rights at end of life ratified that the decision must be made by the physician that is in charge of the patient, after recording parents' wishes and asking for the opinion of a colleague. [23,24] Our study had some limitations. First it involved a single PICU, one that participated in the development of the guidelines. Our study must be considered as a pilot study; a twenty-centre prospective study is about to start in few months. The second limitation is due to its self-monitoring design. In order to avoid biases of declarative studies, we took care to only record objective data, such as facts, dates, actors etc.

[25] Because of the absence of an independent investigator, decision motivations and discrepancies between perception by physicians and nursing staff could not be studied. Nevertheless, quantitative studies remain useful for evaluating the implementation and feasibility of guidelines, for inducing local reflection on practices, and for orienting qualitative studies.

We chose to detail all the types of decisions separately (figure 1), instead of pooling in order to perform statistics, because it is more illustrative of the variety of situations and more representative of their complexity. Practices could be optimally surveyed in a permanent PICU network, with a common database. This database could be anonymously fed by members, who would receive their individual position compared with the summary of median practices of the entire group.

CONCLUSION

The GFRUP's guidelines seem to be fully applicable in most cases and to have a positive effect on better formalising procedures, and better informing parents and preparing them for the decision, but probably not modify the ethical principles on which the decisions are based. Main difficulties identified were anticipating the correct date for decision-making meeting and involving nursing staff members in the procedure. Children for whom the procedure was interrupted without a formal decision raised the question: was the decision fair for them? This pointed out the need for medical criteria, which should systematically impose the continuation of the decision-making process toward a formal decision, in order to ensure a fair decision in each case.

  Patients' severity was assessed by the Paediatric Risk of Mortality score (PRISM), and performance at admission and discharge were assessed by the Paediatric Overall Performance Category score (POPC). [12, 13] Dates, durations, places, and actors were recorded at each step of the decision-making process. Parents' wishes were classified into three

categories: maximum supportive care, not expressed, and limitation of treatments. Parents' reactions after the decision were classified into three categories: opposition, resignation, or approval. Results were expressed as median values, and ranges in brackets. Fisher's exact test and Wilcoxon's signed rank test were used for qualitative and quantitative comparisons, respectively, as well as Spearman's test for correlations. P < 0.05 was considered as statistically significant.

Table 2 : Comparison of ethical question-raising and non question-raising children

 2

		Non question raising	Question raising	Comparison
		children	children	(Fisher)
		median (min -max)	median (min -max)
	All children	n = 912	n = 55
	Age (months)	60 (1 -565)	24 (3 -479)	p=0.005
	PRISM score	4 (0 -52)	14 (1 -52)	p<0.0001
	POPC at admission	1 (1 -5)	2 (1 -5)	p=0,019
	POPC at discharge	1 (1 -6)	6 (3 -6)	p<0.0001
	Survivors	n = 878	n = 21
	Age (months)	59 (1 -564)	17 (4 -431)	p=0.002
	PRISM score	4 (0 -41)	10 (1 -35)	p<0.0001
	POPC at admission	1 (1 -4)	1 (1 -4)	p=0.933
	POPC at discharge	1 (1 -5)	4 (1 -6)	p<0.0001
	Deceased children	N = 34	n = 34
	Age (months)	55 (2 -496)	41 (1 -37)	p=0.378
	PRISM score

Table 4 : Parents' wishes before the decisions and reactions after its presentation.

 4

		Group in which procedures were interrupted n = 24	Group in which decision was made without special decision making meeting n = 7	Group in which a special decision making meeting was organized n = 24
		Fathers Mothers	Fathers	Mothers	Fathers	Mothers
	Parents' wishes :
	Limitation	9	10	1	1	18	21
	Maximal treatments	5	3	0	0	0	2
	Not expressed	9	11	6	6	6	1
	Parents' reaction :
	Approval	-	-	1	1	16	17
	Resignation	-	-	0	0	5	5
	Opposition	-	-	0	0	0	0
	Not formally announced	-	-	6 a	6 a	3 b	1 b

Acknowledgments:

We greatly thank Franco Carnevale for its help in writing and reviewing this manuscript.

Decisions were made without a special decision-making meeting for seven children, who all died (6 DNRO, and 1 decision to withhold a liver transplantation project). These children were older (92 months vs. 4, p=0.012), and had a higher PRISM score (29 vs. 11, p=0.009) than those for whom a special decision-making meeting was organized.

Among children for whom the procedure was completed, six decisions were made whereas one of the parents had not formally expressed any wish during the family conferences, and two voiced their opposition to the limitation of treatment. In this group, there was one decision to continue treatment according to parents' wishes, four DNROs, and three withholding decisions.

Presenting and implementing decisions

The decision was presented to parents, during a median 20 minute (10-60) family conference, for 22 of the 24 children for whom a special decision-making meeting was organized, and in one of the seven emergency situations. The decision was approved by at least one of the parents in 18 cases and parents were resigned in 5. In six situations in which a decision was made without a special decision-making meeting, poor prognosis and the futility of treatment were presented during a single family conference. Reactions were not formally expressed and/or recorded.

Delay in implementing the decision was 0.5 day (0-69). Both nurse and physician were present at the bedside during the implementation of the decision in the 14 cases of withdrawing lifesustaining treatments. The option of being present was offered to parents for 13 of the 14 children, and they were present for 6.

Children's outcomes according to decision are indicated in figure 1. All of the seven children for whom a DNRO was given at a special meeting, survived. Among the four children for whom a withholding decision was made at a special meeting, three survived and one died. All the 14 children for whom a decision to withdraw treatments was made at a special meeting died. All the seven children for whom a limitation decision was made without formal meeting died. Eight of the nine children who survived despite DNRO were referred to the paediatric neurology department with a severe encephalopathy, and one returned home for palliative care. The POPC score for these patients was 4 (3-5) at discharge. The POPC score of the 11 patients for whom the procedure was interrupted because of clinical improvement was 4 (1-4) at discharge.

DISCUSSION

In our study, the incidence of questioning about the appropriateness of treatment was 5% of admitted children, representing more than 8% of PICU days. The decision-making procedure was interrupted for 44% of children and completed for 56%. In most cases where the recommendations were applied, the main difficulties encountered were finding an appropriate time for a special decisionmaking meeting and involving the nursing staff in the procedure.

Because our patients were included before questioning began, our study, when compared with previous ones recording modes of death. [3, [4], [START_REF] Devictor | Forgoing life-sustaining treatments in children: a comparison between Northern and Southern European pediatric intensive care units[END_REF], provides original data. The incidence and prevalence of ethical questioning were both high, reflecting a high level of routine questioning as encouraged by GFRUP's guidelines. Question-raising children were younger and had worse severity and performance scores at admission than the others, pointing out previous quality of life and severity of illness as questioning factors. Survivors in the question-raising population had a worse performance score at discharge than other survivors, which points out risk of disability as an other questioning factor. Dead children in the question-raising population had less severe PRISM score than other children who died, pointing out the role of questioning (and probably the role of decision) in mortality rate. The 11 children for whom the procedure was stopped without a formal decision because of "clinical improvement" pointed out the problem of the medical conditions for initiating the procedure.

Was the GFRUP's procedure fair for these 11 children who survived with severe neurological sequels?

Was their situation fairly judged in order to prevent a disability that could not be accepted by their family? Given that they eluded the complete procedure, this question remains unanswered. Definitions of ethical criteria (namely about neurological status and prognosis) that should systematically require the continuation of the process until a formal decision is made should be the next step in developing the guidelines.

Our study also provides data about the feasibility of the procedure. Among the 31 children for whom the procedure was completed, the main GFRUP's recommendations were applicable in most cases, namely early ethical questioning, parents' wishes recording, formal decision-making meeting, and formal presentation of the decision to parents. The seven bedside decisions did not contradict GFRUP's guidelines. Because these children had a higher PRISM score, we can postulate that these decisions actually corresponded to emergency situations, in which planning a special meeting would not be realistic.

The main difficulties in implementing the guidelines were anticipating the correct date for the meeting (mostly scheduled for the following day) and involving nurses in the procedure. Procedural elements that were proposed by GFRUP are strongly inspired by Habermas' philosophical theory about the ethics of discussion [START_REF] Habermas | De l'éthique de la discussion[END_REF]. Authentic debate, which is proposed for resolving ethical conflicts, requires that all caregivers are used as decision-making agents, and thus, that nurses take part in the procedure. In our study, ten special decision-making meetings were organized without a nurse, or with a nurse who was in change of the patient for the first time. In our study, nurses were present at less than 20% of family conferences. This lack of participation contrasted with their constant presence at the patient's bedside at the time of implementation of the decision, corresponding with a more traditional role. In our PICU, conditions for nurses' participation have been previously formally discussed, in order to make it compatible with French legal texts that define their role (literally in French "own role of nurses"). [15] The fact that physicians have previously analysed medical conditions before considering the possible limitation of treatment, was recognized as protecting nurses from transgressing their legal role. The lack of nurses' participation, even partly explained by the difficulties in scheduling family conferences and decision-making meetings, suggested that their level of involvement in the procedure remained lower than ideally conceptualised in the authentic debate philosophical model.

Even if formal US guidelines have been available since 1994, whether practices in US PICUs follow guidelines or not remains unknown. [START_REF] Aap | American Academy of Pediatrics Committee on Bioethics: Guidelines on foregoing life-sustaining medical treatment[END_REF][START_REF] Frader | Forgoing life support across borders: who decides and why?[END_REF] However, data obtained from a recent European study, pointed out interesting trends, which might help assess the effect of guideline implementation in our PICU. This study prospectively compared forgoing life-sustaining treatments in 27 PICUs from South-European countries (mainly French ICUs), vs. 12 PICUs from North-European countries. [START_REF] Devictor | Forgoing life-sustaining treatments in children: a comparison between Northern and Southern European pediatric intensive care units[END_REF].

The authors noticed that the decisions were more often documented in Northern PICUS (100% vs. 48%; p=0.001), that parents' opinions were more often recorded (62 vs. 42%; p=0.06), and that parents were more often informed of the decision (95% vs. 68%; p=0.01). They attributed these differences to the use of guidelines in North-European countries. [START_REF] Aap | American Academy of Pediatrics Committee on Bioethics: Guidelines on foregoing life-sustaining medical treatment[END_REF][START_REF] Aap | Ethics and the care of critically ill infants and children. American Academy of Pediatrics Committee on Bioethics[END_REF][START_REF] Truog | Recommendations for end-of-life care in the intensive care unit: The Ethics Committee of the Society of Critical Care Medicine[END_REF] Our data were in accordance with those obtained from North-European countries; illustrating the positive role of guidelines in formalising and documenting the decisions. Also, the interval between the decision and its application Competing interests: none declared