Alexandre Gouskov
email: gouskov_am@mail.ru

Mikhail Guskov
email: mikhail.guskov@ensam.eu

Philippe Lorong
email: philippe.lorong@ensam.eu

Grigoriy Panovko
email: gpanovko@yandex.ru

Alexander M Gouskov

Bauman Moscow

Bauman

Dr. of Sc Grigory Panovko

INFLUENCE OF FLANK FACE ON THE CONDITION OF CHATTER SELF-EXCITATION DURING TURNING

Keywords: continuous cutting stability, nonlinear dynamics, tool-workpiece interaction, cutting stiffness, flank face, ploughing, chatter, turning, Poincaré-Andronov-Hopf bifurcation

This paper addresses a modelling approach for cutting tool and workpiece material interaction with ploughing taken into account. In the proposed model the distributed contact on the flank face is replaced by a concentrated additional cutting edge characterised by two physical parameters and bringing about a new delay term into the dynamical system. It is shown that under monoharmonic excitation of the tool on the direction orthogonal to the cutting velocity, it is possible to isolate the effect of the flank face and observe experimentally its parameters. The influence of the ploughing on the instability boundaries of continuous cutting is investigated. An analytical expression is obtained for the effective linear damping coefficient due to ploughing and depending on the cutting velocity.

Introduction

Various approaches have been proposed for modeling the ploughing phenomena during the history of the cutting process investigation. The historical qualitative description of ploughing is given by [START_REF] Tobias | A new approach of formulating the transfer function for dynamic cutting processes[END_REF]. Mainly, the following phenomena accompanying the ploughing are observed: increase of friction forces, flank wear, increase of cutting forces, unstable domains reduction, especially for low cutting velocities, etc. As for the macroscopic dynamics, most works elaborate one of the two following approaches: either a friction term, linear or nonlinear, is introduced as a function of the relative normal velocity of the cutting edge w.r.t. the processed surface [START_REF] Fofana | Machining stability in turning operation when cutting with a progressively worn tool insert[END_REF]), or a force term proportional to the volume swept by the tool's flank face [START_REF] Enders | A dual-mechanism approach to the prediction of machining forces, part 1: model development[END_REF]; [START_REF] Lee | Modeling of the process damping in chatter vibration[END_REF]; [START_REF] Moradi | Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: Forced oscillation and stability analysis[END_REF]). These phenomena result in apparent damping, proposed by [START_REF] Tobias | A new approach of formulating the transfer function for dynamic cutting processes[END_REF], also referred to as process damping [START_REF] Altintas | Manufacturing automation. Metal Cutting Mechanistics, Machine Tool Vibrations, and CNC Design[END_REF]). A more detailed description of ploughing force, based on the flank face-workpiece interference volume, has been presented by Wu (1989). This approach has then been applied to various processes, such as drilling [START_REF] Guibert | Influence of the ploughing effect on the vibratory drilling behaviour[END_REF]) or milling [START_REF] Mehdi | Modelling cutting force including thrust and tangential damping in peripheral milling process[END_REF]). In practical applications, the ploughing is sometimes modelled directly by a drastic increase in damping [START_REF] Seguy | Surface roughness variation of thin wall milling, related to modal interactions[END_REF]). By the following, the mechanical aspect of the interaction of the tool's flank face with the machined surface during straight turning (fig. 1, fig. 2 left), under orthogonal cutting conditions in x-y plane (the tool is supposed stiff in z-direction and relatively compliant in x-direction). Thus only the z-oriented cutting edge-related kinematics are considered along the x-axis. Under turning, a complex process of tool-workpiece interaction and of chip formation is observed (fig. 2 left). A wide review of the state of the art in modelling and investigation of turning dynamics and stability is provided by Siddhpura and Paurobali (2012).

It is also noticed that the interaction effects on the flank face during steady cutting are impossible to single out and in the overall behaviour and is an unobservable parameter. It is although pointed out that with the decrease of the cutting speed, the effects of the ploughing phenomena influence sensibly the chatter onset and can lead to an important change in the energy dissipation [START_REF] Tarng | An analytical model of chatter vibration in metal cutting[END_REF]; [START_REF] Lee | Modeling of the process damping in chatter vibration[END_REF]) .

Recently, an alternative, mechanistic-type approach has been developed, based on the representation of the flank face interaction via a fictitious auxiliary cutting edge, following the main edge closely [START_REF] Paris | Influence of the ploughing effect on the dynamic behavior of the self vibratory drilling head[END_REF]; [START_REF] Bondarenko | Parameters Identification on the Ploughing Force Model by an Experimental Approach[END_REF]; [START_REF] Bondarenko | Etude mesoscopique de l'interaction mechanique outil/piece en contribution sur le comportement dynamique du systeme usinant[END_REF]). These works had shown the relevance of auxiliary edge model in case of drilling and serve as basis to the developments of the present paper. The goal of the present work is to provide a representation of the flank face interaction via the secondary cutting edge concept in case of turning, to validate its relevance w.r.t. ploughing and to investigate its impact on the dynamic stability of quasi-steady turning.

We first begin, in section 2, by introducing our ploughing model based on the usage of an auxiliary cutting edge. Definition of the surface generation, including the new cutting edge, is also given in this the section. We then detail, in section 3, the tool-workpiece interaction model. The proposed model is elaborated in order to mix, in a consistent way, cutting and ploughing contributions into the total cutting force. The effect of the auxiliary cutting edge for monoharmonic axial vibrations of the tool at a multiple of the workpiece rotation frequency is studied in section 4. It exhibits the contribution of the auxiliary cutting edge on the cutting force work induced by the vibrations. At last, in section 5, dynamics of vibration cutting is considered. A comparison with 'classical' approaches of process damping is proposed. The interaction of the flank face with the processed material is manifested by additional forces and by change in resulting surfaces geometry (material's peening). To model the interaction on the flank face, we propose to replace the whole flank face by one auxiliary cutting edge [START_REF] Bondarenko | Parameters Identification on the Ploughing Force Model by an Experimental Approach[END_REF]; [START_REF] Bondarenko | Etude mesoscopique de l'interaction mechanique outil/piece en contribution sur le comportement dynamique du systeme usinant[END_REF]), situated at distance b from the principal cutting edge (fig. 2). This interaction on flank face is reduced to a cutting process with coefficient (this concept will be precised in the following) K c0 . The introduction of two parameters -{b, K c0 } -allows one to consider observable (measurable) cutting forces caused by both the cutting itself and ploughing, from one common viewpoint. The parameters related to the principal cutting edge will be marked with the subscript p, those related to the auxiliary edge -with the subscript c.

Equations of new surfaces generation.

Geometrical equations for the new surfaces generated by the principal and the auxiliary cutting edges during the cylindrical surface turning (or drilling) [START_REF] Gouskov | Dynamic Models Generalization of Manufacturing Systems with Single-Point Cutting Considering Equations of New Surface Formation' Nonlinear Dynamics and Control of Mechanical Processing[END_REF]) are written as follows:

x p (t) = x 0 -V t + u(t), x c (t) = x 0 -V t + u(t), D p (t) = x s -L c (t -T + ∆T ) -x p (t), D c (t) = x s -L p (t -∆T ) -x c (t), h p (t) = max(0, D p (t)), h c (t) = max(0, D c (t)), L p (t) = L c (t -T + ∆T ) + h p (t), L c (t) = L p (t -∆T ) + h c (t), L p (t ≤ 0) ≡ 0, L c (t ≤ 0) ≡ 0, (1)
with x p -coordinate of the principal cutting edge, measured from the spindle, along its axis; x 0 -initial position of the cutting edge; x s -coordinate of the part's free end; uaxial displacement of the cutting edge with respect to its nominal position, caused by the deformation of the tool support assembly; D p -distance from the cutting edge at instant t to the surface generated by the auxiliary cutting edge at instant t -(T -∆T ), T -workpiece rotation period, ∆T -time corresponding to the rotation at angle b/R, b -distance between the principal and the auxiliary edges along the direction of V c ; R -machined surface radius; h p -principal cutting edge's cutting thickness; L p -coordinate of the surface generated by the principal cutting edge, measured from the free end {x 0 ≥ x s }. Analogous parameters for the auxiliary cutting edge are denoted by the c subscript -{x c , D c , h c , L c }. The kinematical relations (1) allow one to compute the coordinates of the surfaces generated by turning -L p (t), L c (t), as well as the uncut thicknesses of the removed material h p (t), h c (t) and the position of the cutting edges x p (t), x c (t) for a given motion of the tool u(t), with initial conditions: x 0 , x s , L p (t ≤ 0), L c (t ≤ 0), defined on the initial set.The variables D p (t), D c (t) are auxiliary, and allowing to account for discontinuous cutting.

The feed per turn is a = V T , with V -axial feed rate. The delay between the principal and the auxiliary cutting edge ∆T is computed as follows:

T = 1 f , C = 2πR, β = b C , ∆T = βT,
with f -workpiece rotation frequency. The time interval between the passage of the auxiliary and the principal cutting edges is T -∆T = T (1 -β).

In case when only the principal cutting edge is engaged (cutting without ploughing -

h c ≡ 0 ⇒ L c (t) = L p (t -∆T )) the system of equations (1) reduces to x p (t) = x 0 -V t + u(t), D p (t) = x s -L p (t -T ) -x p (t), h p (t) = max(0, D p (t)), L p (t) = L p (t -T ) + h p (t), L p (t ≤ 0) ≡ 0.
(2) Two types of continuous cutting.

• Continuous cutting with the principal edge alone -h c ≡ 0, h p > 0 ∀t.

In this case, the equation system (2) applies. D p is always positive, D p > 0 ∀t and can be eliminated from the writing because h p (t) ≡ D p (t):

L p (t) = x s -x p (t), h p (t) = V T -(u(t) -u(t -T )). (3)
For quasistatic cutting (u(t) = const) the uncut chip thickness reads

h p (t) = V T = a. (4)
• Continuous cutting with both edges -h c > 0, h p > 0 ∀t.

In this case one has to consider the whole system (1), while D p , D c can again be eliminated:

L p (t) = x s -x p (t), h p (t) = V (T -∆T ) -(u(t) -u(t -(T -∆T ))) , L c (t) = x s -x c (t), h c (t) = V ∆T -(u(t) -u(t -∆T )) .
(5)

For quasistatic cutting (u(t) = const) the uncut chip thicknesses read

h p (t) = a(1 -β), h c (t) = aβ. (6)
The equations (3)-( 5) are also valid for the of absolutely rigid tool case (u ≡ 0).

Tool-workpiece interaction model

The tool-workpiece interaction model defines the relation between the cutting force P and the uncut chip thickness h and is typically determined experimentally in quasistatic conditions (u(t) = const) under assumption of unique cutting part. In the present study it is only necessary to deal with the component of the cutting force in the direction of vibration, ie direction x, fig. 2. The cutting force P is thus here a scalar.

The uncut chip thickness in our case equals the feed per turn a. In these conditions, the contributions of the cutting force (principal edge) and of ploughing (auxiliary edge) are impossible to distinguish. It would be of interest to the experimenter to represent the cutting force model in such a manner that the quasistatic force has expression does not depend whether the ploughing is present or not. In the following, the fractional-rational model proposed in [START_REF] Bondarenko | Etude mesoscopique de l'interaction mechanique outil/piece en contribution sur le comportement dynamique du systeme usinant[END_REF]; [START_REF] Brissaud | A more realistic cutting force model at uncut chip thickness close to zero[END_REF]; [START_REF] Paris | Influence of the ploughing effect on the dynamic behavior of the self vibratory drilling head[END_REF] will be used. The experimental data is processed using the similarity theory framework [START_REF] Gouskov | Experimental determination of drilling forces based on dimensional analysis and similarity theory[END_REF]). Under assumption of unique cutting edge (one point cutting model -1PC), the resulting cutting force P (t), can be written as follows:

P (t) = K 0 H h(t) H + r h(t) 2 H 2 1 + h(t) H . ( 7
)
with {K 0 , H, r} -experimental coefficients, h(t) -chip thickness, units:

[K 0 ] = N.m -1 , [H] = m, [r] = 1, [h] = m.
The parameter H serves as a characteristic length scale for the interaction in a given toolworkpiece pair [START_REF] Brissaud | A more realistic cutting force model at uncut chip thickness close to zero[END_REF]).

The ploughing force's contribution can be accounted for via an auxiliary cutting edge, as proposed in [START_REF] Bondarenko | Parameters Identification on the Ploughing Force Model by an Experimental Approach[END_REF]. Under assumption of two cutting edges (two point cutting model -2PC), the resulting cutting force P (t) is a sum of contributions due to the principal cutting edge -P p (t), and to the auxiliary one -P c (t):

P (t) = P p (t) + P c (t), P p (t) = K p0 H p hp(t) Hp + r p hp(t) 2 H 2 p 1 + hp(t) Hp , P c (t) = K c0 h c (t), (8)
with {K p0 , H p , r p , K c0 } -experimental coefficients; {h p (t), h c (t)} -uncut chip thickness for the principal and auxiliary edges. In general, the parameters {h p (t), h c (t)} are defined by the equations (1). Static stiffness coefficients for each model (K for 1PC; K p , K c for 2PC), are fundamental for the stability evaluation in case of continuous cut. These coefficients define the slope of the thickness-force function:

K = ∂P ∂h = K 0 κ(h/H; r), κ(h/H; r) = r + 1 -r (1 + h/H) 2 , K p = ∂P ∂h p = K p0 κ p (h p /H p ; r p ), κ p (h p /H p ; r p ) = r p + 1 -r p (1 + h p /H p ) 2 , K c = ∂P ∂h c = K c0 . (9)
For given material, tool and chosen cut depth B (chip width in the z direction, see fig. 1, given the orthogonal cutting conditions) the quantities {K 0 , K p0 , K c0 , r, r p } (9) remain constant. Also, the normalized stiffness coefficient {κ, κ p }, depending on the normalised cut thicknesses {h/H, h p /H p } and dimensionless parameters {r, r p }, varyin finite ranges

r ≤ κ ≤ 1, r p ≤ κ p ≤ 1.
The coefficients {K 0 , K p0 , K c0 }, equal to the cut stiffness when the uncut chip thickness tends to zero (see equation ( 9): h, h p → 0), for a given cut depth B. It is important to mention that while K 0 and K p0 can be obtained experimentally by classical approaches, the auxiliary edge's parameter K c0 would require specific tests, involving vibrations in the feed direction at multiples of the workpiece rotation frequency, as pointed out by [START_REF] Bondarenko | Parameters Identification on the Ploughing Force Model by an Experimental Approach[END_REF].

According to dimensional analysis, these coefficients would depend on a characteristic stress quantity for the workpiece material (such as yield limit, ultimate strength, elasticity modulus) σ L in the following way [START_REF] Brissaud | A more realistic cutting force model at uncut chip thickness close to zero[END_REF]):

K 0 = γσ L B, K p0 = γ p σ Lp B, K c0 = γ c σ Lc B ( 10
)
here {γ, γ p , γ c } are dimensionless coefficients, depending mainly on the cutting edges' shape, sharpening, coatings, etc. The nature of these coefficients for the two edges can be substantially different because of the respective physical phenomena at stake in cutting and ploughing.

During the quasistatic cutting, the conditions (4), ( 6) are verified and, after substitution into ( 7), ( 8) we obtain the following equation

K 0 H a H + r a 2 H 2 1 + a H = K p0 H p a(1-β) Hp + r p a 2 (1-β) 2 H 2 p 1 + a(1-β) Hp + K c0 aβ.
By balancing the terms with equal powers of a, we obtain the relations connecting the parameters {K 0 , H, r} with {K p0 , H p , r p , K c0 , β}:

K 0 = K p0 (1 -β) + K c0 β, K 0 r H = K p0 r p H p (1 -β) 2 + K c0 H p β(1 -β), 1 H = 1 -β H p . ( 11
)
It is of practical interest to represent the auxiliary edge-related cut stiffness as K c0 via a factor w.r.t. the principal edge cut stiffness K p0

K c0 = ψK p0 .
It should be noticed that the flank face stiffness is substantially higher than that of the principal face -ψ > 1. The solution of (11) in terms of the principal edge's parameters {K 0 , H, r} → {K p0 , H p , r p } reads as follows:

K p0 = K 0 1 -β + βψ ⇒ K 0 = K p0 (1 -β + βψ), r p = r(1 -β + βψ) -βψ 1 -β ⇒ r = r p (1 -β) + βψ 1 -β + βψ , H p = H(1 -β) ⇒ H = H p 1 -β . ( 12
)
By adding the auxiliary cutting edge, instead of three "observed" parameters, {K 0 , H, r}, we now consider five -{K p0 , H p , r p , β, ψ}. Three of these parameters, namely {K p0 , H p , r p } are determined univocally via {K 0 , H, r} and via two internal parameters related to the auxiliary cutting edge -{β, ψ} (12). The relation for the case β = 0 (without considering two edges), according to the tool-workpiece interaction model, (8) corresponds to (7) and the kinematical equations (1) reduce to (2). I.e., the internal parameters {β, ψ}, accounting for ploughing, cannot be determined from quasistatic cutting experiments and only qualitative analysis is possible in this context.

Monoharmonic axial vibrations of the tool

Consider continuous cutting involving both cutting edges h c ≥ 0, h p ≥ 0, ∀t with superimposed axial monoharmonic vibration of the tool with the oscillation period T e :

u(t) = e sin(ϕ(t)), ϕ(t) = 2π T e t,
with e vibration magnitude. Suppose the workpiece rotation period is a multiple of that of the tool oscillation: T = T e n, n = 1, 2, 3, • • • . This case is interesting because when only the principal edge is engaged, the uncut chip thickness is constant h(t) = h p (t) = const and thus the cutting force would be constant also (3). However, when both edges are involved -principal and auxiliary,-thicknesses cut by each edge {h p (t), h c (t)} vary periodically, according to (5), and can be expressed in the following way:

h p (t) = a(1 -β) -∆u p (t), h c (t) = aβ -∆u c (t), (13)
with

∆u p (t) = u(t) -u(t -T (1 -β)) = e(1 -cos B) sin(ϕ(t)) -e sin B cos(ϕ(t)), ∆u c (t) = u(t) -u(t -T β) = e(1 -cos B) sin(ϕ(t)) + e sin B cos(ϕ(t)), (14)
with B = 2πnβ. The condition for continuous cutting writes (from second relation in ( 13) and the expression of ∆u c (t) in ( 14)):

e ≤ 1 2 aβ.

Since the distance between the cutting edges is substantially smaller than the turned surface radius, β << 1, the principal edge uncut chip thickness will have a small periodic component max |∆u p | ≤ a(1 -β). The cutting force (8) can be written as a sum of a constant and periodic parts, P 0 and ∆P (t) respectively:

P (t) = P 0 + ∆P (t),
or, more specifically,

P 0 = K 0 H α + rα 2 1 + α , ∆P (t) -K p0 κ p (α, r p )∆u p (t) -K c0 ∆u c (t). (15)
Here α = a/H -is the feed per turn, divided by a characteristic distance scale of the cutting process model ( 7). This expression for ∆P is a simplification where the cross terms of ∆u p and ∆u c are neglected. The periodic part of the cutting force ∆P (t) = ∆P (t + T e ) includes an inphase ∆P S sin(ϕ(t)) and quadrature ∆P C cos(ϕ(t)) components.

The quadrature component realizes a nonzero work over a period of tool oscillation

∆W Te = t=Te t=0 ∆P (t)du(t) = -πK p0 e 2 (ψ -κ p (α, r p )) sin B. ( 16
)
The stiffness of the auxiliary cutting edge is substantially higher than the principal one, i.e. as κ p (α, r p ) < 1 and ψ > 1 we have ψ > κ p (α, r p ), and for those relative frequencies n, for which sin B > 0, B = 2πnβ the average work of the cutting forces turns out to be negative ( 16). This leads to energy dissipation caused by the flank face work. At the same time, if sin(2πnβ) < 0, which is possible if (j -1/2)/β < n < j/β, j = 1, 2, • • • , then, according to ( 16), the cutting force would perform positive work ∆W Te > 0. Thus, in spite of the intuitive behavior this force can serve as a source of excitation of vibrations of a machining system. For example, when b = 0.02, positive work is possible in the frequency range 25 < n < 50 . It could be a possible explanation for vibration auto-excitation in machining systems working at small cutting velocities and high relative frequencies oscillation (it should be noticed that when ψ < κ p (α, r p ), ploughing might cause oscillation at high cutting velocities also).

In general, for random ratio between the period of axial vibration T e and the workpiece rotation period T , the work of cutting forces over one oscillation period is computed as follows:

∆W Te = -πK p0 e 2 [ψ sin(2πnβ) + κ p (α, r p ) sin(2πn(1 -β))] , n = T T e . (17)
If in (17) one has β = 0, then ∆W Te = -πK p0 e 2 κ(α, r p ) sin(2πn),

and it appears that for the case of only one cutting edge, there exist frequency ratio values, for which the cutting process is a source of energy to the system ∆W te > 0, and the frequency of vibrations is not a multiple to the rotation frequency sin(2πn) < 0. It is important to notice that for integer n, in absence of flank face interaction, the power of cutting forces is a constant value and the vibrational component (18) would be zero.

It is practical to represent the numerical results in a universal, dimensionless framework. For scale factors of time, distance, and force, {T * , L * , P * } we take

T * = T, L * = H, P * = K 0 H.
Then we can introduce the following dimensionless quantities:

∆Π = Π -Π 0 , ∆Π p = Π p -Π p0 , ∆Π c = Π c -Π c0 ,
dimensionless feed and oscillation magnitude

α = a L * , ε = e L * ,
dimensionless work of cutting forces over one oscillation period

∆Ψ Te = ∆W Te P * L * = -πε 2 ψ sin(2πnβ) + κ p (α, r p ) sin(2πn(1 -β)) 1 -β + βψ ,
dimensionless vibratory speed of the cutting part of the tool

ν = T * L * du dt .

Example of flank face influence on process damping

On fig. 3 a dimensionless cutting force model according to (7), ( 8), ( 12), ( 15) is shown. The influence of the effective length of the flank face (distance form the principal to the auxiliary cutting edge expressed by β) under axial vibration of the tool at a multiple frequency of that of the workpiece rotation is shown on fig. 4,5. One can notice the following features:

• the approximate computation based on (15) provides the results that are very close to the full ones (without neglecting cross terms),

• for small relative vibration frequencies (n = 3), the ploughing leads to damping (∆Ψ Te < 0),

• at high vibration frequencies (n = 30), on the contrary, the ploughing can induce vibration of the machining system (∆Ψ Te > 0).

It can be seen that with an increase in β for low relative frequencies of vibrations, the amplitude of cutting forces also increase (fig. 4 -dimensionless time

t = T τ, d dτ () = () ,
-dimensionless forces -dimensionless stiffnesses

Π = P kH , Π p = P p kH , Π c = P c kH , (
K = K k , K p = K p k , K c = K c k , K 0 = K 0 k , -dimensionless thicknesses H p = H p H , α = a H , -dimensionless size parameters {X p , X, ξ, Λ p , Λ c , η, η p , η c , ∆ p , ∆ c } = 1 H {x p , x c , u, L p , L c , h, h p , h c , D p , D c }.( 20
)
We also introduce the following notations

f 0 = 1 2π k m , f = 1 T , F = f f 0 = V c R m k ,
with f 0 -tool's eigenfrequency, f -workpiece rotation frequency, F -relative frequency of the workpiece rotation (rotation frequency, devided by the tool's eigenfrequency). The tool dynamics eqation ( 19) takes the following form:

F 2 4π 2 ξ + 2ζ F 2π ξ + ξ = Π. (21)
The new surface generation relations (1) become

X p (τ ) = X 0 -τ + ξ(τ ), X c (τ ) = X 0 -τ + ξ(τ ), ∆ p (τ ) = Λ c (τ -1 + β) -X p (τ ), ∆ c (τ ) = Λ p (τ -β) -X c (τ ), η p (τ ) = max(0, ∆ p (τ )), η c (τ ) = max(0, ∆ c (τ )), Λ p (τ ) = Λ c (τ -1 + β) + η p (τ ), Λ c (τ ) = Λ p (τ -β) + η c (τ ), Λ p (τ ≤ 0) ≡ 0, Λ c (τ ≤ 0) ≡ 0. ( 22
)
The cutting model for the principal and auxiliary edges (8) can be written as follows

Π(τ ) = K p0 H p ηp(τ ) Hp + r p ηp(τ ) 2 H 2 p 1 + ηp(τ ) Hp + K c0 η c (τ ), (23)
with

K p0 = K 0 1 -β + βψ , K c0 = ψK p0 .
Respective characteristic stiffness coefficients from ( 9) are computed as follows

K = ∂Π ∂η = K 0 κ(η; r), κ(η; r) = r + 1 -r (1 + η) 2 , K p = ∂Π ∂η p = K p0 κ p (η p /H p ; r p ), κ p (η p /H p ; r p ) = r p + 1 -r p (1 + η p /H p ) 2 , K c = ∂Π ∂η c = K c0 . (24)
Equations ( 21), ( 22), ( 23) describe dynamics of turning of cylindrical surfaces with ploughing taken into account via two cutting edges (model 2CP). Kinematical relations (22) enable investigations of discontinuous cutting by means of additional variables {Λ p , Λ c , ∆ p , ∆ c } (20), ( 22). For the case β = 0 these relations can be applied to the case of absence of ploughing -η c ≡ 0 and η = η p . In the following the problem of stability of continuous cutting is analyzed to bring forward the influence of the ploughing on the stability boundaries. More specifically, the case of continuous engagement of both edges is considered (η c > 0, η p > 0, ∀τ ). In this case, the equations of new surfaces generation ( 22) simplify and enable the explicit expression of uncut chip thickness for each edge:

η p (τ ) = α(1 -β) + ξ(τ -1 + β) -ξ(τ ), η c (τ ) = αβ + ξ(τ -β) -ξ(τ ). (25)
Continuous cutting stability.

Consider the case of continuous cutting without vibrations ξ(τ ) = ξ 0 = const. From relations (25) the uncut chip thicknesses read

η 0 p (τ ) = α(1 -β), η 0 c (τ ) = αβ. (26)
From equations ( 23) one finds the constant cutting forces:

Π 0 p = K p0 H p α + r p α 2 1 + α , Π 0 c = K p0 ψαβ, Π 0 = Π 0 p + Π 0 c = K 0 α + rα 2 1 + α . (27)
The undimensional cutting stiffness (24) takes the following form:

κ 0 (α; r) = r + 1 -r (1 + α) 2 , κ 0 p (α; r) = r p + 1 -r p (1 + α) 2 . ( 28
)
In the following, the zero superscript for quantities (28) will be omitted. An example of data according to ( 27), ( 28) is given on fig. 6. It is remarkable that the cut stiffness varies in finite range.

The unperturbed motion corresponds to the cutting with constant tool deflection ξ 0 , determined by equations ( 21), ( 27)

ξ 0 = Π 0 . (29)
For small oscillations around the reference state described by ( 26), ( 27), ( 29) the tool's deflection writes as follows: ξ = ξ 0 + δξ(τ ). The equations ( 21), ( 23), ( 25) can be linearized w.r.t. the variation δξ, yielding the variation equations of motion :

F 2 4π 2 δξ(τ ) + 2ζ F 2π δξ(τ ) + δξ(τ ) = = K p0 κ p (α; r p )[δξ(τ -1 + β) -δξ(τ )] + ψ[δξ(τ -β) -δξ(τ )] . (30)
For fixed set of cut depth (parameter B in equation ( 10)), tool and material, the quantities {ζ, K p0 , r p , ψ, β} would be constant. Control parameters would be: cutting velocity F and feed per turn α. The parameter α is interrelated to κ p via equation ( 28), and the force value Π p (α), see fig. 3, determines the tangent slope (fig. 6)

α = -1 + 1 -r p κ p -r p . (31)
Finally, the stability evaluation with ploughing taken into account, corresponds to the determination of the stability boundaries on the plane {F, κ p } or {F, α} according to (31) or {F, κ} according to (28).

The solution of the equation ( 30) can be replaced by an exponential form (Euler's substitution) δξ(τ ) = δξ 0 e λτ . Thus, one obtains the characteristic equation.

F 2 4π 2 λ 2 + 2ζ F 2π λ + 1 + K p0 κ p (1 -e -λ+λβ ) + ψ(1 -e -λβ ) = 0. (32)
If in the equation (32) one assumes β = 0, K p0 → K 0 , κ p → κ, the resulting equation corresponds to the classical case for one cutting edge,

F 2 4π 2 λ 2 + 2ζ F 2π λ + 1 + K 0 κ(1 -e -λ ) = 0, (33)
analyzed in most works on stability of continuous cutting [START_REF] Altintas | Manufacturing automation. Metal Cutting Mechanistics, Machine Tool Vibrations, and CNC Design[END_REF]; [START_REF] Tobias | A Theory of Regenerative Chatter[END_REF]).

The boundaries of instability zones correspond to the locus of points for which the characteristic exponent λ is purely imaginary -λ = 2πis, i = √ -1, s ∈ R. It is of interest to notice that in this case, the static bifurcation (Euler's bifurcation) λ = 0 doesn't existand that only the dynamic bifurcation (Poincaré -Andronov -Hopf bifurcation) is possible. After substitution λ = 2πis into the equation ( 32) and real and imaginary part separation, one obtains two transcendent equations

-F 2 s 2 + 1 + K p0 κ p [1 -cos 2πs(1 -β)] + ψ(1 -cos 2πsβ) = 0, 2ζF s + K p0 [κ p sin 2πs(1 -β) + ψ sin 2πsβ] = 0, (34)
which determine, in parameterized form, the values of {F, κ p } on the stability boundary {F (s), κ p (s)} . The solution of the system (34) is sought under assumption F > 0, r p ≤ κ p ≤ 1. Depending on the values of parameters K p0 , β, ψ, ζ, there would exist finite or infinite solution branches for (34). Fig. 7 shows the results of computation of stability boundaries for the case from fig. 6 -{β = 0.02, ψ = 1.2, K p0 = 4.9801 with the damping ζ = 0.02. It is important to remark that, for these graphs, the cut depth B is taken constant.

Only the chip thickness evolves with its connected quantities κ, κ p and α. The areas of instability of continuous cutting are green-colored and the extrema of respective boundary curves are shown with red points. Fig. 8 shows analogous results for β = 0 with the parameter values, corresponding to fig. 7 {K p0 , β, ψ, ζ}, i.e. the ploughing effects are not considered. These plots correspond entirely to the classical results, such as shown by [START_REF] Altintas | Manufacturing automation. Metal Cutting Mechanistics, Machine Tool Vibrations, and CNC Design[END_REF]. Nevertheless, as for the rational-fractional cutting force model, the stiffness κ cannot be smaller than r = 0.2 (28), a part of instability domain becomes unavailable for experimental observation. I.e. there exists a range of cutting velocity values (parameters F ), in which the solution of (34) would exist for κ p < r p , which does not agree with (28), since κ p > r p , ∀α > 0. This means that in this range the vibrations exist for any value of feed. This fact is observable in reality but cannot be explained without a tool-workpiece interaction model with limited stiffness (fig. 6). Fig. 8 features analogous results for the case when the ploughing effect is not accounted for (β = 0). By comparing fig. 7 and8, we can notice that the ploughing would lead to a reduction of unstable areas, especially a low cutting speeds. This fact, that is observed in practice, cannot be explained in the framework of classical model. The reduction of the cut stiffness K 0 = K 0 /k = γσ L B/k reduces the unstable areas in the plane {F, κ p }, {F, κ}, {F, α}. The results for K 0 = 0.5 are shown on fig. 9, this stiffness is ten times lower than in the case presented on fig. 7. The increase of the K 0 enlarges instability areas. Fig. 10 shows the results for K 0 = 50, which is ten times higher, than for the fig. 7.

The influence of parameters {ψ, β} is illustrated by the results on fig. 11, 12. Thus, the developed model allows investigation of influence of all the parameters determining cutting dynamics phenomena, including the parameters of the tool's fixation characteristics. The measurement of cutting forces in quasistatic mode allows determining the parameters {K 0 , H, r}. The measurement of vibrations for a tool with known characteristics {m, k, ζ} enables the computation of stability boundaries, for example on the plane {F, α}, which gives access to quantities {β, ψ}, characterizing ploughing.

Ploughing-caused damping modification.

Consider the case, when the flank face-related delay is relatively small β 1, and apply the following approximation

1 -e -λ+λβ 1 -e -λ , 1 -e -λβ λβ, K p0 κ p K 0 κ.
The equation (32) becomes analogous to the single-edge cutting (33) The resulting overall damping ζ Σ would consist of two terms:

F 2 4π 2 λ 2 + 2ζ Σ F 2π λ + 1 + K 0 κ(1 -e -λ ) = 0. (35)
ζ Σ = ζ + ζ c ,
with ζ c linear damping, caused by the flank face work:

ζ c = πK c0 β F πK 0 ψβ F = K 0 2 √ km ψb V c . ( 36
)
with V c = 2πR/T -cutting velocity. The characteristic equation ( 35) corresponds to the variation equation (30) in the following form:

F 2 4π 2 δξ(τ ) + 2ζ Σ F 2π δξ(τ ) + δξ(τ ) = K 0 κ(α; r)[δξ(τ -1) -δξ(τ )].
Thus, the influence of the ploughing can be represented as linear damping ζ c (36), proportional to the ploughing force and inversely proportional to the cutting velocity V c . The expression of the efficient damping (36) reflects a fact well known in practice: the influence of ploughing increases at low cutting velocities (this is why in drilling, peening occurs under the center of the tool) [START_REF] Tobias | A new approach of formulating the transfer function for dynamic cutting processes[END_REF]). The influence of ploughing on the boundaries of the stability area boundaries for turning is shown on fig. 13. The quantity (K c0 b/V c ) is called linear cutting damping coefficient, accounting for the ploughing effect. This is consistent with the interference volume-based damping description.

Conclusion

A macroscopic mechanistic model framework for turning including ploughing effect is proposed, based on the concept of a fictitious auxiliary cutting edge, representing the flank face interaction. This auxiliary cutting edge is situated closely behind the principal one. The latter represents the cutting itself, as classically stipulated in literature. In this context, the tool-workpiece interaction model in this work is characterised by 5 parameters {K 0 , H, r, b, K c0 } and describes the nonlinear dynamics of continuous and interrupted cutting. The first three cutting parameters {K 0 , H, r} are related to the principal edge cutting force model coefficients (the rational-fractional formulation is used in the present work). These quantities can be evaluated experimentally in the quasi-static cutting case via widespread protocols. The work of the auxiliary cutting edge is characterised by two parameters: (1) geometrical parameter b, related to the size of the flank face; (2) stiffness parameter K c0 , connected to the interaction of the flank face with the machined material.

The application if the above mentioned approach to the investigated turning operation leads to the following observations:

1. The resulting dynamics involve two delays {T -∆T, ∆T }. For vanishing ploughingrelated delay ∆T → 0 the model is identical to the classical model of cutting with single edge.

2. The variation of the auxiliary edge parameters {b, K c0 } has major influence on position and shape of the instability zones for continuous cutting.

3. The use of rational-fractional cutting law with finite cutting stiffness variation provides an explanation for a practically observed fact: for certain parameter combination there is a range of cutting velocities, inside which the vibrations exist at any feed per turn.

4. The additional values {b, K c0 }, characterising the ploughing, can either be determined from an experiment with vibrations in the feed direction, at frequencies multiples of the workpiece rotation rate, or from experimental measurement of instability boundaries (auto-oscillation onset) for continuous cutting process.

5. An asymptotical reduction of the model leads to an analytical expression of the linear damping coefficient including the influence of ploughing. This coefficient is proportional to the flank face force interaction coefficient and inversely proportional to the cutting speed.

For further developments, an experimental investigation could constitute a natural continuation of the presented theoretical framework.

Figure 1

 1 Figure 1 Schematic of the turning operation

2

  Schematic of the cutting part of the tool with the auxiliary cutting edge on the flank face; b flank face effective width, Vc cutting speed, V feed rate 2 Ploughing modelling description Auxiliary cutting edge.

  (a)) and the dissipated energy due to the cutting process also increases. The work of the flank face is the main contribution to the vibratory part of the cutting forces (fig.5(b) and 5(c)). Analogous data is available for high frequency vibrations (n = 30). However, as distinct from the low frequency case the work of the flank face can lead to positive energy input, as determined by the phase relations between the cutting force and the tool vibrations, which is clearly seen in the force-displacement diagram -fig.5(d).

Figure 3

 3 Figure 3 Distribution of the cutting force (black line) between the principal (blue line) and auxiliary (red line) cutting edges.

Figure 4

 4 Figure 4 Influence of the effective flank face length β on the characteristics of the cutting for low frequency axial vibration (blue line, n = 3) and for high frequency axial vibration (red line, n = 30), solid line: full computation, cross: approximation (15).

Figure 5

 5 Figure 5 Cutting process characteristics variation for low frequency axial vibration (blue line, n = 3) -vibrations lead to energy dissipation (∆ΨT e < 0) and high frequency (red line) -vibration leads to energy input into the system (∆ΨT e > 0).

Figure 6

 6 Figure 6 Quasistatic cutting forces Π = Πp + Πc and cut stiffness κ, κp vs feed per turn.

Figure 7

 7 Figure 7 Instability zones for continuous cutting on parameter planes {F, κp}, {F, κ}, {F, α} with β = 0.02.

Figure 8

 8 Figure 8 Areas of instability of continuous cutting in three planes of parameters {F, κp}, {F, κ}, {F, α} at β = 0 -no ploughing.

Figure 9

 9 Figure 9 Reduction of instability regions. Case K0 = 0.5 (compare to fig. 7).

Figure 10

 10 Figure 10 Enlargement of instability regions. Case K0 = 50 (compare to fig. 7).

Figure 11

 11 Figure 11 Raise of the instability regions on planes {F, κp}, {F, κ} is caused by the increase in stiffness of the flank face, ψ = 3 (compare to fig. 7).

Figure 12

 12 Figure 12 Deformation of instability regions, caused by the increase in β = 0.03 (compare to fig. 7), i.e. in the effective auxiliary edge distance.

Figure 13

 13 Figure 13 Stability areas for continuous cutting without ploughing (blue line) and with ploughing taken into account (red line).

Acknowledgement

The research was partially supported via the Agreement N o 14. 579.21.0042 25.08.2014 (id RFMEFI57914X0042) between OAO 'VNIIINSTRUMENT' and the Ministry of Education and Science of the Russian Federation on the subject "Development of equipment and technology for nano-dimensional machining of optical materials by monocrystalline and abrasive tools under quasi-plastic cutting".


Julien Morin
email: julien.morin@univ-amu.fr

Adrien Gandolfo

Brice Temime-Roussel

Gregory Brochard

Virginie Bergé

Sasho Gligorovski

Henri Wortham
email: henri.wortham@univ-amu.fr

Key parameters influencing the uptake of m-xylene on photocatalytic paints

Keywords: Indoor Air, Photocatalysis, Uptake coefficient, Cellulose Nanocrystals, Flow Tube, PTR-MS

Given the toxic nature of many volatile organic compounds (VOCs) present within indoor environments, it is necessary to develop new materials to eliminate them. Photocatalytic paints represent a promising technology to remove the indoor pollutants but they are not optimised yet. Here we evaluate the capacities of one conventional white-wall paint, three photocatalytic paints containing 3.5, 5.25 and 7% of nano-TiO 2 PC 500, and two photocatalytic paints with a hybrid cellulose nanocrystals-nano-TiO 2 (CNC-nano-TiO 2 ) to eliminate m-xylene from the indoor environment. In particular, we assess the impact of nano-TiO 2 content, light intensity, relative humidity (RH), surface temperature (288-320 K) and pigment volume concentration (PVC) on uptake of m-xylene. Uptake coefficients of m-xylene increase by a factor 3, 5 and 3, respectively, as a function of nano-TiO 2 content, irradiance and PVC. In contrast, uptakes of m-xylene decrease for a factor of 2 and 3, as a function of RH, and surface, suppressing the photocatalytic activity. The addition of CNC-nano-TiO 2 in the binder induces limited binder degradation. These are very promising results which may help to improve the performances of indoor photocatalytic paints aimed to eliminate indoor airborne pollutants.

INTRODUCTION

Volatile organic compounds (VOCs) represent ubiquitous indoor air pollutants [START_REF] Bolden | New Look at BTEX: Are Ambient Levels a Problem?[END_REF][START_REF] Salthammer | Formaldehyde in the Indoor Environment[END_REF]. Some VOCs are known to cause human health effects and VOC compounds, such as formaldehyde, benzene, dichloromethane, have been identified as carcinogens [START_REF] Thepanondh | Airborne Volatile Organic Compounds and Their Potential Health Impact on the Vicinity of Petrochemical Industrial Complex[END_REF]. The indoor sources of VOCs are numerous and include emissions from building itself, decorative material (paints, vanishes…), furniture, inhabitants' activities (cooking, smoking…) and domestic cleaning products, among others. Recent studies carried out in France [START_REF] Verriele | The MERMAID Study: Indoor and Outdoor Average Pollutant Concentrations in 10 Low-Energy School Buildings in France[END_REF] and in Europe [START_REF] Geiss | The AIRMEX Study -VOC Measurements in Public Buildings and Schools/Kindergartens in Eleven European Cities: Statistical Analysis of the Data[END_REF] shown a VOCs indoor-to-outdoor environment concentration ratios up to 14.3. In occidental countries, humans spend on average over 90% of their lifetime within indoor settings [START_REF] Roberts | National Human Activity Pattern Survey Data Base[END_REF]. Based on these two observations, it is necessary to develop methods to reduce VOCs levels in order to improve indoor air quality. This approach include different techniques such as biofiltration, adsorption, condensation, incineration and photocatalytic oxidation (PCO) [START_REF] Sattler | Method for Predicting Photocatalytic Oxidation Rates of Organic Compounds[END_REF][START_REF] Zhong | Modeling and Physical Interpretation of Photocatalytic Oxidation Efficiency in Indoor Air Applications[END_REF][START_REF] Zhong | Photocatalytic Air Cleaners and Materials Technologies -Abilities and Limitations[END_REF]. The photocalytic system allows to oxidize, as well as reduce, air pollutants adsorbed on semiconductor surface. PCO is intensively studied and considered as a promising technology [START_REF] Zhao | Photocatalytic Oxidation for Indoor Air Purification: A Literature Review[END_REF] to improve indoor air quality.

Benzene, Toluene, Ethylbenzene and o-m-p Xylenes also called BTEX have been extensively studied in indoor air because of their toxicity [11][12][13][14] and their high measurements frequency.

For instance, Hazrati et al . [START_REF] Hazrati | Preliminary Assessment of BTEX Concentrations in Indoor Air of Residential Buildings and Atmospheric Ambient Air in Ardabil, Iran[END_REF] summarized house BTEX concentrations in different countries. Their concentrations range as 1-5 ppb, 3-10 ppb, 1-5 ppb and 2-15 ppb for benzene, toluene, ethylbenzene and xylenes, respectively. The main sources of xylenes are vehicles exhaust [START_REF] Ineris | Exposition Par Inhalation Au Benzène, Toluène, Éthylbenzène, et Xylènes (BTEX) Dans l'air[END_REF].

The degradation of m-xylene has been studied on different supports as a function of Relative Humidity (RH) [START_REF] Palau | UV Photocatalytic Oxidation of Paint Solvent Compounds in Air Using an Annular TiO2-Supported Reactor[END_REF][START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF][START_REF] Jo | Heterogeneous Photocatalysis of Aromatic and Chlorinated Volatile Organic Compounds (VOCs) for Non-Occupational Indoor Air Application[END_REF][START_REF] Ao | Photodegradation of Volatile Organic Compounds (VOCs) and NO for Indoor Air Purification Using TiO2: Promotion versus Inhibition Effect of NO[END_REF], irradiance [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF] and nano-TiO 2 content [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF]. To the best of our knowledge, there is no previous studies focused on the influence of surface temperature, aging and Pigment Volume Concentration (PVC) of photocatalytic materials on the m-xylene degradation. The study of Strini et al. [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF] has shown the increase of the photocatalytic activity with increase of light intensity. The improved photocatalytic ability was also observed with increase of nano-TiO 2 content [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF]. Jo et al. [START_REF] Jo | Heterogeneous Photocatalysis of Aromatic and Chlorinated Volatile Organic Compounds (VOCs) for Non-Occupational Indoor Air Application[END_REF] observed no impact of RH on photocatalytic activity whereas two other studies showed an influence of RH on photocatalytic efficiency. At low concentration of m-xylene (46 ppb) [START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF] a decrease of photocatalytic activity has been observed with increase of RH. At high concentration (460 ppb) of m-xylene [START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF] an increase between 0 and 45% of RH and a decrease above 45% of RH; of photocatalytic activity have been observed. These different studies have been performed on photocatalytic thin films [START_REF] Jo | Heterogeneous Photocatalysis of Aromatic and Chlorinated Volatile Organic Compounds (VOCs) for Non-Occupational Indoor Air Application[END_REF], glass fibers [START_REF] Palau | UV Photocatalytic Oxidation of Paint Solvent Compounds in Air Using an Annular TiO2-Supported Reactor[END_REF] and cement mortars [START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF][START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF] but never on photocatalytic paints. Tryba et al. [START_REF] Tryba | Photocatalytic Decomposition of Benzo-[a]-Pyrene on the Surface of Acrylic, Latex and Mineral Paints. Influence of Paint Composition[END_REF] have studied the degradation of benzo[a]pyrene by photocatalytic paints but they have not assessed the impact of different environmental and physical parameters on photocatalytic efficiency to eliminate indoor VOCs. Additional studies are recommended to improve the knowledge o, this matter.

In this study we have chosen m-xylene as a model compound because: 1) it is commonly observed in indoor environment [START_REF] Hazrati | Preliminary Assessment of BTEX Concentrations in Indoor Air of Residential Buildings and Atmospheric Ambient Air in Ardabil, Iran[END_REF], 2) it is not emitted by the studied paints [START_REF] Morin | Application of a Mineral Binder to Reduce VOC Emissions from Indoor Photocatalytic Paints[END_REF] thus avoiding experimental artefacts, 3) it presents hazardous effects on human health (neurologic effects, digestive disorder, irritation…) [14] and 4) it is not an easily degradable compound due to the relative stability of aromatic rings with respect to its oxidation and reduction process.

In the present work, the uptake coefficients of m-xylene on various paints (non-photocatalytic, hereafter, reference paint and photocatalytic paints) were determined under different experimental conditions in presence of UV irradiation. The influence of key parameters driving the reaction was evaluated by the comparative approach. The influence of environmental parameters (surface temperature, RH, irradiance intensity) as well as paint physical parameters (photocatalyst type and content, paint aging and paint porosity) on mxylene degradation have been examined.

MATERIALS AND METHODS

2.1.Experimental study

A double wall flow tube photoreactor was connected to High Sensitivity-Proton Transfer Reaction-Mass Spectrometry (HS-PTR-MS) (IONICON Analytik, Austria). The operational procedure of flow tube photoreactor has been described in detail by Gandolfo et al. [START_REF] Gandolfo | Unexpectedly High Levels of Organic Compounds Released by Indoor Photocatalytic Paints[END_REF] and Morin et al. [START_REF] Morin | Application of a Mineral Binder to Reduce VOC Emissions from Indoor Photocatalytic Paints[END_REF]. The schematic diagram of the experimental setup is presented in Figure 1.

Experimental details that are particularly relevant to this work are given below. The flow tube is made of borosilicate glass with an internal volume of 131 cm 3 and was coupled to a temperature-controlled circulating bath (RC6 LAUDA, Germany) which allows to perform the experiments at different surfaces temperatures between 288 and 320 K (±1 K).

Experiments were carried out at 1 atm total pressure of synthetic air (Linde Gas, France, >99.999 stated purity). The glass plate recovered by the paint was introduced into the flow tube reactor with the painted side upward oriented. Inside the flow tube, a glass made movable injector was inserted into the flow tube to inject m-xylene and vary the residence time and thus asses the kinetics of the heterogeneous reactions.

The flow tube reactor was placed in a stainless steel box with four UV fluorescent lamps (Philips TL-D 18W Actinic BL, 340-400 nm, λ max = 368 nm, length = 60 cm) mounted side by side on the upper part of the box above the flow tube photoreactor. The UV-lamps simulated UV solar irradiation and could be operated individually. The spectral irradiance of the UV lamps used in this work had been determined previously [START_REF] Bartolomei | Formation of Indoor Nitrous Acid (HONO) by Light-Induced NO2 Heterogeneous Reactions with White Wall Paint[END_REF]. The integrated spectral irradiance (340<λ<400 nm) was estimated to be 4.9, 8.8, 13.5 and 18.6 W m -2 for 1, 2, 3 and 4 lamps, respectively. Gaseous m-xylene was generated using a gas-phase generator (PUL 200, Saint Chamas, France). A sealed permeation cell consisting of a Teflon tube (perfluoroalkoxy, 4.0×6.4 mm, 8 cm long) filled with pure m-xylene (Sigma-Aldrich, ≥ 99.5%) was used to generate gasphase m-xylene. The permeation cell was placed in the oven chamber of the gas-phase generator. At the exit of the oven, a constant flow of 10 sccm (Brooks SLA, Series mass flow controller, in the range 0-10 sccm, ±1% stated accuracy) of gaseous m-xylene was allowed to enter the injector. A sheath synthetic air flow of 190 sccm (Brooks SLA, Series mass flow controller, in the range 0-500 sccm, ±1% stated accuracy) was allowed to enter the flow tube to dilute the m-xylene flow. To better simulate realistic indoor concentration, all experiments were carried out at ~ 50 ppb of m-xylene.

Relative humidity was adjusted by splitting the sheath synthetic air flow into a dry flow and a humidified flow. For all the experiments, the RH was measured online at the exit of reactor by a hygrometer "Hygrolog NT2" (Rotronic) with "HygroClip SC04" probe and ranged from 2 to 70% with accuracy of ±1.5%.

The m-xylene mixing ratio was measured in real time by a HS-PTR-MS by following its protonated molecular pic (m/z 107). Formaldehyde (m/z 31), acetaldehyde (m/z 45) and acetone (m/z 59) were also monitored as intermediates by-products. The HS-PTR-MS high time resolution (10 seconds) allows us to measure rapid changes in gas phase concentrations.

The drift temperature, drift voltage and a pressure were fixed at 333±1 K, 500±1 V and 2.02±0.01 mbar respectively, that corresponded to the E/N value of 124 Townsend (1 Townsend = 10 -17 V cm 2 ), where E is the electric field (V cm -1 ) and N is the ambient air number density within the drift tube (cm -3 ). The calculation of VOCs mixing ratio and surface emission fluxes is described in detail by Morin et al. [START_REF] Morin | Application of a Mineral Binder to Reduce VOC Emissions from Indoor Photocatalytic Paints[END_REF].

Preparation of paints

Paints were formulated and produced by the paint manufacturer ALLIOS (Marseille, France). TITANE PC 500 in anatase form with 85% of TiO 2 nanoparticle was used as a photocatalyst. TITANE PC 500 represents ultrafine TiO 2 powder with specific area of 350 m 2 g -1 and particle size between 3 and 5 nm. A mixture of ground additives (slurry) was prepared with 35% (w/w) active nanosized TiO 2 . Then, other paint constituents (architectural constituent of paints, i.e., CaCO 3 and micrometric TiO 2 ) were mixed with 10, 15 and 20% of the slurry to reach 3.5, 5.25 and 7% (w/w) of photocatalytic active TiO 2 nanoparticles, respectively. The TiO 2 nanoparticles are not present in the reference paint. The prepared paint is applied on the glass plate by dint of a spiral film applicator. This methodology allows to obtain controlled and reproducible wet paint thickness of 100 µm. Then, the paints were dried in an oven ventilated by clean air during 21 days at 296 K and 55% of RH resulting in a uniform thickness film of 40 µm.

To investigate the impact of porosity on the degradation rates, three paints with different porosities were developed. To assess the paint porosity, it was necessary to introduce the Critical Pigment Volume Concentration (CPVC). CPVC is a specific Pigment Volume Concentration (PVC) in which the voids between the solid particles (structural agents and pigments) are just filled with the binder [START_REF] Gandolfo | The Impact of Photocatalytic Paint's Porosity on Indoor NOx and HONO Levels[END_REF]. The PVC and CPVC are linked to the paint porosity as follows:

(Eq.1)

The value of CPVC is not clearly known but it can be estimated between 50-60% (manufacturer information). For this study, three paints with PVC of 53, 72 and 80% were considered. The calculation of PVC were shown previously by Gandolfo et al. [START_REF] Gandolfo | The Impact of Photocatalytic Paint's Porosity on Indoor NOx and HONO Levels[END_REF].

In another series of paints, the standard nano-TiO 2 (PC 500) was replaced by a hybrid cellulose nanocrystals-nano-TiO 2 (CNC-TiO 2 ) in the paint preparation to increase nano-TiO 2 dispersion in the slurry. This addition allowed to form hybrid CNC-TiO 2 nanoparticles which may improve the photocatalytic activity of TiO 2 . The aim of this hybrid nanoparticle was to reduce the quantity of nano-TiO 2 embedded in the paint and keeps high photocatalytic efficiency. In this work, two photocatalytic paints with 0.16 and 0.23% (w/w) of nano-TiO 2 have been studied. Photocatalytic paints with hybrid CNC-nano-TiO 2 and the photocatalytic paint with 3.5% of nano-TiO 2 PC 500 have been aged in a accelerated weathering chamber for 500 hours and 1000 hours according to the ISO norm 16474-3 [27,[START_REF] Truffier-Boutry | Characterization of Photocatalytic Paints: A Relationship between the Photocatalytic Properties -Release of Nanoparticles and Volatile Organic Compounds[END_REF]. Aging of 500 hours correspond to an important aging of paint and an aging of 1000 hours correspond to a paint of end-of-life.

The paints, except CNC paints, were applied on one side of glass plates that were 29 cm long and 1.9 cm wide according to a standard operating procedure developed by the manufacturer ALLIOS [START_REF] Gandolfo | The Effectiveness of Indoor Photocatalytic Paints on NOx and HONO Levels[END_REF]. The CNC paints were applied on Leneta supports that were 29 cm long and 1.9 cm wide. To assure proper fit of the Leneta surface into the reactor, the later were fixed on a glass plate with wire to both ends prior to kinetic experiments.

2.3.Kinetic measurements

The aim of this study was to evaluate the uptake coefficients (γ) of m-xylene on reference paint and on photocatalytic paints. The uptake coefficients were determined using the following equation [START_REF] Finlayson-Pitts | Chemistry of the Upper and Lower Atmosphere : Theory, Experiments, and Applications[END_REF]:

(Eq.2)
where k 1st is the pseudo-first order rate constant of m-xylene loss (s -1 ), ω is the mean molecular velocity (cm s -1 ) and V/S represents the ratio of the volume of the reactor to surface of the glass plate (cm). k 1st was determined by the slope of ln(C 0 /C x ) plotted as a function of the residence time (t). C 0 is the initial concentration of m-xylene in position P 0 . In this case, gaseous m-xylene is not exposed to the paint. C x is the concentration of m-xylene at different positions from P 1 to P 4 (Table 1). The difference of concentrations between C 0 and C x corresponds to amount of mxylene consumed by its reaction with the paint surface. Each position was hold during about 30 min to get stabilized signal and reliable measuring points. After each position change, the injector was pushed in position P 0 to go back to the initial conditions. The variation of the concentration in function of the injector position enabled to calculate the pseudo-first order rate constant [START_REF] Bartolomei | Formation of Indoor Nitrous Acid (HONO) by Light-Induced NO2 Heterogeneous Reactions with White Wall Paint[END_REF][START_REF] Gandolfo | The Impact of Photocatalytic Paint's Porosity on Indoor NOx and HONO Levels[END_REF][START_REF] George | Photoenhanced Uptake of Gaseous NO2 on Solid Organic Compounds: A Photochemical Source of HONO? Faraday Discuss[END_REF][START_REF] El Zein | Interaction of NO 2 with TiO 2 Surface under UV Irradiation: Measurements of the Uptake Coefficient[END_REF]. A typical experiment and the assessment of pseudo-first order rate constant of m-xylene are presented in SI (Figure S1-S2). Blank experiments have been performed to ensure that no wall loss occurs during experiments and corrections have been applied to the obtained results.

The Cooney-Kim-Davis (CKD) method was used to correct the uptake coefficients from diffusion limitation in the flow tube [START_REF] Behnke | Production and Decay of ClNO2 from the Reaction of Gaseous N2O5 with NaCl Solution: Bulk and Aerosol Experiments[END_REF][START_REF] Cooney | Analyses of Mass Transfer in Hemodialyzers for Laminar Blood Flow and Homogeneous Dialysate[END_REF]. Under the applied experimental conditions, the estimated correction by CKD was less than 10%.

The experimental conditions are given in Table 2.

RESULTS AND DISCUSSION

3.1.Nano-TiO 2 content

The influence of the quantity of nano-TiO 2 on the uptake coefficients of m-xylene is presented in Figure 2. The uptake coefficient for the reference paint is (7.3±2.3)•10 -7 and increases up to

(2.0±0.5)•10 -6 for the photocatalytic paint at 7% of nano-TiO 2 . The linear relation between uptake coefficient and nano-TiO 2 content is described as follows:

(Eq.3)

When the nano-TiO 2 quantity increases, the quantity of OH radicals produced increases [START_REF] Hoffmann | Environmental Applications of Semiconductor Photocatalysis[END_REF] on the paint surface which accelerates the degradation of m-xylene. For this reason, the increase of quantity of TiO 2 nanoparticles from 0 to 7%, improves the removal of m-xylene by a factor of 3 which is in agreement with the reported factor of 4 in a previous study focused on removal of o-xylene [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF] on cementitious photocatalytic materials.

Due to improved removal efficiency towards m-xylene, the photocatalytic paint containing 7% of nano-TiO 2 was used to assess the impact of RH, surface temperature, light intensity and pigment volume concentration. The effect of light intensity on the uptake coefficients of m-xylene on reference paint and on photocatalytic paint containing 7% of nano-TiO 2 has been evaluated (Figure 3). The uptakes of m-xylene on a reference paint only slightly increase with the variation of spectral irradiance from (5.7±1.0)•10 -7 in dark up to (9.7±1.4)•10 -7 at 18.6 W m -2 . In contrast, the uptake of m-xylene on a photocatalytic paint with 7% TiO 2 nanoparticles increases for a factor of 3, from (1.2±0.4)•10 -6 in dark up to (3.5±0.4)•10 -6 under maximum light irradiation of 18.6 W m -2 . The linear relation depicted in plot is described by the equation (Eq.4):

3.2.UV irradiation intensity

(Eq.4)

The increase of light intensity leads to enhanced formation of OH radicals formed on the paint surface which in turn leads to accelerated degradation of m-xylene [START_REF] Toor | Photocatalytic Degradation of Direct Yellow 12 Dye Using UV/TiO2 in a Shallow Pond Slurry Reactor[END_REF].

A similar trend of linear increase of the degradation of toluene on glass fiber as a function of light intensity was observed by Palau et al. [START_REF] Palau | UV Photocatalytic Oxidation of Paint Solvent Compounds in Air Using an Annular TiO2-Supported Reactor[END_REF] and the degradation of o-xylene on cementitious material by Strini et al. [START_REF] Strini | Measurement of Benzene, Toluene, Ethylbenzene and o-Xylene Gas Phase Photodegradation by Titanium Dioxide Dispersed in Cementitious Materials Using a Mixed Flow Reactor[END_REF]. In their work, an increase by a factor 2.5 was observed that is in agreement with the factor 2 measured here.

These results show that the experiments were performed under light unsaturation and that the surface chemical reaction is the rate-determining step.

3.3.Relative humidity

The impact of the RH on the uptake coefficients is shown in Figure 4.

RH (%)

0 % 7 %
The decrease of the uptake by a factor 2 is in good agreement with the observed decreasing conversion ratio (46 ppb of m-xylene) by a factor of 1.5 as the RH increased from 0 to 70% [START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF]. This phenomenon can be ascribed to a competitive adsorption between water and mxylene molecules on the paint surface. At low humidity, the adsorption competition on semiconductor surface is limited which allowed the more efficient degradation of m-xylene.

As the humidity increases, absorbed water molecules on nano-TiO 2 competes with the mxylene adsorption. Consequently, the photocatalytic heterogeneous reactivity is reduced at high relative humidity [START_REF] Zhong | Modeling and Physical Interpretation of Photocatalytic Oxidation Efficiency in Indoor Air Applications[END_REF].

At very high mixing ratio of m-xylene (460 ppb), Martinez et al. [START_REF] Martinez | BTEX Abatement by Photocatalytic TiO2-Bearing Coatings Applied to Cement Mortars[END_REF] observed an increased removal efficiency of m-xylene at 45% RH which further decreased for RH between 45 and 80%. Such increase of removal efficiency of xylene (230 ppb) on photocatalytic materials has also been observed by Palau et al. [START_REF] Palau | UV Photocatalytic Oxidation of Paint Solvent Compounds in Air Using an Annular TiO2-Supported Reactor[END_REF] for RH comprised between 4 and 70%.

3.4.Surface temperature

To the best of our knowledge, the impact of surface temperature on the uptake coefficients of m-xylene has not been studied previously. The surface temperature varied between 288 and 320 K (Figure 5). Figure 5 shows that the uptake coefficients of m-xylene decreased significantly as the temperature increases followed by a saturation effect. At 288 K; the uptake coefficient is (2.8±0.4)•10 -6 and decreased up to (7.6±2.9)•10 -7 at 308 K. At higher temperatures than 308 K, the uptakes of m-xylene remain stable. For the range of temperatures between 288 and 308 K, the solid line in Figure 5 represents the regression line which corresponds to the following equation (Eq.6):

(Eq.6)

The reduced removal efficiency of photocatalytic paint with 7% TiO 2 nanoparticles at higher temperatures can be ascribed to the reduced contact time between gaseous m-xylene and the paint surface. Namely, as the surface temperature increases m-xylene desorb more rapidly and thus decrease the contact time with the paint surface. In that way, the contact time becomes not sufficient to achieve the degradation process [START_REF] Barakat | Influence of Temperature on the Photodegradation Process Using Ag-Doped TiO2 Nanostructures: Negative Impact with the Nanofibers[END_REF]. The uptakes of m-xylene for temperature range between 308 and 320 K, (7.6±2.9)•10 -7 , fall in the same range as the uptake of m-xylene on a reference paint, (7.3±2.3)•10 -7 . Hence, the observed plateau in Figure 5 indicates that at higher temperature than 308 K, the removal of m-xylene is not driven by the photocatalytic process.

3.5.Effect of pigment volume concentration (PVC)

The removal of m-xylene was also evaluated on photocatalytic paints containing 7% of nano-TiO 2 with PVC of 53%, 72% and 80% (Figure 6). The uptake coefficients of m-xylene increase from (8.6±2.4)•10 -7 to (2.3±0.3)•10 -6 as the PVC increases from 53 to 80%. This increase of photocatalytic efficiency towards the removal of m-xylene can be ascribed to the fact that the increase of the porosity allows gaseous m-xylene to penetrate more easily through the paint and increase the contact time with the OH radicals which are generated by the irradiation of TiO 2 nanoparticles [START_REF] Hoffmann | Environmental Applications of Semiconductor Photocatalysis[END_REF]. Similarly, the increase of porosity on a commercial 3.0x10

PVC (%)

0 % 7% paint induced faster degradation of methyl ethyl ketone [START_REF] Giosuè | Improving the Impact of Commercial Paint on Indoor Air Quality by Using Highly Porous Fillers[END_REF]. Jansson et al. [START_REF] Jansson | Zeolite-TiO2 Hybrid Composites for Pollutant Degradation in Gas Phase[END_REF] observed accelerated degradation of formaldehyde by zeolite/TiO 2 .

3.6.CNC and aging

The aging of three photocatalytic paints with various photocatalysts namely PC 500, CNC 0.5 and CNC 0.72 have been examined (Figure 7). The PC 500 represents the photocatalytic paint with 3.5% of nano-TiO 2 and CNC 0.5 and CNC 0.72 paints contain 0.5 and 0.72% of hybrid cellulose nanocrystals (CNC) embedded in that paint that correspond to 0.16% and 0.23% of nano-TiO 2 , respectively. At first sight, the three paintings are identical in term of color and appearance regardless of the aging. The uptake coefficient of m-xylene on the paint PC 500 increased with the aging. After 500 or 1000 hours of aging, uptake coefficients are 3 times higher than for the fresh dry paint. On the other hand, the aging has no effect on paint containing CNC-TiO 2 hybrid nanoparticles. The effect of aging on the binder of the paint was previously observed by Truffier-Boutry et al. [START_REF] Truffier-Boutry | Characterization of Photocatalytic Paints: A Relationship between the Photocatalytic Properties -Release of Nanoparticles and Volatile Organic Compounds[END_REF]. Once the binder was degraded, nano-TiO 2 became more accessible to interact with mxylene; hence, increased the removal efficiency. This hypothesis is confirmed by the results presented in Figure 7 for the paint PC 500. However, the consumption of m-xylene is not altered anymore after 500 hours of aging. This can be explain by the fact that after 500 hours the paint binder is completely degraded and cannot further influence the photocatalytic process.

For CNC paints, the uptake coefficients of m-xylene are independent of the aging process.

Thus, the hybrid CNC-nano-TiO 2 plays a protective role of the binder, limiting the contact between the OH radicals and m-xylene.

By-products formation

In theory, the photocatalytic oxidation (PCO) should lead to the total mineralization of pollutants in CO 2 and H 2 O [START_REF] Hoffmann | Environmental Applications of Semiconductor Photocatalysis[END_REF]. Unfortunately, the PCO is known to produce volatile aldehydes and other partially oxidized by-products that can be released back to indoor air [START_REF] Gandolfo | Unexpectedly High Levels of Organic Compounds Released by Indoor Photocatalytic Paints[END_REF][START_REF] Auvinen | The Influence of Photocatalytic Interior Paints on Indoor Air Quality[END_REF]. Formaldehyde, acetaldehyde, acetone, formic acid et acetic acid were produced due to the incomplete mineralization [START_REF] Hodgson | Performance of Ultraviolet Photocatalytic Oxidation for Indoor Air Cleaning Applications[END_REF]. Formaldehyde and acetaldehyde have been observed as by-products during p-xylene degradation [START_REF] Farhanian | Photocatalytic Oxidation Air Cleaner: Identification and Quantification of by-Products[END_REF], whereas formaldehyde, acetaldehyde and acetone during toluene degradation [START_REF] Debono | Ternary Mixture Effect on Ppb Level Photocatalytic Oxidation: Removal Kinetic, Reaction Intermediates and Mineralization[END_REF]. The mixing ratios of m-xylene, formaldehyde, acetaldehyde and acetone in position P 0 and P 4 are shown in Figure 8. In this experiment approx. 13 ppb of m-xylene has been degraded in position P 4 . If 100% of this compound is converted, a 2.55•10 10 molecules cm -2 s -1 of VOCs would have been formed.

In order to compare m-xylene consummation and by-products formation, we normalized observed mixing ratio to exposed paint surface area and reaction time to obtain the surface emission fluxes. For the mixing ratio and surface emission fluxes calculation, we used the method presented in detail by Morin et al. [START_REF] Morin | Application of a Mineral Binder to Reduce VOC Emissions from Indoor Photocatalytic Paints[END_REF]. The surface emission fluxes of formaldehyde, acetaldehyde and acetone due to the reaction between molecules present in the binder and radical species produced by the photocatalyst (nano-TiO 2 ) is 1.77•10 11 , 9.33•10 10 , 1.07•10 10 molecules cm -2 s -1 , respectively. The sum of surface emissions fluxes for these three compounds is 2.81•10 11 molecules cm -2 s -1 . The additional emission of VOCs due to m-xylene degradation would correspond to an increase of about 9% of the surface emission flux.

Moreover, a part of degraded m-xylene is mineralized to CO 2 and H 2 O [START_REF] Debono | Ternary Mixture Effect on Ppb Level Photocatalytic Oxidation: Removal Kinetic, Reaction Intermediates and Mineralization[END_REF][START_REF] Binas | Photocatalytic Oxidation of Gaseous Benzene, Toluene and Xylene under UV and Visible Irradiation over Mn-Doped TiO2 Nanoparticles[END_REF]. Debono et al. [START_REF] Debono | Ternary Mixture Effect on Ppb Level Photocatalytic Oxidation: Removal Kinetic, Reaction Intermediates and Mineralization[END_REF] observed a mineralization up to 76% for toluene that decreased the quantity of VOCs potentially formed at 2% or 5.81•10 9 molecules cm -2 s -1 which represents the uncertainly of the measurements. For this reason, no difference has been observed in the mixing ratios of this by-product between the position P 0 and P 4 (Figure 8); hence, the formed by-products cannot be determined in this study.

To identify and quantify the formed products due to the degradation of m-xylene, the same approach as Debono et al. [START_REF] Debono | Ternary Mixture Effect on Ppb Level Photocatalytic Oxidation: Removal Kinetic, Reaction Intermediates and Mineralization[END_REF] should be applied based on pure nano-TiO 2 . This method will allow to determine the formed by-product but it will not be relevant from environmental point of view. Surely, many efforts are needed to optimize the photocatalytic paints and establish as a safe option for removal of indoor pollutants.

CONCLUSION

The influence of nano-TiO 2 content, relative humidity, light intensity, surface temperature, pigment volume concentration, type of nanoparticles and aging, on the degradation of mxylene on photocatalytic paints have been assessed under UV irradiation. The obtained results contribute to improve the knowledge on a poorly documented area that is the removal of VOCs by photocatalytic paints in indoor air. The results are crucial for the development of an optimal formula for photocatalytic paint as a function of environmental and physical parameters.

The increase of nano-TiO 2 content and the PVC improve the removal of m-xylene by a factor of 3. The application of innovative CNC nanoparticles do not impact significantly the photocatalytic activity of the paint in comparison of widely used TiO 2 nanoparticles. Paint aging has no influence on removal of m-xylene by paint containing CNC photocatalyst but the removal efficiency increased for the paints containing PC 500 nano-TiO 2 . However, the aging of the paint implies environmental problem because of the emission of nanoparticles in the air. This subject is out of the scope in this study but deserves an attention from a healthcare point of view.

The increase of light intensity improved the removal efficiency of m-xylene by a factor 5. In contrast, high surface temperature and RH slowed down the degradation of m-xylene.

In order to assess the impact of photocatalytic paints on indoor air quality, we suggest a simple calculation to compare the lifetime of m-xylene through the major removal pathways in an indoor environment [START_REF] Manoukian | Emission Characteristics of Air Pollutants from Incense and Candle Burning in Indoor Atmospheres[END_REF]. The consumption of m-xylene by photocatalytic paint is considered for a model room of 50 m 3 with a constant irradiated wall surface of 3 m 2 . From the experimental results from this study, the removal rate of m-xylene is estimated to be 7.3•10 -6 s -1 for a non-aged photocatalytic paint containing 7% of nano-TiO 2 with a PVC of 72% at 40% of RH under a spectral irradiation intensity of 8.8 W m -2 and a surface temperature of 298 K. The lifetime associated to this removal pathway is approximatively 38 hours while the lifetime due to the oxidation by gas-phase OH radicals (assuming a mean OH concentration of 5•10 5 radicals cm -3 [START_REF] Carslaw | A New Detailed Chemical Model for Indoor Air Pollution[END_REF] and bimolecular rate constant of k OH+m- xylene = 2.3•10 -11 molecules cm -3 s -1 [START_REF] Kramp | On the Uncertainties in the Rate Coefficients for OH Reactions with Hydrocarbons, and the Rate Coefficients of the 1,3,5-Trimethylbenzene and m-Xylene Reactions with OH Radicals in the Gas Phase[END_REF]) is 24 hours, and 2 hours for a typical air exchange rate of 0.5 h -1 [START_REF] Murray | Residential Air Exchange Rates in the United States: Empirical and Estimated Parametric Distributions by Season and Climatic Region[END_REF]. Under these conditions, the main removal pathway of m-xylene is air exchange rate which account for more than 99% of its elimination. The photocatalytic degradation and OH oxidation account only minor contribution to the removal of m-xylene from the indoor air.

The future formulation of an optimized photocatalytic paint should consider the influence of the physical (quantity of TiO 2 nanoparticles, type of photocatalyst, and PVC), and environmental (RH, light intensity, surface temperature) parameters on the degradation of indoor air pollutants. In the future, photocatalytic oxidation must be studied under visible irradiation because 45% of solar irradiation is in visible region (400-700 nm) against only 4% for in the UV region of wavelengths.

Figure 1 :

 1 Figure 1: Schematic illustration of the experimental setup. Permeation oven (a), mass flow controller (b), on/off valve (c), needle valve (d), relative humidity system (e), reactor + glass paint (f), UV-lamps (g), RH probe + hygrometer (h).

Figure 2 :

 2 Figure 2: The effect of nano-TiO 2 content on uptake coefficients of m-xylene. m-xylene mixing ratio: 50 ppb, temperature: 296 K, RH: 40%, light intensity: 8.8 W m -2 , PVC: 72%, aging: 0 hour, nano-TiO 2 PC 500. The line represents the linear regression. The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 3 :

 3 Figure 3: The effect of light intensity on uptake coefficients of m-xylene. m-xylene mixing ratio: 50 ppb, temperature: 298 K, RH: 40%, PVC: 72%, aging: 0 hour. Photocatalytic paint: 7% nano-TiO 2 PC 500 (filled triangle) and reference paint (empty triangle). The line represents the linear regression of the plotted data. The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 4 :

 4 Figure 4 : The effect of RH on uptake coefficients of m-xylene. m-xylene mixing ratio: 50 ppb. Photocatalytic paint: 7% nano-TiO 2 PC 500 (filled square) and reference paint (empty square), light intensity: 8.8 W m -2 , temperature: 295 K, PVC: 72%, aging: 0 hour. The line represents the linear regression. The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 5 :

 5 Figure 5 : The effect of surface temperature on uptake coefficients of m-xylene. m-xylene mixing ratio: 50 ppb. Photocatalytic paint: 7% nano-TiO 2 PC 500 (filled lozenge) and reference paint (empty lozenge), light intensity: 8.8 W m -2 , RH: 37%, PVC: 72%, aging: 0 hour. The line represents the linear regression. The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 6 :

 6 Figure 6 : The effect of PVC on uptake coefficients of m-xylene. m-xylene mixing ratio: 50 ppb. Photocatalytic paint: 7% nano-TiO 2 PC 500 (filled triangle) and reference paint (empty triangle), temperature: 296 K, light intensity: 8.8 W m -2 , RH: 37%, aging: 0 hour. The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 7 :

 7 Figure 7: The effect of aging and photocatalyst on uptake coefficients of m-xylene. m-xylene: mixing ratio: 50 ppb, temperature: 296 K; light intensity: 8.8 W m -2 , RH: 37%, paint PC 500 (circle), paint CNC 0.5 (lozenge) and paint CNC 0.72 (square). The errors bars are derived from uncertainties associated to uptake coefficient.

Figure 8 :

 8 Figure 8: Temporal profile of formaldehyde (red line), acetaldehyde (green line), acetone (blue line) and m-xylene (dark line) mixing ratio (ppb) at temperature: 296 K, RH: 37%, light intensity: 18.6 W m -2 , aging: 0 hour, photocatalytic paint: 7% of nano TIO 2 PC500. In the part (A), injector is in position P 0 and in part (B) in position P 4 .

Table 1 :

 1 Distance to the end of reactor (cm), exposed paint surface (cm 2 ) and contact time (s) between gaseous m-xylene and paint as a function of movable injector position.

	Position	Distance (cm)	Exposed surface (cm 2 )	Contact time (s)
	P 0	0	0	0
	P 1	4	7.6	5.4
	P 2	8	15.2	10.9
	P 3	15	28.5	20.4
	P 4	22	41.8	29.9

Table 2 :

 2 Experimental conditions

	Experiments	content w/w (%) Nano-TiO 2	temperature Surface	(W m -2 ) RH (%) Irradiance	PVC (%)
			(K)
	1	0, 3.5, 5.25 and 7	296	40	8.8	72
	2	0 and 7	298	40	0-18.6	72
	3	7	295	0-70	8.8	72
	4	7	288-320	37	8.8	72
	5	7	296	40	8.8	53-80
	6	NCC : 0.16, 0.23	298	40	8.8	NA*
		PC 500 : 3.5
	* Not available

ACKNOWLEDGMENTS

The authors acknowledge gratefully LABEX SERENADE (no.ANR-11-LABX-0064) funded by the French National Research Agency (ANR) through the PIA (Programme Investissement d'Avenir). S.G. acknowledges the funding support by National Natural Science Foundation of China (No. 41773131, No. 41977187).

ASSOCIATED CONTENT Supporting Information

Typical experiment of m-xylene degradation (Figure S1), loss of gas phase m-xylene as a function of exposure time (Figure S2).

Notes

The authors declare no competing financial interest.


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text:
Gatien Falconnier

Anthony Vermue

Etienne-Pascal Journet

Laurent Bedoussac

Eric Justes

Assessment of the impact of climate change in temperate zone on grain legume yield and N 2 fixation

legumes and the associated provision of ecosystem services are the cornerstone of more sustainable cropping systems, yet the impact of climate change on their performance has not been extensively quantified. Based on previous experiments carried out in south-western France with low biotic stress, we calibrated the STICS soil-crop model for spring pea (SP), winter pea (WP) and winter faba bean (WF) and evaluated its quality of prediction on an independent dataset. STICS was used to explore the effect of climate change scenarios on the legumes performance. Assuming no change in crop management, mean and inter-annual variability of grain yield and N 2 fixation were assessed for historical , mid-term (2020-2040) and long-term (2060-2080) periods, considering projections from two Global Circulating Models (GCM) and two Representative CO 2 Concentration Pathways (RCP), i.e. RCP 4.5 and RCP 8.5. The GCMs consistently predicted no significant change in rainfall amounts and patterns but indicated a 1.7°C and 2.5°C increase in average temperature over the growth period in the long term under RCP 4.5 and RCP 8.5 respectively. Therefore, simulations indicated no extra water stress on grain yield and N 2 fixation of these legumes.

The increase in temperature entailed a shortening in crop duration and a slight but significant increase in the temperature stress factor values for grain filling, for photosynthesis and for N 2 fixation during the reproductive period (+1% to +13 % depending on temperature stress, crop and RCP). Under RCP 4.5, yield decreased by 23 to 34% (depending on crop) in the long term. Average fixed N 2 decreased by 16% to 34%. Probability of yield failure (i.e. yield below the 20 th percentile of historical yield) increased from 20 to 50, 54 and 58% for WF, WP and SP respectively. Probability of N 2 fixation failure increased from 20 to 34, 50 and 53% for WP, WF and SP respectively. In contrast, under RCP 8.5, the CO 2 fertilisation effect would offset the decrease in yield due to the increase in temperature and simulations predicted a 8 to 13 % average yield increase in the long term. Average N 2 fixation would benefit from the increase in biomass and increase by 15 to 23%. Probability of yield failure would increase slightly, from 20 to 21, 25 and 27% for WF, WP and SP respectively. Probability of N 2 fixation failure would increase for spring pea (from 20 to 31%) but decrease for winter faba bean (from 20 to 13%) and winter pea (from 20 to 11%). The increased probability of yield and N 2 fixation failure simulated with the RCP 4.5 scenario indicates the need for technical and transformational adaptations for grain legumes to deliver the expected ecosystem services with future climate. Under RCP 8.5, better yield and N 2 fixation highlight the opportunity represented by climate change for inclusion of grain legume in cropping systems. Key-words : STICS, pea, faba bean, risk


domain: shs sdv info

text:
Subclinical hypocalcemia in dairy farms with low milk yield and its consequences on health

L. Alves de Oliveira 1 , C. Astruc 1 , P. Otz 1 , R. Eicher 2 [START_REF] Gillet | Proc. 29th World Buiatrics Congress[END_REF] VetAgro Sup, Université de Lyon, 69280 Marcy, France (2) Biokema SA 1023 Crissier, Switzerland laurent.alves@vetagro-sup.fr

Introduction: Subclinical hypocalcemia (SCHC), i.e. calcemia levels (Ca) below 2 mmol/L 2,3 or 2,1 mmol/L 4 within 48 hours after calving without clinical signs, is a common metabolic disorder in dairy cows. Cows with SCHC are more likely to develop displaced abomasum, ketosis, dystocia, uterine prolapse, retained placenta and mastitis. SCHC prevalence in USA herds is very high, ranging from 39% 2,3 (Ca < 2) to 78% 4 (Ca < 2,1). The objective of our study was to determine if the importance of SCHC in mid-mountain herds in France (Monts du Lyonnais) is the same as in USA.

These herds have lower production levels, different breeds and a diet with an important part of grass.

Materials & methods:

The study was conducted on 115 cows from 14 farms of the clinic of the Veterinary School of Lyon as part of a care follow-up. Calcemia was measured 12 to 24 hours after calving. Assisted calving (breeder or veterinarian), placental retention, metritis, clinical mastitis, clinical ketosis and displacement of the abomasum were recorded. A control of the milk production was carried out each month by the National DHIA testing system. The statistical analysis was carried out using R software (Chi2, Student, Mann-Whitney Wilcoxon) and Excel (odds ratio).

Results: 33 or 45 cows had a Ca lower than 2 or 2,1 mmol/L, respectively (28.7% or 39% of our sample). 15.2% of the primiparous, 40.6% of the lactations 2, 47.8% of the lactations 3 and 62.5% of the lactations 4 and + had a Ca lower than 2,1 mmol/L. The prevalence of SCHC is significantly lower in primiparous cows vs multiparous cows. A significant effect of breed (P < 0.04) was observed on Ca, 46.8% of the Holstein cows vs 33.3% of the Montbéliardes had a Ca lower than 2,1 mmol/L. Among the 115 cows, 39 had an assisted calving, 15 had placental retention, 15 showed a metritis and 29 a clinical mastitis. No clinical ketosis or displacement of the abomasum was reported.

Cows with SCHC had an increased risk of placental retention (OR = 7, [95% CI = 2.1-25.6], p = 0.002) and of assisted calving (OR = 2, [95% CI] = 0.9 -4.7], p = 0.08). Milk yield (mean of the 3 first monthly controls) was higher for hypocalcemia cows : 32.4 kg (± 2.2) vs 28.2 kg (± 1.5), p = 0.002. No difference could be shown for protein level, fat content and somatic cell counts. Discussion: The prevalence of SCHC in our study is rather high, although lower than those reported in USA and in the only French study 1 (45%). This is probably related to the lower production level of the herds in our study. This also explains that Montbeliardes have less subclinical hypocalcemia than Holstein. The association between SCHC and postpartum diseases described in the literature is present. Nevertheless, for some diseases, this association could not be found because of the small size of our sample. This study shows that the prevention of hypocalcemia is important also in herds with relatively low milk yield.

The authors thank VETALIS Technologies (Châteaubernard, France) for their financial support.


text:
Varieties and cropping systems for an agroecological production Why such a deficit in lentil production ?

• Despite economic and agronomic advantages:

 High selling price  No need for N fertilization [1]  Diversification of rotations [2] • Low and unstable productivity  3 major yield-reducing factors Weeds Up to 100% losses [3] Bruchids Up to 50% losses [4] Lodging Up to 100% losses [5] [1] Peoples et al. 2002 [2] Angus et al. 2015 [3] Wang et al. 2013 [4] Laserna-Ruiz et al. 2012 [5] Carr et al. 1995

Varieties and cropping systems for an agroecological production Why such a deficit in lentil production ?

• Despite economic and agronomic advantages:

 High selling price  No need for N fertilization [1]
 Diversification of rotations [2] • Low and unstable productivity  3 major yield-reducing factors

Weeds

Up to 100% losses [3] Bruchids Up to 50% losses [4] Lodging Up to 100% losses [5] ? ? ?

Can intercrops (IC) lower these reducing factors compared to sole crops (SC) ?

VASCO Team

Varieties and cropping systems for an agroecological production

Field experiments 2015 and 2016 •••

 2016 INRA Auzeville (SW France) • Experimental plots, no inputs • Low N mineral content at sowing (30 kg N ha -1 ) • 4 lentil and 2 spring-wheat cultivars • 100% lentil + 17% wheat in intercrop • Both crops sown and harvested simultaneously 30/08/18 Contact: Loic.vig@gmail.com VASCO Team Varieties and cropping systems for an agroecological production Yield gap concept (adapted from Evans 1993 and Van Ittersum et al. 2013) (e.g. bruchids), Weeds, Pollutants 30/08/18 Contact: Loic.vig@gmail.com VASCO Team Varieties and cropping systems for an agroecological production Effect of intercrops (IC) on actual grain yields • Total IC actual grain yield > lentil SC Complementary use of resources, notably N • Lentil IC actual grain yield < lentil SC Strong competition of wheat over lentil • Effect on actual gross margins ? of intercrops (IC) on actual gross margins • Total IC gross margin < lentil SC IC are less profitable than lentil SC Lentil determines IC gross margins  Lentil price = 4 × wheat price MechanicalGrain quality (e.g. broken, small grain, bruchiddamaged residues) 30/08/18 Contact: Loic.vig@gmail.comVASCO TeamVarieties and cropping systems for an agroecological production Effect of intercrops (IC) on bruchid damage rate• No effect of IC on bruchidsIC not a lever to lower bruchids• Important impact of bruchids• Effect of year and lentil cultivarTrial not designed for such study systems for an agroecological production Effect of intercrops (IC) on marketable gross margins • Total IC marketable gross margin > lentil SC IC is an insurance and a Intercropping lentil with wheat Lowers lentil lodging Has no effect on bruchid damages • Economic analysis Should consider marketable yield Indicates lentil crop is currently far from optimum

30/08/18 Contact: Loic.vig@gmail.com

	[1] Peoples et al. 2002
	[2] Angus et al. 2015
	[3] Wang et al. 2013
	[4] Laserna-Ruiz et al. 2012
	[5] Carr et al. 1995
	3

30/08/18

Contact: Loic.vig@gmail.com

VASCO Team

Varieties and cropping systems for an agroecological production Effect of intercrops (IC) on lentil harvest efficiency

VASCO Team

Varieties and cropping systems for an agroecological production Effect of intercrops (IC) on lentil harvest efficiency

VASCO Team

Varieties and cropping systems for an agroecological production Thanks for your attention