Laurence Girolami
email: laurence.girolami@univ-tours.fr

Frédéric Risso

Physical modeling of the dam-break flow of sedimenting suspensions

We develop a physical model of the dam-break flow of fine non-cohesive particles initially fluidized by a gas. By revisiting previous experiments, we show that the dynamics of such flows involves two uncoupled phenomena. On the one hand, the settling of the particles is the same as that of a non-flowing suspension, so that the mass flux of particles that deposit can be related solely to the properties of the suspension. On the other hand, the flow of the gas-particle mixture is similar to that of an equivalent fluid of constant density and negligible viscosity. The momentum lost by the flowing mixture is equal to the product of the deposited mass flux and the longitudinal velocity. These properties allow us to model the time duration of the flow as the time taken by the particles to settle and the slope of the final deposit as the ratio between the growth rate of the deposit height and the velocity of the front of the dam-break flow. Finally, these findings lead to the formulation of consistent shallow-water equations involving specific terms of mass and momentum transfer at the bottom wall, which can be used to compute the dense lower layer of ash flows generated by a volcanic eruption. They also provide tools for the interpretation of field measurements by geologists.

I. INTRODUCTION

The fluidization of fine non-cohesive powders by a gas can lead to the formation of a dense, homogeneously expanded suspension that deflates and settles progressively once the gas supply is vanished. The mobility of such fluidized mixtures can be considerable, especially when they travel large distances down gentle slopes, as usually observed in some catastrophic episodes of explosive volcanic eruptions. They represent thereby one of the most important natural hazards encountered in geophysics [START_REF] Rampino | Volcanic winter and accelerated glaciation following the Toba super-eruption[END_REF][START_REF] Robock | Volcanic eruption and climate[END_REF][START_REF] Dartevelle | Origin of the Mount Pinatubo climactic eruption cloud: Implications for volcanic hazards and atmospheric impacts[END_REF]. The physical description of these flows has become a major issue for the prediction of both the eruption time and the surface affected by the deposits, which may depend on the initial conditions at the vent. This step requires therefore the determination of relevant scaling laws that may be achieved first through an experimental analysis, performed in a well-controlled geometry, such as a rectangular dam-break channel, which enables us to both generate a dense homogeneous suspension in the locked reservoir as well as a gravitational sedimenting current that travels down the channel [START_REF] Rottman | Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel[END_REF][START_REF] Simpson | Gravity currents in the environment and the laboratory[END_REF][START_REF] Eames | Aerated granular flow over a horizontal rigid surface[END_REF][START_REF] Hogg | The effects of hydraulic resistance on dam-break and other shallow inertial flows[END_REF][START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Lajeunesse | Granular slumping on a horizontal surface[END_REF][START_REF] Hogg | Lock-release gravity currents and dam-break flows[END_REF][START_REF] Cantero | Granular collapse in a fluid: Role of the initial volume fraction[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF].

Previous studies, conducted in this way, have revealed important features of these flows.

Once released down the channel, the suspension collapses from a height h 0 to form a quasiinviscid current, the front of which travels at a quasi-constant speed U F that scales with the gravitational velocity √ gh 0 [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Lajeunesse | Granular slumping on a horizontal surface[END_REF][START_REF] Hogg | Lock-release gravity currents and dam-break flows[END_REF][START_REF] Cantero | Granular collapse in a fluid: Role of the initial volume fraction[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. As the mixture is flowing, the particles sediment at a velocity U sed and form a deposit at the bottom of the channel that grows at a velocity U agg .

Surprisingly, the values of U sed and U agg measured during the mixture is flowing are found to be approximately constant both in time and all along the channel [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF][START_REF] Girolami | Dynamique et sédimentation des écoulements pyroclastiques reproduits en laboratoire[END_REF][START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF][START_REF] Girolami | Towards a quantitative understanding of pyroclastic flows: Effects of expansion on the dynamics of laboratory fluidized granular flows[END_REF]. Moreover, they are also equal to those determined in the same sedimenting mixture while confined, without flowing, within the locked reservoir. This remarkable result suggests that ash particles within dense natural pyroclastic flows settle at a rate that could be predicted independently of the flow dynamics. Altogether, these results suggest that the flow of the mixture through the channel, hereafter referred to as dam-break flow, and the settling of the particles, hereafter referred to as particle sedimentation, are very weakly coupled.

The objective of the present study is to propose a physical analysis of these results in order to reveal the underlying mechanisms. By assuming that dam-break flow and particle sedimentation are independent, we derive mathematical expressions that relate together the global characteristics of the phenomenon: front velocity U F , sedimenting velocity U sed , overall flow duration T , height h d∞ and length L of the final deposit. These relations are validated by revisiting previous laboratory experiments conducted with volcanic ash by one of the authors [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF][START_REF] Girolami | Dynamique et sédimentation des écoulements pyroclastiques reproduits en laboratoire[END_REF][START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF][START_REF] Girolami | Towards a quantitative understanding of pyroclastic flows: Effects of expansion on the dynamics of laboratory fluidized granular flows[END_REF]. They can be used by volcanologists to infer the flow characteristics from the properties of a deposit. In addition, they can also provide a model for the mass and momentum transfers between the flowing mixture and the bottom wall, which enables the way to shallow-water numerical simulations of pyroclastic flows that travel down variable slopes.

The paper is organized as follows. Section II presents the flow configuration and known results. Section III develops the physical model and compare its predictions to experimental results. Consequences upon the modelling of the flow mixture are drawn in section IV. Final discussion and conclusions are set out in section V.

II. REFERENCE FLOW CONFIGURATION AND KNOWN RESULTS

Despite the multiplication of sophisticated models able to reasonably compute the behaviour of turbulent dilute surges [START_REF] Dobran | Assessing the pyroclastic flow hazard at Vesuvius[END_REF][START_REF] Clarke | Transient dynamics of vulcanian explosions and column collapse[END_REF][START_REF] Todesco | Pyroclastic flow hazard assessment at Vesuvius (Italy) by using numerical modeling. I. Largescale dynamics[END_REF][START_REF] Neri | Multi-particle simulation of collapsing volcanic columns and pyroclastic flow[END_REF][START_REF] Dartevelle | Numerical modeling of geophysical granular flows: 2. Computer simulations of plinian clouds and pyroclastic flows and surges, Geoch[END_REF][START_REF] Esposti-Ongaro | Large-eddy simulation of pyroclastic density currents, Quality and Reliability of Large-Eddy Simulations[END_REF], simulations of dense pyroclastic flows still fail to reliably predict the flow duration, in particular because of a lack of relevant models for the term of bottom friction employed to capture the deceleration and arrest of the suspension during its final course [START_REF] Doyle | Modeling dense pyroclastic basal flows from collapsing columns[END_REF][START_REF] Doyle | A two-layer model for the evolution and propagation of dense and dilute regions of pyroclastic currents[END_REF][START_REF] Meruane | Dynamics of dense granular flows of small-andlarge-grain mixtures in an ambient fluid[END_REF][START_REF] Shimizu | A numerical shallow-water model for gravity currents for a wide range of density differences[END_REF]. Such a scientific lock needs to be addressed first experimentally in order to capture the main features of these flows and to relate the initial suspension geometry and properties to those of the final deposit. Dam-break flow configurations, commonly used in this purpose [START_REF] Lajeunesse | Granular slumping on a horizontal surface[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF], turn out to be the more consistent tool able to provide a local description of the flow and particles trajectories, and thus to infer the key parameters that govern such sedimenting suspensions. Specifically, they can help to understand how the mixture properties can control the pyroclastic flow dynamics. The sedimentation velocity in the non-flowing case (fig 1c) has been recently analyzed [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF] for fine heated particles including volcanic ash of random shape and almost spherical synthetic particles (FCC) [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF]. In any case, it is well described by the following semiempirical expression,

U sed = U ref 8.6 1 - Φ s Φ pack 0.45 with U ref = gρ s (1 -Φ s ) d 2 18 µ f , ( 1
)
where g is the gravity acceleration, ρ s the density of solid particle material, µ f the gas mentation for a given initial heap. Remarkably, it turns out to be sufficient to encapsulate all the geometric properties of the volcanic ash.

Note that eq (1) is valid under specific conditions. First, it requires a high density ratio ρ s /ρ f between the two components of the mixture and a small particle Reynolds number, defined as Re p = ρ f U sed d/µ f . Then, the suspension has to be fully fluidized and homogeneous, which reduces to the case where the solid volume fraction Φ s lies in between the two boundaries, Φ up and Φ low , which respectively represent the limit of fluidization and the limit of stability of the mixture. Above Φ up , particles form arches and a part of their weight is supported by the reservoir walls. Below Φ low , gas bubbles form and the suspension becomes heterogeneous. Between Φ up and Φ low , the particles weight is thus fully supported by the gas whose pressure is hydrostatic. Then, the gas velocity U f (Φ s ) necessary to fluidize the suspension (fig 1c), and measured by means of flowmeters, is equal to the sedimentation velocity U sed (Φ s ), determined from the settling of the top surface. Fully fluidized homogeneous gas-particles suspensions are solely obtained with non-cohesive materials belonging to the group A of the Geldart's classification [START_REF] Geldart | Types of gas fluidization[END_REF] but can expand significantly only with finer or lighter group C powders provided that they are heated at a temperature sufficient (> 100 • C) to remove the effects of moisture, similarly to the volcanic ash investigated in [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF] which joined the group A, while exhibiting lower values of both Φ low /Φ pack and Φ up /Φ pack reported in Table I, with Re p < 0.025 (0.1 ≤ U sed ≤ 1 cm/s). Since Φ low /Φ pack remains quite large for solid gas-particles mixtures, the hydrodynamic interactions between particles play an important role in the regime under consideration. It is therefore not relevant to extrapolate relation [START_REF] Rampino | Volcanic winter and accelerated glaciation following the Toba super-eruption[END_REF] to values of Φ s much lower than Φ low in the expectation of finding the value of an isolated particle.

When the gate is opened, the particle sedimentation is initiated simultaneously to the dam-break flow (figs 1d and 2). The fluidization technique, which enables significant variation of Φ s within the mixture [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF], allows us to distinguish the dynamics of dry granular materials governed by frictional interactions (Φ s > Φ up ) [START_REF] Lajeunesse | Granular slumping on a horizontal surface[END_REF][START_REF] Rondon | Granular collapse in a fluid: Role of the initial volume fraction[END_REF] from that of fully fluidized suspensions (Φ s < Φ up ) [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]. This paper focuses on the second case, which is the subject of the present study. Regarding the sedimentation, U sed is found to be the same as in the non-flowing case [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF][START_REF] Girolami | Dynamique et sédimentation des écoulements pyroclastiques reproduits en laboratoire[END_REF][START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF][START_REF] Girolami | Towards a quantitative understanding of pyroclastic flows: Effects of expansion on the dynamics of laboratory fluidized granular flows[END_REF] and can therefore still be described by eq [START_REF] Rampino | Volcanic winter and accelerated glaciation following the Toba super-eruption[END_REF]. Regarding the dambreak flow, it involves three phases that can be distinguished by considering the velocity U F of the front [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF][START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF]: a brief initial acceleration associated with the column collapse, a second phase where the front velocity remains constant (U F = U F 2 ), and a final deceleration that lasts until the flow ceases. As noted in [START_REF] Roche | Experimental observations of water-like behavior of initially fluidized, dam break granular flows and their relevance for the propagation of ash-rich pyroclastic flows[END_REF], similar phases are observed in the case of a water flow, but the final deceleration involves different mechanisms. The second phase is largely dominant and involves a velocity that is determined by gravity:

U F 2 = k √ gh 0 .
The specific value of k, which depends in a complex way on the initial column collapse, has not been modelled so far. It is observed to vary approximately between the value k = √ 2 corresponding to a vertical free fall and the value k = 2 associated with a dam-break under shallow-water condition [START_REF] Hogg | The effects of hydraulic resistance on dam-break and other shallow inertial flows[END_REF][START_REF] Ungarish | A shallow-water model for high-Reynolds-number gravity currents for a wide range of density differences and fractional depths[END_REF].

At the end of the process, the particles form a deposit characterized by a maximal height h d∞ and a total length L + x 0 (fig 1e).

In the next section, we shall formulate physical hypotheses based on the known features previously reminded and that will allow us to derive expressions able to relate the initial Note that the picture is not a pure side view, but taken from a point above the surface. The whitish zone corresponds to the surface the suspension seen in perspective. The two inserts are pictures of volcanic ash (on the left) and FCC particles (on the right).

conditions of the mixture (h d 0 ,Φ s ,Φ pack ,U ref ) to the global properties of the flow (U sed ,T )

and of the final deposit (h d∞ ,L). The validity of this model will be assessed by revisiting the experiments conducted by Girolami [START_REF] Girolami | Dynamique et sédimentation des écoulements pyroclastiques reproduits en laboratoire[END_REF], which consisted in releasing highly expanded suspensions made with hot volcanic ash and gas from a reservoir down to an impermeable channel (figs 1d,e). These experiments were presented in detail in a series of articles [START_REF] Girolami | Propagation and hindered settling of laboratory ash flows[END_REF][START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF][START_REF] Girolami | Towards a quantitative understanding of pyroclastic flows: Effects of expansion on the dynamics of laboratory fluidized granular flows[END_REF], where extensive information was provided on the local flow dynamics. These data have been reprocessed here such as extracting the bulk flow features required for evaluating the present model. The particles and the range of volume fractions investigated are the same as those studied in our recent work devoted to the sedimentation in a non-flowing condition [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF]. The considered cases involved two samples of natural volcanic ash, Ash 1 and Ash 2 , each made with particles of different shapes and sizes characterized by a specific size distribution, as well as a sample of almost spherical synthetic FCC particles (Table I). The materials were fully fluidized, then released down the channel until motion ceased (fig 2). In a first set of experiments ("Set 1"), performed with all different materials, Φ s was varied by increasing the fluidization velocity, and so the height h 0 of the suspension, while the mass of particles was kept constant. In a second set of experiments ("Set 2"), performed with Ash 1 , Φ s was varied by changing the mass of particles whereas the initial height h 0 was fixed. The reservoir dimension (x 0 =300 mm) and the channel width (w 0 =150 mm) are much larger than the particle size (<250 µm). The front velocity was found to range between 0.75 and 2 m/s. The Reynolds number Re db of the dam-break flow can be estimated by considering that the mixture can be described as an equivalent fluid of density ρ m and viscosity µ m .

According to [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF], the kinematic viscosity µ m /ρ m at large concentrations (Φ s /Φ pack 0.95) hardly reaches that of water. The Reynolds number Re db , based either on the channel width w 0 or the initial height h 0 , is thus larger than 10 5 .

To sum up, the experiments are characterized by the following physical ranges of param-

eters: Re p 1, ρ s /ρ f 1, Φ low < Φ s < Φ up and
Re db 1, which are expected to be representative of the dense basal ash flows generated by volcanic eruptions.

III. PHYSICAL MODEL AND VALIDATION

In this section, we develop a physical description, from previous experimental observations described in section II, in the aim of formulating the model hypotheses that will allow us to derive mathematical relations between the main flow features and the final deposit. Then, we shall validate these predictions by comparison with experiments.

A. Hypotheses and predictions

Our flow model is based on the three following hypotheses. Hypothesis H1 amounts to neglect the existence of the short acceleration and deceleration phases of the dam-break flow. The front velocity is thus equal to its average value, which is the ratio between the total length L traveled by the flow and its total duration T ,

U F = L T . (2)
Hypotheses H2 and H3 imply together that the particle sedimentation velocity within the moving layer is given by eq (1) and only depends on the initial particle volume fraction Φ s , the particles properties involved in U ref and Φ pack , and gravity acceleration. By considering the mass conservation of particles between a homogeneous suspension at concentration Φ s and a deposit at concentration Φ pack , these two hypotheses also lead to the following relation between the sedimentation velocity U sed and the aggradation velocity U agg of the deposit,

Φ s U sed = (Φ pack -Φ s )U agg . (3)
Note that even if the sedimentation velocity is oriented downward while the aggradation velocity is oriented upward, U sed and U agg are chosen here to be positive. Since the growth velocity of the deposit is constant, its height h d (x, t) can be obtained as the product of U agg by the time t d of deposition. In the reservoir (x ≤ x 0 ), t d is simply the time t elapsed since the stop of the gas supply. In the channel (x > x 0 ), it is the time taken between the gate opening and the considered distance reached by the mixture,

t d = t -(x -x 0 )/U F . The deposit height is hence given by h d (x, t) = U agg t for x ≤ x 0 , (4)
h d (x, t) = U agg t - x -x 0 U F for x > x 0 . (5)
According to eqs (4)-( 5), the shape of the deposit is represented by the dark gray zone on fig 1d-e. Within the reservoir, its top forms a horizontal line located at a height that increases with time according to eq [START_REF] Rottman | Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel[END_REF]. Within the channel, it is a straight line with a negative slope s that does not vary in time,

s = ∂h d (x, t) ∂x = - U agg U F = - T U sed L 1 Φ pack Φs -1 . ( 6
)
At the end of the process (fig 1e), the shape of the final deposit is hence described by the juxtaposition of a rectangle of length x 0 and height h d∞ = U agg T with a triangle of height

x 0 and length L. Since, according to hypothesis H2, their concentrations are the same, the mass conservation implies that the volume of final deposit is equal to that of the initial bed (fig 1a). This allows us to relate the final deposit height, h d∞ , to that of the initial packed bed, h d 0 ,

h d∞ = βh d 0 with β = x 0 x 0 + L 2 , (7)
Using eqs ( 4), ( 3) and ( 7), the total flow duration can be written as

T = h d∞ U agg = β h d 0 U agg = β h d 0 U sed Φ pack Φ s -1 . (8)
This result helps us to understand how the particle sedimentation and the dam-break flow combine to determine T . The dam-break flow stretches the gas-particle mixture by a factor 1/β > 1 in the longitudinal direction and squeezes it by a factor β < 1 in the vertical direction. This deformation does not change the particle concentration that remains homogeneous, neither alters the particles settling that occurs at a constant velocity. However, the time taken by the particles to settle is reduced by a factor β compared with the non-flowing case because the travel to the bottom wall is reduced by the same amount. Since the flow lasts until all the particles have deposited, T is thus also reduced by a factor β.

It is worth mentioning that a constant particle concentration also implies that a rapid deformation of the suspension due to the dam-break flow does not generate any pressure gradient within the interstitial gas, which therefore remains hydrostatic, as in the nonflowing sedimentation case. Therefore, no pore-pressure effect is expected to occur provided that the gas is assumed to be incompressible. This condition is fulfilled when the pressure at the bottom of the suspension is small compared to atmospheric pressure, which is the case for a moving layer of less than one or two meters thick. The present results are thus applicable without correction to small-volume pyroclastic flows.

B. Experimental validation

Now, we compare our model predictions with experimental results.

Figure 3 shows the experimental ratio L/(T U F 2 ) as a function of the normalized initial particle concentration Φ s /Φ pack . Whereas the front velocity significantly varies with the particle concentration, this ratio is remarkably constant and reasonably close to unity in all cases. We can therefore conclude that hypothesis H1 is reasonable. In the rest of this section, we consider a constant front velocity given by eq [START_REF] Robock | Volcanic eruption and climate[END_REF].

Black curves in fig 4 show various experimental profiles of the final deposit in the channel

(x 0 ≤ x ≤ L).
In agreement with our model, the experimental deposits have almost a triangle shape. The blue curves are straight lines that connect the points of coordinates (0,βh d 0 ) and (L,0), where the values of h d 0 and L are taken from the experiments. They fit the experimental profiles quite well, which confirms the validity of eq [START_REF] Hogg | The effects of hydraulic resistance on dam-break and other shallow inertial flows[END_REF]. slope and the ratio between the front and sedimentation velocities.

Finally, we examine the total flow duration. Figure 6a shows the experimental values of T as a function of Φ s /Φ pack . We observe that T strongly depends on the particle concentration and varies between the various cases involving different materials or test conditions. Fig- predicted by eq [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF].

ure 6b shows the ratio between the experimental values of T and those calculated by means of eq [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF], where again the values of U sed are taken from non-flowing experiments. This ratio remarkably gather the results around unity whatever the experimental conditions, confirming the relevance of eq [START_REF] Roche | Experimental study of gasfluidized granular flows with implications for pyroclastic flows emplacement[END_REF].

Despite the rather crude nature of hypotheses H1-3, the relations they allow us to derive between the initial conditions before release, the global characteristics of the flow of the mixture and the geometry of the final deposit are in good agreement with experimental results. These hypotheses therefore draw a correct first approximation of the dam-break flow of sedimenting suspensions. The proposed relations thus constitute a reliable guide for the analysis of laboratory flows as well as natural ones.

IV. CONSEQUENCES ON THE MODELLING OF THE FLOW MIXTURE

We have analyzed the flow deposit left by a highly-expanded non-cohesive gas-particle suspension which has flowed at high Reynolds number in a horizontal straight channel. We showed that all the features of the final deposit, as well as the overall time duration of the flow, can be explained by assuming that the particle sedimentation is the same as that observed in a non-flowing homogeneous suspension which settles in a tank. That means that the sedimentation process is not influenced by the complex flow of the mixture through both the fluidization tank and the channel. It occurs at a constant velocity U sed (hypothesis H3) while maintaining a constant particle volume fraction (hypothesis H2). This conclusion has been obtained by taking advantage that the front velocity U F of the dam-break flow in the investigated configuration remains constant during almost the entire process (hypothesis H1). However, in contrast with the sedimentation velocity which can be determined from the sole knowledge of the initial properties of the suspension [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF], the dam-break flow does depend on the geometry of the channel. In particular, U F is not expected to be constant in general and, for example, will change if the channel slope varies. The prediction of the profiles of the suspension height, h(x, t), and of the average horizontal velocity of the mixture, ũ(x, t), as well as the prediction of U F (t) in any geometry, requires us to solve the equations of mass and momentum conservation. Although the flow within the fluidization reservoir involves both significant horizontal and vertical velocities, the flow of the mixture within the channel is almost parallel and can be described under the shallow-water approximation.

Shallow-water equations are commonly used to describe the flow of a heavy fluid into a lighter one [START_REF] Hogg | The effects of hydraulic resistance on dam-break and other shallow inertial flows[END_REF], as well as that of a fluid laden by solid particles into the same fluid [START_REF] Bonnecaze | Particle-driven gravity currents[END_REF].

The reader is referred to [START_REF] Ungarish | An introduction to gravity currents and intrusions[END_REF] for a comprehensive exposition of these equations in various possible configurations. Here, we consider a suspension of particles in a gas of negligible density flowing at high Reynolds number. The top of the suspension (z = h) is a free surface at atmospheric pressure through which there is no exchange of mass or momentum. At the bottom (z = h d ), the suspension flows above a rigid deposit with which it exchanges mass at rate ṁ and where it undergoes a friction τ p . Under these conditions, the one-dimensional equations write

∂(ρ m δ h ) ∂t + ∂(ρ m δ h ũ) ∂x = ṁ, (9)
∂(ρ m δ h ũ) ∂t + ∂(ρ m δ h ξ ũ2 ) ∂x + z=h z=h d ∂p ∂x dz = τ p , ( 10
)
where p is a local pressure, ρ m = Φ s ρ s is the mixture density, ũ = 1 δh z=h z=h d u dz is the velocity u of the mixture averaged over the thickness δ h = h -h d , ξ = 1 ũ2 δh z=h z=h d u 2 dz is a correction factor accounting for the shape of the velocity profile, which is unity when u is independent of z.

In general, an additional equation is required to account for the evolution of the particle concentration [START_REF] Bonnecaze | Particle-driven gravity currents[END_REF]. However, for the type of flows under consideration, the concentration Φ s remains constant throughout the flowing layer and equal to Φ pack within the deposit. It is worth mentioning that the consistency of our model with a constant particle concentration is ensured by the particular relation, given by eq. 3, that exists between the sedimentation velocity and the aggradation velocity. Note that shallow-water equations are often formulated in terms of the whole height h(x, t) of the gas-particle mixture, which is the sum of the height h d (x, t) of the growing deposit and the thickness δ h (x, t) of the flowing mixture.

Here, we have preferred to express them in terms of δ h (x, t) because it is better suited to describe transfers between the deposit and the flowing layer. Moreover, the fact that the aggradation velocity is constant leads to a simple expression for the deposit height,

   h d (x, t) = 0 for 0 ≤ t ≤ t x , h d (x, t) = (t -t x )U agg for t > t x , (11)
where t x is the time taken for the front to reach the location x, which is equal to (x -x 0 )/U F in case the front velocity is constant.

Numerical simulations of the dam-break flow of such a suspension in a channel, based on shallow-water equations, are presented in [START_REF] Shimizu | A numerical shallow-water model for gravity currents for a wide range of density differences[END_REF]. The solved equations are similar to eqs ( 9)-( 10), but written in terms of whole thickness h(x, t) instead of the thickness δ h (x, t) of the sole moving layer and ṁ is thus taken equal to zero. By modelling τ p as a viscous friction, the authors could found a correct front velocity for phase 2 but largely overestimated the total time duration T of the flow. Finally, they introduced an additional solid friction to force the flow to stop in a reasonable time. Such a combination of solid and viscous frictions is often considered to interpret such flows [START_REF] Doyle | Modeling dense pyroclastic basal flows from collapsing columns[END_REF][START_REF] Doyle | A two-layer approach to modelling the[END_REF][START_REF] Procter | Mapping block-and-ash flow hazards based on Titan 2D simulations: a case study from Mt. Taranaki, NZ[END_REF][START_REF] Kelfoun | Suitability of simple rheological laws for the numerical simulation of dense pyroclastic flows and long-runout volcanic avalanches[END_REF][START_REF] Shimizu | The run-out distance of large-scale pyroclastic density currents: A two-layer depth-averaged model[END_REF]. However, we have shown that T is not determined by the friction on the channel bottom but is controlled by the time taken by the particles to settle. The present results actually lead to simple expressions for ṁ and τ p when eqs 9-10 are written in terms of δ h .

The mass transfer from the moving layer to the deposited layer is given by the product of the aggradation velocity and the ratio between the volume fractions of these two layers,

ṁ = - Φ pack Φ s ρ m U agg = - Φ pack (Φ pack -Φ s ) ρ m U sed . (12)
The Reynolds number Re db of the flow mixture is larger than 10 5 in laboratory experiments and much larger in natural flows, which implies a very thin boundary layer. Considering that the mixture moves as a plug flow above a fixed deposit is therefore a reasonable assumption, substantiated by a constant front velocity observed in experiments and by the velocity profiles determined with an optical flow method [START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF]. In the absence of any significant vertical shear within the moving layer, ξ = 1 and as the pressure is hydrostatic, this leads

to z=h z=h d ∂p ∂x dz = z=h z=h d ∂ ∂x (ρ m g (h -z)) dz = ρ m g 1 2 ∂(δ 2 h ) ∂x + δh ∂h d ∂x . (13)
Furthermore, the momentum lost by the moving layer is only due to the momentum lost by the particles that deposit, passing from a velocity u to rest, so that

τ p = ṁ u , (14)
which is identical to the friction term of the model L defined in [START_REF] Ungarish | An introduction to gravity currents and intrusions[END_REF]. Under these conditions and accounting for the fact that ρ m is constant within the moving layer, shallow water equations write

∂δ h ∂t + ∂(δ h ũ) ∂x = - Φ pack (Φ pack -Φ s ) U sed , (15)
∂(δ h ũ) ∂t + ∂(δ h ũ2 ) ∂x + g 2 ∂(δ 2 h ) ∂x + g δh ∂(h d ) ∂x = - Φ pack (Φ pack -Φ s ) U sed ũ . (16)
Thus, combining eqs ( 15)-( 16) with a model for the sedimentation velocity [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF] should constitute the first-order approximation of a dense layer of pyroclastic flows along the major part of its course, excluding the initial formation which is fully three-dimensional and the very last stage, when the thickness of the boundary layer in which the particles velocity drops from ũ to rest (probably of the order of a few particle diameters) becomes comparable with that of the moving layer. Solving these equations is beyond the scope of this paper. However, it is interesting to estimate τ p from experimental data by making some approximations about the flow in order to discuss the role it plays in the whole process.

The magnitude of τ p can be evaluated by inserting the front velocity U F in eq [START_REF] Girolami | Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows[END_REF]. Then normalizing by ρ s gd, we can build a Shields number,

Sh = τ p ρ s gd , (17)
which compares the friction that forces a particle to stop when depositing with its weight.

Figure 7a shows the experimental values of Sh. In all experimental configurations, Sh is (d) Energy D db lost by dam-break flow due to τ p , calculated under the assumption of a linear longitudinal velocity profile, eq [START_REF] Doyle | Modeling dense pyroclastic basal flows from collapsing columns[END_REF]. mainly sensitive to the particle concentration, becoming four times larger when Φ s /Φ pack increases from 0.65 to 0.95. In any case, it is larger than 20, which means that the cohesion of the deposit is not due to gravity but necessarily results from the solid friction between the particles.

Another way to assess the role of τ p is to analyze the respective contributions of the dam-break flow and of the sedimentation process to the total dissipation of mechanical energy. The total energy that is dissipated during each experimental test is equal to the potential energy of gravity that is released between the beginning and the end of the flow:

E p = M g(h g0 -h gd )
, where M is the total mass of particles, h g0 the elevation of the center of mass of the fluidized mixture before its release in the channel (fig 1b), and h gd that of the final deposit (fig 1e). The value of E p , which can easily be calculated from experimental data, is plotted in fig 7b. Note that it varies significantly according to experimental conditions. Then, we consider the sedimentation process. The dissipation rate per unit volume ε sed during fluidization experiments within the initial reservoir -with the gate to the channel closed -can be obtained as the product of the fluidization velocity, U f , and the pressure gradient within the bed of particles, Φ s ρ s g. Since fluidization and sedimentation processes were shown to be equivalent for a homogeneous suspension [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF], the dissipation during the sedimentation process is given by the same expression with taking U sed in place of U f ,

ε sed = Φ s ρ s gU sed . (18)
Because the sedimentation is independent of the dam-break flow, the value of ε sed given by eq [START_REF] Todesco | Pyroclastic flow hazard assessment at Vesuvius (Italy) by using numerical modeling. I. Largescale dynamics[END_REF] is still relevant for the flowing suspension. The energy dissipated by the sedimentation process is therefore

D sed = ε sed T 0 ϑ(t)dt, (19)
where the volume ϑ(t) of the suspension at time t represents its initial volume ϑ 0 minus the deposited volume,

ϑ(t) = ϑ 0 + T 0 ṁ ρ m w 0 x F (t)dt , (20)
where x F (t) = (x 0 + U F t) is the position of the front and w 0 the width of the channel.

Values of D sed , computed by applying eqs ( 18)- [START_REF] Dartevelle | Numerical modeling of geophysical granular flows: 2. Computer simulations of plinian clouds and pyroclastic flows and surges, Geoch[END_REF] to experimental data and normalized by E p , are plotted in fig 7c. It is interesting to note that the results of the four cases are similar despite significant differences in the total dissipated energy. D sed strongly decreases with Φ s /Φ pack , which indicates that it is mainly controlled by the particle concentration.

However, in any case, the sedimentation contributes less than 10% of the total dissipation. Now, let us consider the energy D db that is dissipated by the dam-break flow. We start by considering the mechanical energy E db which is lost by the moving layer. Because we assume a plug flow, no dissipation occurs within the moving layer and E db reduces to the work of τ p . After summation along the channel (x 0 < x < L) and over the time interval during which the flowing mixture is present ((x -x 0 )/U F < t < T ), we have

E db = - L x0 T x-x 0 U F w 0 τ p u(x, t) dtdx . (21)
Since we do not know the velocity profile in the experiments, we propose to estimate E db by assuming a linear evolution between the reservoir wall at x = 0 and the front position x F (t) which moves at constant velocity U F ,

u(x, t) = (x/x F (t)) U F . (22)
This represents a crude assumption, which is however probably a reasonable first-order approximation since the mixture surface h(x) is observed to be rather smooth and regular (fig 2). One part of E db corresponds to the energy D db that has been dissipated in heat within the boundary layer, while a second part is associated to the potential energy of gravity that has been transferred to the deposit, so that

D db = E db -M gh gd . (23)
Values of D db , computed from experimental data by means of eqs ( 22)-( 21), are plotted in fig 7d. Despite the assumption made regarding the velocity profile and the fact that our model is not expected to be valid during the first and the last stages of the flow, D db /E p is found to be of the order of unity and does not show any well defined trend to evolve with Φ s /Φ pack . We can thus conclude that the present model of τ p is consistent with the experimental data.

V. CONCLUDING REMARKS

The lower layer of pyroclastic flows is made of a gas laden with fine non-cohesive ash particles. Its properties can be investigated by means of laboratory experiments. By revisiting the characteristics of the final deposit and the total time duration measured in such experiments, distinctive properties of these flows have been revealed, which shed light on their dynamics and draw guidelines for the modelling of natural flows of ash generated by a volcanic eruption.

The most striking feature of such flows is the absence of a significant coupling between the sedimentation process and the overall flow of the mixture. Both the volume fraction and the sedimentation velocity of the particles are found not to be influenced by the rapid flow in the channel, which however involves a strong elongation of the mixture in the longitudinal direction. This means that the particles concentration Φ s of the flowing mixture can be considered to be constant in space and time. Also, it implies that the sedimentation velocity U sed is the same than that measured in a non flowing mixture confined within a reservoir, which has been modeled in a previous work as a function of the ratio Φ s /Φ pack between the particle volume fraction and its value at packing [START_REF] Girolami | Sedimentation of gas-fluidized particles with random shape and size[END_REF]. Because Φ s is constant, the mass flux, ṁ, of particles that settle down and the growth velocity U agg of the deposit are directly related to U sed and can be determined from Φ s /Φ pack .

Furthermore, the mixture can be described as an equivalent fluid of constant density ρ m and viscosity µ m . The Reynolds number of the flow mixture is larger than 10 5 in laboratory experiments and much larger in natural flows. In addition, the contribution of the sedimentation process to the dissipation of mechanical energy turns out to be small. Therefore, the mixture can be reasonably approximated as inviscid and moving as a plug flow at velocity u.

The momentum flux that leaves the flowing mixture is thus determined by the momentum lost by the particles as they deposit, τ p = ṁu.

During the longest part of their run, such flows are quasi-parallel and the evolution of both the thickness and the velocity of the moving mixture can be described by shallowwater equations including ṁ and τ p as sink terms of mass and momentum, respectively. The present analyzis of experiments performed in a horizontal channel indicates that this should lead to a good prediction of the total flow duration and of the deposit shape, provided that the front velocity is correct. In addition, numerical solving of shallow-water equations for an inviscid fluid in a similar geometry leads to a constant front velocity in agreement with experiments [START_REF] Shimizu | A numerical shallow-water model for gravity currents for a wide range of density differences[END_REF]. We are therefore confident that shallow water equations with the sink terms proposed here constitute a good tool to predict natural flows of hot dense volcanic ash in any geometry with smooth slope variations, as it is the case when such flows travel down valleys.

Beyond the fact that these equations allow to compute the complete longitudinal evolution of the horizontal velocity and that of the mixture height, the findings of this study can provide precious hints for the interpretation of the geologist's field measurements. As an illustration, let us consider that the following quantities can be estimated from the analysis of sediments: the total run-out distance L, the thickness of the deposit h d∞ , and the slope of the deposit s. Then, if the properties of the ash particles (size, density, packing fraction Φ pack ) can be determined from the analysis of the sediments, the relation between the aggradation velocity, U agg , and the particle volume fraction, Φ s , of the flowing mixture can be estimated.

Combining the results of this study, we have the four following relations, U agg = f (Φ s /Φ pack ), s = U agg /U F , h d∞ = T U agg and U F = L/T , from which the four unknowns Φ s , U agg , U F and T can be evaluated. Of course, if the flow dynamics is computed from shallow-water equations, variations of the topography of the valley can be taken into account to interpret variations of the flow deposit along the flow path.

Figure 1

 1 Figure 1 describes the successive steps of a typical experiment of the dam-break flow of a fluidized suspension. First, the particles are poured into a locked reservoir in order to form a packed bed of height h d 0 (fig 1a). Then, a gas is supplied from the bottom at a given velocity U f such as the suspension expands to a height h 0 at a solid volume fraction Φ s (fig 1b). From that point, two kinds of experiments can be carried out: a first nonflowing defluidization process is performed by stopping the gas injection while the reservoir remains locked (fig 1c); a second flowing and defluidization process is obtained by opening the channel gate simultaneously to the stop of fluidization (fig 1d).

FIG. 1 .

 1 FIG. 1. Schemes of the various experimental configurations: (a) packed state; (b) homogeneously fluidized and expanded suspension; (c) non-flowing defluidization process; (d) simultaneous flow and defluidization process performed through the dam-break flow; (e) final packed deposit after flow has ceased.

FIG. 2 .

 2 FIG. 2. Picture of the dam-break flow of an expanded suspension of volcanic ash heated at 180 • C.

-

  H1. The front velocity U F remains constant during the whole flow duration. -H2. During propagation, the suspension forms two distinct homogeneous and overlying layers, as illustrated in fig 1d: (1) at the bottom, a deposit of volume fraction Φ pack equal to both that of the initial random loosely packed bed (fig 1a) and that of the deposit obtained after defluidization in the non-flowing case (fig 1c); (2) above, a suspension, in which the volume fraction Φ s remains constant during the flow and equal to that of the initial fluidized state (fig 1b). -H3. Within the moving layer (fig 1d), the particles settle at a velocity U sed that is the same as in a non flowing suspension (fig 1c).

FIG. 3 .

 3 FIG. 3.Experimental ratio between the average front velocity , L/T , and the constant velocity of the second phase of the dam-break-flow, U F 2 , as a function of Φ s /Φ pack , for all experiments.

Figure 5 FIG. 4 . 2 FIG. 5 .

 5425 Figure 5 compares the experimental slopes of the final deposit, h d∞ /L, to values calculated by means of eq (6), where U sed is taken from non-flowing experiments at the same Φ s /Φ pack . Both these quantities, plotted on fig 5a as a function of Φ s /Φ pack for all experiments, strongly vary with the concentration. However, their ratio, plotted on fig 5b, is almost constant. It is slightly larger than unity because the average velocity L/T slightly underestimates the front velocity U F 2 of the second flow phase during which the velocity is truly constant (fig 3). This result confirms that eq (6) gives a good approximation of the relation between the deposit

1 Ash : set 2 FCCFIG. 6 .

 126 FIG. 6. Assessment of the model regarding the total duration T . (a) measured values of T as a function of Φ s /Φ pack , for all experiments. (b) Ratio between measured values of T and values

FIG. 7 .

 7 FIG. 7. Analysis of the wall friction τ p and of its contribution to the dissipation from experimental data. (a) Shields number comparing wall friction to particle weight; (b) Potential energy E p released during the total flow duration; (c) Energy D sed dissipated by the sedimentation flow;

TABLE I .

 I low /Φ pack -Φ up /Φ pack 0.66-0.94 0.66-0.95 0.78-0.91 Properties of the materials used in the experiments.

	Solid particle density ρ s (kg m -3 )	1600	1490	1420
	Mean particle equivalent diameter d (µm)	80	65	71
	Range of concentration: Φ


K Zrikem

G Song

A Ait Aghzzaf

M Amjoud

D Mezzane

A Rougier
email: aline.rougier@icmcb.cnrs.fr

UV treatment for enhanced electrochromic properties of spin coated NiO thin films

Keywords: NiO thin films, Sol-gel, UV treatment, Electrochromic properties

Nickel oxide thin films were deposited by sol-gel combined with spin coating method. Herein, the influence of the concentration of the precursor, kind of solvents, stabilizers and type of final treatment (calcination and UV treatment) on the structural, morphological, and electrochromic properties of NiO thin films is reported. Enhanced electrochromic properties, corresponding to a modulation of the optical transmittance under an applied voltage, are established for NiO thin films prepared with methanol as solvent, Triton X-100 as stabilizer and treated by UV using a lamp with low power of 30 W for 5 h. These findings highlight the benefit of using UV treatment, as replacement of annealing step for enhanced NiO electrochromic properties.

Introduction

More recent attention has focused on the issues of energy efficiency that characterize the architecture of this century leading to the development of innovative glazing systems. This aims at reducing heat loss and controlling incoming solar radiation in order to minimize solar gain in summer and maximize it in winter. For this purpose, electrochromic system, able to control the amount of light and heat entering in the interior depending on the seasons, offers key solutions in the form of smart windows [START_REF] Casini | Smart windows for energy efficiency of buildings[END_REF][START_REF] Lampert | Advanced in smart materials technologies -Window[END_REF][START_REF] Granqvist | Electrochromic for smart windows: Oxide-based thin films and devices[END_REF]. Among electrochromic materials, nickel oxide (NiO) has received significant attention due to its anodic coloration leading to neutral color devices when combined with WO3 [START_REF] Rocha | Influence of cycling temperature on the electrochromic properties of WO3 //NiO devices built with various thicknesses Solar Energy Materials and Solar Cell[END_REF].

Electrochromic phenomenon is commonly described as a simultaneous injection/extraction of electrons and ions into/from electrochromic materials [START_REF] Deb | Opportunities and challenges of electrochromic phenomena in transition metal oxides[END_REF]. Indeed, it is generally accepted that the switch from a transparent to a brownish state in anodically colored NiO is related to the redox reactions from Ni 2+ to Ni 3+ states associated with either H + or Li + (de)insertion.

Interestingly, in our group, in the past few years, coloration associated with electrochemical cycling in electrolyte without small cations was reported for non stoichiometric nickel oxide thin films, emphasizing the complexity of the EC mechanism [START_REF] Moulki | Electrochromic performances of nonstoichiometric NiO thin films[END_REF]. The latter also results from the numerous techniques used to grow NiO thin films leading to films of various crystallinities, morphologies and compositions (i.e. Ni/O ratio) [START_REF] Wang | The effect of the oxygen ratio control of DC reactive magnetron sputtering on as-deposited non stoichiometric NiO thin films[END_REF].

Up to know, NiO thin films have been deposited using RF sputtering [START_REF] Chen | Characterization and properties of NiO films produced by RF magnetron sputtering with oxygen ion source assistance[END_REF], co-precipitation method [START_REF] Rahdar | NiO Nanoparticles: Synthesis and Characterization[END_REF], electrochemical deposition [START_REF] Sonavane | Efficient electrochromic nickel oxide thin films by electrodeposition[END_REF], spray pyrolysis [START_REF] Cattin | Properties of NiO thin films deposited by chemical spray pyrolysis using different precursor solutions[END_REF][START_REF] Patil | Preparation and characterization of spray pyrolyzed nickel oxide (NiO) thin films[END_REF], etc., but in the development of soft chemistry, sol-gel method was shown to be one of the most attractive techniques, owing to its simplicity, low cost, and possibility of thin films deposition on large area and flexible substrates at room temperature using UV light [START_REF] Cerc | Sol-Gel prepared NiO thin films for electrochromic applications[END_REF][START_REF] Turgut | Determination of certain sol gel growth parameters of nickel oxide films[END_REF][START_REF] Garcia-Miquel | Nickel oxide sol-gel films from nickel diacetate for electrochromic applications[END_REF]. In addition, the morphology and structural properties of thin films deposited by sol-gel process are very sensitive towards the experimental conditions such as type and concentration of starting materials, pH, nature of solvent, temperature, time of reaction, and drying processes that affect the rate of hydrolysis and condensation reactions.

In this paper, NiO thin films were prepared by sol-gel method combined with spin coating technique. The influence of the concentration of the precursor, solvents, stabilizers and the type of final treatment (calcination and UV treatment) on structural, morphological, and electrochromic properties of NiO thin films is discussed. This study sheds new light on the advantage of UV treatment for NiO thin films deposition suitable for a wide range of substrates, confirming our earlier results on the benefit of this room temperature treatment for nice electrochromic properties [START_REF] Danine | Room temperature UV treated WO3 thin films for electrochromic devices on paper substrate[END_REF].

Experimental

Materials and methods

All the chemical reagents used were of analytical grade and used without further purification.

Several parameters were varied in order to optimize the deposition conditions of NiO thin films by sol-gel via spin coating method. The flowchart of the protocol is shown in Fig. 1.

Nickel acetate (Ni(OCOCH3)2. 4H2O), triton X-100 (C14H22O(C2H4O)n (n=9-10)) or CTAB (C19H42BrN), and methanol (CH3OH) or water (H2O) were used as precursor, stabilizers and solvents, respectively.

The prepared sol solutions were mixed in required amounts and stirred at ambient temperature for 1 h, then at 70 °C for an additional hour and finally at ambient temperature for 4 h. ITO coated glass (commercialized by Solems with a resistance of 80 Ω/sq) was used as substrate.

The obtained sol solutions with different nickel acetate concentrations using both stabilizers in two different solvents, namely water and methanol, were coated on substrates rotated with velocity of 4000 rpm for 30 s.

After deposition, each layer was dried at 175 °C for 20 min. For each thin film, this procedure was repeated 6 times, leading to thickness of hundred nanometers to few micrometers depending on the precursor concentration. The thickness of the films was measured by using Talley Step Profilometer. As an example, for a nickel concentration of 0.3 M, the films thickness is about 470 nm ± 50 nm.

As a final step, the as-grown films were exposed (i) at 300 °C for 2 h in air ambient or (ii) under a UV light for 1 h using a lamp of 160 W or 5 h using a lamp of 30 W.

Characterizations

The film structure was determined by X-ray diffraction using a PANAanalytical X'pert MPD diffractometer with Cu-kα incident radiation. The morphology of the films was characterized by Scanning Electron Microscopy (SEM) (Hitachi Tabletop microscope TM-1000). Cyclic voltammograms (CVs) were recorded on a Biologic potentiostat using a three-electrode cell consisting of Glass/ITO/NiO as working electrode, a Pt sheet as counter electrode and a saturated calomel electrode as reference electrode (ESCE(V) = 0.234 mV/ENH). These electrodes were soaked in 1 M KOH electrolyte (purity (99.99%)). The optical transmittance measurements were carried on a Varian Cary UV-Visible NIR spectrometer. G. : Fm-3m). The cell parameter of 4.188 Å agrees well with the one reported in the literature for NiO while it is slightly higher than the one of the bulk (4.167 Å) [START_REF] Mendoza-Galvan | Comparison of the optical and structural properties of nickel oxide-based thin films obtained by chemical bath and sputtering[END_REF]. An average crystallite size of 55 Å was estimated using the Scherrer formula L = 0.89 λ/βcosθ; where L is the average crystallite size in nm, λ = 0.154056 nm, β the full half-width and θ the diffraction angle.

Results and discussion

Influence of the precursor concentration, solvents and stabilizers nature

Optical properties

The visual appearance of the as deposited films shows a slight brownish coloration of which intensity increases with molar concentration due either to a thickness effect and /or a slight departure from the NiO stoichiometry (i.e. presence of Ni 3+ in Ni1-xO thin films). The optical transmittances of the as-deposited thin films elaborated with different precursor concentrations 0.1 M, 0.3 M and 0.5 M and annealed at 300 °C for 2 h in air ambient are presented in Fig. 3a.

In the as-deposited state, NiO thin films with 0.1 M and 0.3 M exhibit a rather high transparency, while the NiO film with 0.5 M is characterized by a low value of transmittance 30 % at 550 nm against 80 % and 78 % for NiO films with 0.1 M and 0.3 M, respectively [START_REF] Nabeel | Effect of solution molarity on structural and optical properties of nickel oxide thin films prepared by chemical spray pyrolysis technique[END_REF].

In respect of the optical properties, the 0.3 M concentration was kept as precursor concentration for the choice of the solvent and stabilizer.

As shown in the Fig. 3b, whatever methanol or water as solvent, both as deposited NiO thin films present similar optical properties with a transmittance of about 72 % in the visible region.

Therefore, due to better dissolution of nickel acetate in methanol associated with lower boiling point leading to higher homogeneity and smoother surface than water, methanol was kept as solvent [START_REF] Talebian | Sol-gel derived nanostructured nickel oxide films: Effect of solvent on crystallographic orientations[END_REF].

The optical properties of NiO thin films can also be significantly adjusted through the addition of stabilizers. Thus, aiming at increasing the film porosity and consequently providing easy paths for electrolyte penetration further on when cycled in KOH, triton X-100 or CTABsurfactant was added in the sols. The highest transmittance value is shown for triton X-100 as a stabilizer in methanol (transmittance of about 70 %) compared to those of CTAB and without stabilizer (Fig. 3c) [START_REF] Kooti | A facile and mild method for synthesis of nickel oxide nanoparticles in the presence of various surfactants[END_REF]. All these thin layers were annealed at 300 °C for 2 h in air ambient.

Influence of final treatment

The benefit of UV treatment on the electrochromic properties of oxides was earlier demonstrated in our group [START_REF] Danine | Room temperature UV treated WO3 thin films for electrochromic devices on paper substrate[END_REF] while, to our knowledge, earlier studies do not exist for NiO.

Thus, the common heat treatment at 300 °C was compared to two UV treatments using a lamp of 160 W for 1 h and one of 30 W for 5 h.

Structural analysis

The X-ray diffractogramms of the films heat treated at 300 °C and UV treated (160 W/1h; and 30 W/5h) are shown in Fig. 4. The UV treatments lead to the disappearance of the (200) peak located around 43° suggesting a decrease of the film crystallinity in between the film heat treated at 300 °C as compared to the films treated by UV. This trend is confirmed on the 0.5 M thin film as shown in the inset of Fig. 4.

Electrochromic properties

The comparison of the cyclic voltammogramms of the three previous films deposited on ITO glass substrates and cycled in Pt/1M KOH/NiO vs SCE, at a scan rate of 10 mV/s and in a voltage window of [-0.6 V; 0.6 V] shows significant differences. The behavior of the 300 °C annealed films is rather common with a CV shape consisting of two well defined peaks located at 0.4 V in anodic sweep and 0.25 V in cathodic sweep, illustrating a reversible faradic process and a Ni 2+ /Ni 3+ redox reaction associated with the Ni(OH)2/NiOOH phases [START_REF] Bouessay | Electrochemically inactive nickel oxide as electrochromic material[END_REF] (Fig. 5a). Upon cycling the NiO film visually, switch from a transparent to a brownish state in oxidation as expected for its anodic character. The CVs shapes of the UV-treated films are quite different in particular in oxidation, for which the increase in current appears at lower potential than for the annealed films (Fig. 5b). The oxidation peak of the '30 W' is even no more visible as the current shows a sharp increase usually associated with the electrolyte degradation and oxygen formation due to the oxidation of water (2H2O = 4e -+ O2 + 4H + ).

Nevertheless, the presence of the reduction peak as well as the decrease in transmittance as described below (Fig. 6) confirms the film oxidation. For the 160 W films, the anodic peak is even quite large with the appearance of a second wave at higher voltage prior to the increase in current density corresponding to the electrolyte decomposition. The in-situ measurements of the optical transmittance in the bleached (-0.5 V) and colored (0.5 V) states show a larger contrast; expressed at the ratio of the transmittance in the bleached state (Tb) vs the transmittance in the colored state (Tc) for the UV treated films (Fig. 6b). Indeed, the contrast, Tb/Tc, increases from unexpected very low value of 1.05, in respect of the nice CV, to 1.35 (160 W) and 1.51 (30 W). The difference in transmittance of 5 % for the film annealed at 300 °C increases to 20 % for the 160 W film and reaches its highest value of 30 % at 600 nm for the film treated with lower power, namely 30 W. Those results clearly demonstrate in our conditions, the benefit of UV treatment as compared to calcination.

The enhanced EC properties with UV treatment is further confirmed by the evolution of the transmittance that shows a similar change in transmittance of about 5 % for both oxidation and reduction for the annealed film, while the drop in transmittance is rather sharp and of about 15 to 20 % for the film treated by UV (Fig. 7). Upon reduction, the bleaching time is longer than the coloration time in oxidation, emphasizing faster kinetics from Ni(OH)2 to NiOOH.

The higher EC properties of the UV treated films are however associated with very limited cyclability. Indeed, as shown in Fig. 8 with the evolution of the capacity vs the cycle number, the capacity drops of about 50 % after only 7 cycles. The stabilization, appearing till 10 cycles, needs to be further confirmed. The poor cyclability is to be correlated to the poor surface morphology consisting of large cracks for the UV treated films while the one of the calcined film is much smoother (Fig. 9). Such morphology issue is currently being addressed as it limits the benefit of the UV treatment.

Conclusion

The present study was designed to deposit nickel oxide thin films by sol-gel combined with spin-coating method. Their characterization combining various techniques (XRD, SEM, electrochemical and optical measurements) shows an enhancement of the electrochromic properties with UV treatment as the final step. The highest EC properties were established for NiO thin films prepared using methanol as solvent, triton X-100 as stabilizer and treated by UV using a lamp of 30 W for 5 h. Having established a protocol for un-doped NiO film, the influence of Li and phosphor doping on the physico-chemical and EC properties of NiO thin films are currently in progress, aiming at understanding the influence of the p-type character of NiO on its EC behavior. UV treatment -lamp of 160 W for 1 h -lamp of 30 W for 5 h.

  Fig.2presents the X-ray diffractogram of NiO thin film, prepared in methanol using 0.5 M

Figure Captions :Fig. 1 .

 1 Figure Captions :

Fig. 2 .

 2 Fig.2. XRD pattern of NiO thin films prepared from (Ni(acetate)2.4H2O) (0.5M) in methanol, using triton X-100 as stabilizer.

Fig. 3 .

 3 Fig. 3. Optical transmittance of the as-deposited NiO thin films prepared by (a) different precursor concentrations 0.1 M; 0.3 M or 0.5 M, (b) with different solvents, and (c) without and with stabilizers. All films are annealed at 300°C for 2 hr in air ambient.

Fig. 4 .

 4 Fig. 4. XRD patterns of NiO thin films prepared with 0.3M (Ni(acetate)2.4H2O) in methanol, and triton X-100 as stabilizer treated by annealing process, UV light by a lamp of 160 W for 1 hr and UV light by a lamp of 30 W for 5 hr. In inset NiO thin films prepared with 0.5 M (Ni(acetate)2.4H2O) and similar conditions.

Fig. 5 .

 5 Fig. 5. CVs of Pt/KOH 1M/SCE/NiO vs SCE cell prepared with 0.3M (Ni(acetate)2.4H2O) in methanol and triton X-100 as stabilizer treated by (b) annealing process and (b) UV light by a lamp of 160 W for 1 hr and UV light by a lamp of 30 W for 5 hr (b). The cell was cycled with a sweep rate of 10mV/s.

Fig. 6 .

 6 Fig. 6. Optical transmittances of NiO thin films 0.3M (Ni(acetate)2.4H2O)in methanol as a solvent with triton X-100 as stabilizer and treated by (a) annealing process (NiO-M-annealing process), a (b) lamp of 160 W for 1 hr (NiO-UV-160W-1 h), or (c) a lamp of 30 W for 5 hr (NiO-U-30W-5 h), in colored and bleached states.

Fig. 7 .

 7 Fig. 7.In-situ measurement of NiO thin films prepared by 0.3 M of nickel acetate in methanol, triton X-100 as a stabilizer, and treated by annealing process ( NiO-annealing process), UV treatment with a lamp of 30 W for 5 hr ( NiO-UV-30W-5h). [-0.5V; 0.5V].

Fig. 8 .

 8 Fig. 8. Evolution of the capacity of NiO thin films treated by annealing process or by UV using a lamp of 30 W for 5 hr vs cycle number when cycled in Pt/KOM 1 M/SCE/NiO vs SCE cell.

Fig. 9 .

 9 Fig.9. SEM images of NiO thin films prepared with 0.3M (Ni(acetate)2.4H2O) in methanol, and triton X-100 as stabilizer treated by annealing process (NiO-annealing process); UV light by a lamp of 160 W for 1 hr (NiO-UV-160W-1 h) and UV light by a lamp of 30 W for 5 hr (NiO-UV-30W-5 h).

Acknowledgments

The financial supports from the "Hubert Curien/TOUBKAL Program" (Project number: Toubkal/16/35-Campus France: 34730RJ) are gratefully acknowledged. The authors wish to thank Mathias Da Rocha, Alexandre Fargues (optical measurements), Sébastien Fourcade (spin-coating technique) and Nicolas Penin for helpful discussion.


Pamely Zantou

Mikaël Ange Mousse
email: mikael.mousse@univ-parakou.bj

Bethel Atohoun

An intelligent based system for blind people monitoring in a smart home

Keywords: Cane électronique, Capteurs, Surveillance humaine, Maison intelligente Electronic white cane, Sensors, human monitoring, smart home

Les personnes visuellement impaires ont besoin dâaide pour se déplacer en toute sécurité. Pour ce faire plusieurs Outils dâaide au déplacement sont utilisés pour leurs permettre d'être autonome dans leurs déplacements. Parmi ceux-ci, la canne blanche qui est mondialement reconnue comme signe de déficience visuelle. Dans le présent travail, nous mettons en place une canne blanche électronique qui utilise la technologie des capteurs pour prévenir le malade visuel des obstacles qui se dressent sur son chemin dans un rayon de 2m au sol ou en hauteur en lui envoyant des instructions vocales via un kit oreillette. Nous proposons aussi une application mobile de suivi temps du malade visuel et une application WEB pour le contrôle d'accès à l'application mobile.

ABSTRACT.

Visually impaired people need help to travel safely. To make this possible, many travel aids have been designed. Among them, the cane which is considered as a symbol of visual deficiency in the whole world. In this work, we have built an electronic white cane using sensors' technology. This intelligent cane detects obstacles within 2m on the ground or in height, and sends vocal instructions via a Bluetooth headset. We have also built an Android application to track in real time the visually impaired and a WEB application to control the access to the mobile one.

Introduction

Many situations can deprive human beings from freedom. Visual impairment is one that make people completely dependent on their caregivers. Indeed, a visually impaired person cannot move freely or carry out any activity that requires vision. To facilitate their integration into society and allow them to make good decisions while moving, they benefit from external assistance provided by caregivers, trained dogs, white canes, small electronic devices. The white cane remains one of the most widely used tools by visually impaired. It not only enables visually impaired people to avoid obstacles. This device is widely recognized as symbol of blindness. However, it does not allow the visually impaired to freely carry out their daily activities. It does not detect obstacles above the belt such as: truck mirrors, sloped branches, advertising signs. It is also not possible to be aware of the presence of a close obstacle before touching or detecting it. These different situations expose visually impaired people to frequent severe body shocks. To avoid this situation, electronic canes have been invented. They use sensors or stereovision technologies. Tremendous efforts are made today to improve electronic travel aid solutions. Unfortunately, these solutions are almost unused or unknown in most African countries. Over 90% of people suffering from visual impairment live in developing countries. Africa is the most vulnerable continent of all. Moreover, the solutions on the market are not suited to our realities. This paper aims to produce an electronic cane model, easy to use, and suited to Africa's realities.

Based on studies about visually impaired needs, the design of an electronic smart cane seems to be the best way to help them in their daily life. It is globally recognized as a symbol of visual deficiency. It makes the blind feel safe. It is a handy tool that can be easily used by anyone, even disabled people. To overcome problems associated with traditional white canes, Electronic Travel Aids, ETAs, have been invented since the 19th century. In [1], the author defines ETAs as active devices that emit and receive waves (electromagnetic or acoustic) to explore the environment within a certain perimeter, or passive receivers that receive the light reflected by the different obstacles. They process the information and provide the user with information on the configuration of nearby obstacles. Electronic canes identify physical quantities and transform them into information thanks to the knowledge of the physical phenomena involved. They provide information on the shape of obstacles, their dimensions, colours and even the distance between them and the user. ETAs' industry, has been undergoing a constant and remarkable evolution for several years now. Thus, many generations of solutions have been developed. These ETAs can be classified in terms of technologies used to build them. We can identify two main generations of electronic canes. Electronic canes using:

-ultrasound sensors and/or laser and/or IR sensors [2,4,[START_REF] Bibliographie | Contribution a la télémetrie optique active pour l'aide aux déplacements des nonvoyants[END_REF]; -cameras, electro-tactile system, Oh I see (the vOICe), stereovision systems [6,7].

Proposed system

The proposed system is a set of a smart stick and a real time tracking mobile application. The smart stick uses a network of ultrasound and IR sensors to detect obstacles (within a range of 2m in height or on the ground), a Raspberry Pi to process data and a GPS module to collect satellite data. On the one hand, sensors send data collected from the blind's environment to the Raspberry Pi. This last, processes the data and send vocal instructions to the visually impaired through a Bluetooth headset connected to the smart stick. On the other hand, the GPS module forwards satellite information to the Raspberry Pi which processes them. Then, sends them back to mobile and WEB applications via a REST API.

System overview

The proposed system is presented by Fig. 1. The system has three major modules : smart stick, web application and mobile Application. These modules communicate through an API. The intelligent cane is a normal white which embeds sensors.

Choice of sensors

As far as the proposed system is concerned, sensors enable us to evaluate the distance between the visually impaired and obstacles. The most widely used distance sensors are: ultrasound sensors, laser sensors, IR sensors, radar sensors. Some Criteria are used to choose sensors. They are range, precision, cost and interference sensitivity. The laser and radar sensors can detect near and far obstacles. However, laser sensors are very expensive, which contradicts our aim to provide people with an affordable solution. They are also less precise for close obstacles detection. Radar sensors are not able to detect small objects because of their medium accuracy, which is not good for our system. Ultrasound sensors detect close obstacles with a very good accuracy depending on their measurement cone. Nevertheless, very close obstacles are less likely to be detected. IR sensors are very accurate but only detects very close obstacles. Both, ultrasound and IR sensors are cheap and detect small objects. They fit with our system requirements. Actually, we use an ultrasound sensor HC-SR04 and an IR sensor Sharp GP2Y0A02YK0F for the system.

GPS module NEO-6M

The GPS module provides location data (longitude and latitude) from satellites. This is collected with the GPS module EEPROM antenna. It sends a big stream of data in NMEA format. NMEA consists in several sentences. However, we just need one sentence. This sentence starts with $GPGGA. It contains useful information such as: coordinates, time. These information are comma separated. Thus, we can extract information from $GPGGA string by counting the commas. The latitude is found after two commas and the longitude after four commas. The GPS module sends data collected to the cane's process unit which is the Raspberry Pi.

Raspberry Pi

To make the system works, we need a Logical Processing Unit (LPU)to communicate sensors' data to the visually impaired. For this purpose, we can use micro-controllers such as Arduino, PIC18F46k80, etc. However, we are dealing with a two modules system. In fact, we have the stick and a software linked to it. A real computer is the best candidate to make them communicate. Then, we use the Raspberry Pi Zero W as the stick's LPU. It is a mono-card nano computer with a built-in WiFi and bluetooth and needs 5V as operating voltage. The Raspberry Pi Zero W processes data collected by sensors and send them either to the REST API or the users. In fact, it computes the distance between the user and the obstacle and sends vocal instructions to users via a bluetooth headset. The Raspberry Pi W is also responsible of voice synthesis. In fact, it holds a text-to-speech engine, SVOX Pico, which enables us to send vocal instructions to the stick's users.

Electronic configuration

In order to detect obstacles accurately, sensors should be placed at optimal positions on the stick (Fig. 2). We propose a cane of length l, depending on its user height. The angle β, between the cane and the horizontal which is an input parameter. The proposed system uses three sensors. Two ultrasound sensors and an IR sensor. The IR sensor will detect obstacles on the ground and at a distance d1 less than or equal to 1m (d1 ≤ 1m). The lower ultrasound sensor, on the one hand, is placed at distance d4 and will detect obstacles on the ground at a distance d between d1 = 1m and d2 = 2m ( d1 ≤ d ≤ d2). The upper ultrasound sensor, on the other hand, can detect obstacles above the belt up to 2m in height.

Several parameters are involved in the cane's electronic configuration. We will be interesting in finding γ, α, δ, c1 and c2.

γ: the angle between the cane and the upper ultrasound sensor; -α: the angle between the cane and the lower ultrasound sensor; -δ: the angle between the IR sensor and the cane; -c1: the distance between the end of the ultrasound sensor and the floor; -c2: the distance from the end of the IR sensor to the floor. To calculate them, we used geometric properties including the theorem of Al-Khashi or the law of cosines. We have:

           l = 120cm β = 113 d4 = 2 5 .l = 48cm , d5 = d4 -5cm = 43cm d6 = (l-d4) 3 = 24cm d1 = 100cm , d2 = 200cm
The table 3 summarizes the sensors' inclination angles information. .

Results and discussion

Before assembling all the cane's components, we test each of them. Based on the time used by the ultrasound sensor to reach obstacles and analog outputs of the IR sensor we can evaluate our system performances. The table below summarizes results derived from computations and measurements. Even though the proposed solution has been influenced by [3]. The results shows that combining infrared range and ultrasonic sensors may lead

Conclusion

Visually impaired people represent 5% of the world's population. More than 26 millions of them are in Africa. They need a social inclusion like any able-bodied person. This work presents an electronic cane that enables visually impaired to move around without having to resort to caregivers or traditional solutions. Indeed, it helps its user detect obstacles in height as well as on the ground within a radius of 2m, which sends voice commands back to its user to enable him to avoid the obstacle that stands in his path and which has applications to follow him. The proposed cane has limitations that have been raised in the work. This allows us to consider interesting perspectives to improve our work among which implementing a retrace route feature to help the visually impaired parents.

Figure 1 .

 1 Figure 1. System architecture

  Figure 2. Electronic configuration

  decision making system. The proposed system is also connected to mobile application to track the visually impaired people in real time.

	Tableau 2. Comparison of computed and measured results
			Ultrasonic sensor				IR sensor
	Distance (cm)	Time computed (s)	Time measured (s)	Error(s)	Analog output computed	Analog output measured	Error (V)
					(V)		(V)
	50	0.29	0.3	0.01	1.3		1.3	0
	75	0.44	0.45	0.01	0.8		0.7	0.01
	100	0.59	0.62	0.03	0.6		0.59	0.01
	125	0.74	0.78	0.04	0.52		0.51	0.01
	150	0.88	0.92	0.04	0.5		0.485	0.015
	175	1.03	1.07	0.04	0.3		0.282	0.018
	200	1.18	1.23	0.05	0.2		0.09	0.11
	to a better Devices		Detection Range	Time Response	Power Consump-	Stair detection	Tracking module
					tion
	Proposed system		Medium	Fast	Low	Yes	Yes
	New electronic white cane for stair case	Medium	Fast	Low	Yes	No
	detection and recognition using ultra-
	sonic sensor
	New electronic white cane for stair case	High	Fast	Low	Yes	No
	detection and recognition using ultra-
	sonic sensor
	Ultrasonic Spectacles and Waist-belt for	High	Fast	Low	No	No
	Visually Impaired and Blind Person
	Tableau 3. Sensors' inclination angles


est destinée au dépôt

Integrating PET-MR data for a multiparametric approach of tumour heterogeneity in non-small-cell lung cancer (NSCLC)

Florent Besson

To cite this version:

Florent Besson. Integrating PET-MR data for a multiparametric approach of tumour heterogeneity in non-small-cell lung cancer (NSCLC). Imaging. Université Paris-Saclay, 2020. English. NNT : 2020UPASS081. tel-02966153