Xing- Wang

Adlan Merlo

Claire Dupont

Anne-Virginie Salsac
email: anne-virginie.salsac@utc.fr

Dominique Barthès- Biesel

A microfluidic methodology to identify the mechanical properties of capsules: comparison with a microrheometric approach

Keywords:

We present a microfluidic method to measure the elastic properties of a population of microcapsules (liquid drops enclosed by a thin hyperelastic membrane). The method is based on the observation of flowing capsules in a cylindrical capillary tube and an automatic inverse analysis of the deformed profiles. The latter requires results from a full numerical model of the fluid-structure interaction accounting for nonlinear membrane elastic properties. For ease of use, we provide them under the form of databases, when the initially spherical capsule has a membrane governed by a neo-Hookean or a general Hooke's law with different surface Poisson ratios. Ultimately, the microfluidic method yields information on the type of elastic constitutive law that governs the capsule wall material together with the value of the elastic parameters. The method is applied on a population of ovalbumin microcapsules and is validated by means of independent experiments of the same capsules subjected to a different flow in a microrheological device. This is of great interest for quality control purposes, as small samples of capsule suspensions can be diverted to a measuring test section and mechanically tested with a 10% precision using an automated process.

1

Impact Statement

Encapsulation consists in enclosing a substance inside a membrane in order to protect it and control the exchanges with the environment. Recent innovative applications use capsules containing active principles, fragrances, flavors, phase change materials or organ cells. A microfluidic methodology is presented to measure the membrane elastic properties of microcapsules with a liquid core. The method is based on an inverse analysis of the deformed profiles of capsules flowing in a capillary tube. A fluid-structure numerical model that accounts for nonlinear large deformations of the capsule wall, corresponding to a strain-hardening orsoftening material behavior, provides the database for the inverse analysis. The method is applied on artificial microcapsules with a cross-linked ovalbumin membrane and is validated by comparison with measures in a microrheological device. The advantage of the microfluidic method is that it is simple to implement and can be automatized for on-line measurements.

Introduction 2

Encapsulation consists in enclosing some internal substance inside a membrane in order to control the 3 exchanges between the environment and the internal medium. The capsule contents are thus prevented 4 from dispersing or degrading and can eventually be released where and when needed. Capsules are 5 found in nature in the form of cells, bacteria, seeds, and eggs. For example, a red blood cell (RBC) 6 is a natural capsule that transports hemoglobin, allows oxygen and carbon dioxide exchanges through with a strain-softening behavior, as exhibited by polymer membranes with rubber-like elasticity. For 29 membranes with a network of strong covalent bonds, the strain-hardening behavior is often modeled 30 by a Skalak (SK) law, which was initially designed to represent the mechanical behavior of the bi-layer membrane of the red blood cell (Skalak et al., 1973). However, for artificial capsules, the generalized 32 Hooke's law (GH), which corresponds to the thin membrane limit of a homogeneous three-dimensional 33 law, constitutes an interesting alternative to the SK law. Indeed, the GH law assumes a linear relation 34 between the stress and the deformation in the reference undeformed configuration, but exhibits a nonlin-35 ear strain-hardening behavior under large deformation. Furthermore, it can account for variable degrees 36 of wall area distensibility.

37

Experimentally, the measurement of the wall mechanical properties is difficult because capsules are 38 small and fragile. For biological cells such as RBCs with a very deformable lipid bi-layer membrane, 39 micropipette aspiration (Heinrich & Rawicz, 2005) or optical tweezers (Avsievicha et al., 2020) have 40 been proposed. Those methods are not adapted to measure artificial microcapsules with a size ranging 41 from a few tens of micrometers to a millimeter, because the deforming forces that are applied are a few 42 pN. If this force level is sufficient to substantially deform cells, it is much too low to have any measurable effect on capsules. Correspondingly, different techniques to test capsules have been proposed over the 44 years, such as compression between two parallel plates for millimeter-size particles (Carin et al., 2003; e = 1 2 (F T • F -I ), where F = ∂ x/∂ X is the gradient of the transformation and I the identity tensor. Two invariants of e can be defined as

I 1 = tr(F T • F) -2 = λ 2 1 + λ 2 2 -2, I 2 = det(F T • F) -1 = λ 2 1 λ 2 2 -1, (1)
where λ 1 and λ 2 represent the in-plane principal extension ratios. Invariant I 1 measures the shear deformation, whereas I 2 measures the local surface dilation. Since the membrane is infinitely thin, the three-dimensional stresses in the membrane are replaced by Cauchy tensions (forces per unit arc-length of deformed surface). The Cauchy tension tensor σ depends on a strain energy function w s (I 1 , I 2 ) per unit undeformed surface area

σ = 1 λ 1 λ 2 F • ∂w s ∂ e • F T . ( 2
)
Several constitutive laws with constant material coefficients have been proposed to govern energydeformation relationships. They are usually derived from classical three-dimensional laws in the limit where the initial thickness h of the capsule wall tends to zero. The surface shear modulus is then related to the usual three-dimensional shear modulus G by G s = hG.

(3)

The simplest law, for isotropic and hyperelastic materials, is the generalized Hooke's (GH) law, in which w s is a quadratic function of e:

w GH s = G s tr(e 2 ) + ν s 1 -ν s [tr(e)] 2 = G s 4 2I 1 -2I 2 + 1 1 -ν s I 2 1 , (4)
where tr(e) denotes the trace of e and -1 < ν s < 1 is a surface Poisson ratio. The area dilation modulus

94 is then K s = G s (1 + ν s )/(1 -ν s )
, which implies that ν s → 1 corresponds to an area incompressible 95 membrane. Note that σ is a linear function of e for small deformation (F ≃ I ), but becomes a nonlinear function of e for large deformation, with a strain-hardening type behavior.

97

The two-dimensional form of the Neo-Hookean (NH) law, classically used to describe volumeincompressible rubber-like materials, is given by

w NH s = G s 2 I 1 -1 + 1 I 2 + 1 . (5)
Because of the hypothesis of volume incompressibility, area dilation is balanced by membrane thinning 98 so that K s = 3G s . Under large deformation, the Cauchy tensions exhibit a strain-softening type behavior.

99

In order to describe anisotropic biological bi-layers (such as the red blood cell membrane), Skalak et al. (1973) proposed a purely two-dimensional law (SK) with independent surface shear and area dilation modulus

w SK s = G s 4 (I 2 1 + 2I 1 -2I 2 ) + CI 2 2 . ( 6
)
The area dilation modulus is K s = (1 + 2C)G s , in which the dimensionless parameter C regulates the 100 resistance to area dilation. Under large deformation, the Cauchy tensions exhibit a strain-hardening type 101 behavior, that becomes more pronounced as C increases.

102

For C = 1 and ν s = 0.5, corresponding to K s = 3G s , the three NH, GH, SK laws have the same small-103 deformation behavior, but predict different material responses for large strains (Barthès-Biesel et al., 104 2002;Lac et al., 2004).

105

When the inertia of the capsule membrane is neglected, the local equilibrium equation of the membrane reads where ∇ s is the surface gradient and q is the load, i.e. the external force per unit area of deformed capsule surface C t at time t. A no-slip condition is also imposed at the capsule wall

∇ s • σ + q = 0, ( 7
) (¡,¢) C S in S out 10l l O z y a (¡,¢) L p L z L 1 L 2 z y 0 (a) (b) (c)
v(x, t) = ∂ x(X, t)/∂t x ∈ C t , (8)
where v(x, t) is the velocity of the fluids on the capsule deformed surface.

106

Fluid-structure coupling and numerical method 107

The flows of the internal and external liquids are governed by the Stokes equations, subjected to no slip conditions on the capsule wall and on the flow domain outer boundary B. The velocity of the capsule wall is given by an integral equation (Pozrikidis, 2005)

v(x) = v ∞ (x) - 1 8π µ C t J • qdS( y) + B J • f + dS( y) , x ∈ C t . (9)
where v ∞ (x) is the unperturbed flow velocity in absence of capsule. The force q on the membrane is determined from the mechanics of the capsule wall (Equation 7). The additional friction force on the domain boundaries f + must be computed as part of the solution (Hu et al., 2012). The Green function J is defined as

J = 1 || x -y|| I + (x -y) ⊗ (x -y) || x -y|| 3 . ( 10
)
The problem is governed by the following non-dimensional parameters:

108

• The size ratio a/l, where l is the flow characteristic length, to yield the velocity of the membrane. A second-order Runge-Kutta method is then used to integrate 117 equation ( 8) and obtain the new deformed position of the membrane material points. This information 118 is sent to the FEM solid solver to compute the load q, which is then sent to the fluid solver to repeat the 119 process. The explicit nature of the time integration, implies very small time steps for the scheme to be 120 stable. Here, we use a time step ∆tV /l = 5 × 10 -4 , which guarantees stability. All the reported results

121

pertain to a steady state, for which the surface area of the capsule varies by less than 10 -3 × (4πa 2 ) 122 over a non-dimensional time tV/l = 1. The precision of the numerical scheme has been shown to be 123 O(∆h c /l) 2 when P1 elements are used (Walter et al., 2010;Dupont et al., 2015).

Numerical prediction of the capsule deformed shape

125

Deformation of a capsule flowing in a cylindrical tube 126

We first consider the case where a closely fitting capsule is subjected to a bounded Poiseuille flow 127 with mean velocity V , created in a straight channel with a circular cross section of radius l (Figure 128 1a). We seek the steady motion and deformation of a centered capsule. Since there is a liquid film 129 around the capsule (Figure 1b), its velocity v c is different from V and must be computed as part 130 of the solution. Presently, results are available for capsules with a NH or SK membrane flowing in 131 circular (Pozrikidis, 2005;Lefebvre & Barthès-Biesel, 2007;Hu et al., 2012) or square section tubes 132 (Kuriakose & Dimitrakopoulos, 2011;Hu et al., 2013). In this section, we provide new results for 133 capsules with a GH membrane law.

134

The capsule centre O is initially located on the channel axis, in the middle of the tube (total length 20l) and is moved back there at each time step. The flow domain boundary B consists of the channel wall and of the entrance S in and exit S out sections. On the channel wall, no-slip conditions are enforced. The entrance and exit sections are far enough from the capsule for undisturbed Poiseuille flow conditions to prevail

v ∞ = 2V [1 -(x 2 + y 2 )/l 2 ]e z . ( 11
)
The coupled BIM-FEM solver is used, where the characteristic dimension of the channel boundary 135 elements is ∆h w /l = 0.14, except in a central part with length 2l, where a refined mesh is used with 136 ∆h w /l = 0.07. For a/l ≥ 0.9, we pre-deform the capsule into an ellipsoid that can fit inside the channel 137 and we then follow the same procedure, while accounting for the induced pre-deformation stresses.

138

For a specific membrane law, the problem solution yields the capsule deformed profile and velocity 139 v c /V for given values of a/l and Ca s . The overall capsule deformation is quantified with two parameters: 140 the total length L z /l and the parachute depth L p /l that are easy to measure experimentally (Figure 1b). The results are similar to those reported previously for other membrane laws. The capsule length L z 144 increases with flow strength. A parachute always forms for confinement ratios up to 0.9, with depth 145 L p increasing with Ca s . For higher confinements a/l > 0.9, the parachute forms only when the flow 146 strength exceeds a critical value Ca sc , which increases with a/l: specifically Ca sc increases from 0.03 147 to 0.06 when a/l increases from 1 to 1.1.

148

The new results in Figure 2 pertain to the effect of the membrane dilation modulus as measured by 149 ν s . We first note that ν s has no effect on the front profile of the capsule for given values of a/l and Ca s .

150

The same remark applies to the global capsule profile for small flow strength (e.g. Ca s = 0.01) and 151 thus moderate deformation (Figure 2a). Any influence of ν s occurs at the rear of the capsule: the main 152 effect of a reduced resistance to dilation is an increase of the parachute depth (Figure 2b,c), resulting in 153 a sharp parachute edge at high flow strength (Figure 2c). When such a sharp edge appears, the capsule 154 is near the transition to continuous elongation, where it cannot reach a steady shape.

155

The plots in Figures 3a,b give the evolution of the two lengths L z and L p (characterizing the capsule 156 deformation) with the confinement ratio a/l and capillary number Ca s . Note that the capsule velocity 157 v c is larger than the average flow velocity V , due to the film around the capsule (Figure 3c). The ratio as a consequence, a capsule with a strain-softening NH membrane deforms more than capsules with 166 strain-hardening SK or GH membranes (Figure 4a). Eventually, the large (a/l = 1.1) NH capsule

Deformation of a capsule in a simple shear flow 189

The deformation of a spherical capsule in a simple shear flow is well documented (see the review by Barthès-Biesel (2016) and the references therein). The influence of different membrane laws (NH, SK) has been studied, except for the case where the capsule wall is governed by a GH law with different values of the surface Poisson ratio. It is thus one aim of this paper to fill this void and provide a full database for this situation. We now consider the case where the capsule is freely suspended in an unbounded simple shear flow with undisturbed velocity given by where γ is the shear rate. The flow problem is governed by Equation ( 9), where the boundary B is taken is also of 248 order ±2%.

v ∞ = γye z . (12)

249

The inverse analysis strategy consists of identifying the mechanical properties from the experimental deformed profiles using the data-driven automatic procedure of Quesada et al. (2020). The databases contain the predicted steady-state values of L z and L p as functions of parameters Ca s and a/l for the different constitutive laws (NH, GH ν s = 0.5, 0.2, 0) corresponding to Figures 3 and5. For a given constitutive law, we project the experimental values L ex p z and L ex p p onto the (L z , L z -L p ) hypersurface that contains all the admissible solutions. The corresponding Ca s and a/l values are identified by means of diffuse approximation. This approximation uses a local weighted least squares fitting that is valid in a small neighborhood created within the lengths-space around the point (L

ex p z , L ex p z -L ex p p )
and containing 14 neighbors of the database. Knowing the lengths-parameters relationship for the 14 1. 1. Size ratio a/l, surface capillary number Ca s , surface shear modulus G s and non-dimensional modified Hausdorff distance H/a corresponding to the different profile fits of Figure 8. The NH and GH (ν s = 0.2, 0.5) results correspond to Fit 1.

data points, we deduce the values of Ca f it s and (a/l) f it for the measured lengths by solving an inverse problem. The surface representing v c /V as a function of a/l and Ca s is decomposed into triangles with vertices on the database points. The point {Ca f it s , (a/l) f it } corresponds to one triangle of the velocity surface and the ratio (v c /V ) f it is the distance weighted average of the values of v c /V on the three vertices (Delaunay triangulation procedure). The membrane shear modulus G s is then

G s = µv ex p c Ca f it s V v c f it . ( 13
)
As a check, we compute the numerical deformed profile of the capsule, corresponding to the values 1. For the smaller capsule (a/l ≃ 0.9), the five fits are equally good in terms of

261

Hausdorff distance, but lead to a 27% dispersion of shear modulus values (G s = 0.048 ± 0.0013N/m):

262
this dispersion is mostly due to the fact that, for capsules smaller than the tube radius (a/l ≤ 0.9), the 263 lengths L z or L p do not vary much with Ca s (Figure 5) thus a small variation of L z leads to a large 264 variation of Ca s . For the larger capsule (a/l ≃ 1), the Hausdorff distance is near the acceptable limit of 265 0.06a (except for Fit 4 which is discarded), mainly, because the tips are not fitted very well. However, the 266 capsule being large, the dispersion is only 13% on the shear modulus values (G s = 0.039 ± 0.0005N/m).

267

This shows that an absolute value of the precision of the inverse analysis procedure cannot be evaluated on the law as shown in Table 1.

299

The non-linear constitutive law, which is appropriate to model the capsule membrane, is the one that 300 yields the same constant value of G s for any deformation level Λ. Note that all laws should lead to the 301 same small deformation value of G s , since they are then equivalent.

302

The results from the microfluidic device are shown in Figure 10, where the values of G s , obtained This validates the microfluidic approach to measure microcapsule properties.

Conclusion 353

The main objective of this paper was to propose a microfluidic methodology to measure the elastic 354 properties of a population of microcapsules. Why this method? Because the operating principle is simple 355 and the experimental set-up fairly inexpensive, apart from the vizualisation devices (microscope and 356 high-speed camera), which are indispensable to any dynamic micro-apparatus. The method is based on nonlinear membrane elastic properties, which we provide under the form of databases for an initially to decide which law is best adapted to describe the constitutive behavior of the membrane material. On

390

The feasibility study on artificial ovalbumin capsules allows us to define the optimal conditions to 391 diminish the impact of inherent uncertainties. For the microfluidic method to be precise, the capsule 392 global deformation should be large enough, i.e. the elongation ratio Λ of the perimeter of the observed 393 profiles should be larger than 1.05. Furthermore, the size ratio between the capsule and the tube radii, 394 should not be smaller than 0.9: indeed, for smaller ratios, the deformation does not vary much with 395 flow strength, thus leading to large errors in the determination of the latter. Note that the capsule must 396 be transparent enough to allow measurement of the penetration length of the parachute, which is an 397 essential feature of the deformation. Consequently, the microfluidic method will not work on opaque 398 capsules, whereas the rheometric method would still be pertinent.

399

Potentially, the great strength of this technique is that it allows to determine the type of membrane 400 constitutive behavior: strain-hardening or -softening. This is very important as, under given flow stress, 401 strain-softening capsules may be more prone to deformation induced damage than strain-hardening ones.

402

Furthermore, the microfluidic method is well adapted for quality control, as it allows small batches of a 403 capsule suspension to be diverted from a production line to a measuring test section. Of course, images

Figure 1 .

 1 Figure 1. Schematic illustration of an initially spherical capsule (contour C 0 ) subjected to Poiseuille flow in a cylindrical channel with radius l (a). Typical lengths characterizing the capsule deformation (contour C t at time t): L z , L p in the channel (b) and L 1 , L 2 in an unbounded simple shear flow (c).

  of Ca s and of ν s on the deformed profiles of the capsule are shown in Figure2.

  143

  158v c /V decreases from 2 for zero size capsules (that would travel with the maximum fluid velocity) to 159 almost unity for very large capsules (that would travel with almost the average fluid velocity).

Figure 2 .Figure 3 .Figure 4 .Figure 5 .

 2345 Figure 2. Tube flow: effect of flow strength and surface Poisson ratio ν s on the steady-state capsule profile in the yz-plane. (a) Ca s = 0.01; (b) Ca s = 0.07; (c) Ca s = 0.15.

  Figure5for strain-softening and strain-hardening membranes (where SK results have been eliminated, 174

  188

Figure 6 .

 6 Figure 6. Simple shear flow: plots of the (a) capsule deformation in the shear plane and (b) profile semi-axis L 3 along the vorticity direction for NH and GH laws.

190

  far enough from the capsule center for the perturbation f + to be negligible. As a consequence only 191 the first integral remains in Equation (9). The only problem parameters are then the capillary number, 192 now defined as Ca s = µ γa/G s and the ratio K s /G s . For a given membrane law, the model provides 193 the deformed profile of the capsule as a function of Ca s . As the deformed capsule is approximately 194 ellipsoidal, we determine its ellipsoid of inertia which has semi-principal axes L 1 , L 2 in the shear plane 195 (Figure 1c) and L 3 in the vorticity direction. The deformation in the shear plane is then quantified by the 196 Taylor parameter D 12 = |L 1 -L 2 |/(L 1 + L 2 ). Results for D 12 are available in the case K s /G s = 3 for NH, 197 SK and GH membranes (Lac & Barthès-Biesel, 2005; Walter et al., 2010; Dupont et al., 2015), and L 3 198 is never given, although it is necessary to determine the deformed capsule volume. New results for GH 199 and NH membranes are thus presented in Figure 6, where the relation between D 12 and Ca s is given as 200 well as the evolution of L 3 with D 12 . For a GH membrane, the effect of decreasing ν s , i.e. the dilation 201 modulus, is to increase the deformation for the same flow strength. For ν s = 0, the capsule undergoes 202 continuous elongation and eventually ruptures for Ca s 0.4. The same phenomenon appears around 203 Ca s = 1 and D 12 ≃ 0.6, for a NH membrane. 204 The plots of Figure 6 are simple to use: for a given membrane law, the value of deformation D 12 205 yields the value of L 3 and Ca s . Knowing L 3 , L 1 and L 2 , it is easy to compute the volume of the capsule 206 and its initial radius a. The elastic modulus G s is obtained from Ca s , knowing the values of γ and µ, 207 both given by the shear apparatus.

Figure 7 .

 7 Figure 7. (a) Microfluidic set-up; (b) microrheometry set-up. All lengths are in µm.

  (a, d) Experimental image of the capsule in a cylindrical tube (diameter 75 µm) with extracted contour (full line); (b, e) two potential fits of the extracted profiles using a NH law; (c, f) Profile fits with different membrane laws. The parameters of the different fits are gathered in Table

Figure 9 .

 9 Figure 9. Experimental image of the capsule in a simple shear flow with extracted contour. The scale indicates 75 µm.

268

  with a single parameter such as H/a as it depends on the quality of the fit and also on the capsule size 269 and deformation level. The same procedure can be applied to fit the profile with other membrane laws 270 as shown in Figures 8c,f where only the results of Fit 2 are shown. Of course, the values of G s depend 271

  of wall elasticity using microrheometry 273 We now use a microrheometric device to determine the capsule membrane properties by subjecting 274 the particles to a simple shear flow. A 10 ml volume of a capsule suspension in glycerol (volume deformation D 12 from which we deduce Ca s and L 3 /a using the plots in Figure 6. The capsule radius is thus a = √ L 1 L 2 L 3 /a and the shear modulus is G s = µ γa/Ca s . The capsule presented in Figure 9 is 292 subjected to a 350 s -1 shear rate in a fluid with viscosity 0.756 Pa.s. The radius is a = 45 µm and the 293 deformation D 12 = 0.38 provides a value of shear elastic modulus equal to G s = 0.044 N/m for a NH 294 membrane and to 0.024 or 0.038 N/m for a GH membrane with ν s = 0.5 or 0.2, respectively. a capsule suspension in both set-ups, we can have results on a population. In order 297 to compare the values of G s obtained with different membrane laws, it is convenient to use the mean 298 profile elongation Λ = p/2πa where p is the perimeter of the capsule deformed profile in the yz-plane.

303Figure 10 .

 10 Figure 10. Plots of surface shear modulus G s as a function of capsule mean deformation Λ. Symbols represent the constitutive law. The lines show a linear best fit for the corresponding points. The shaded areas correspond to the mean value G s ±25% obtained with microrheometry.

Figure 11 .

 11 Figure 11. Left to right: successive profiles of a capsule showing continuous elongation in a square section channel (100 × 100 µm 2 , a = 50 µm, V c ∼ 23 mm/s, µ = 0.92 Pa.s). The capsule has travelled about 200 µm between two successive profiles and is clearly undergoing break-up in the last picture. Images taken by E. Hasiak.

  351

  352

382

  average though, the high-deformation values of the membrane shear elastic modulus are the same with 383 the two methods for any given law: this validates the microfluidic methodology. A further potentiality of 384 the microfluidic methodology is that once G s is known, it is possible in principle to check if the capsule 385 membrane is strain-softening (NH law) or strain-hardening (GH law). This can be done by increasing 386 the flow rate to exceed the critical value of Ca s past which continuous elongation occurs when the 387 membrane is strain-softening. If continuous elongation is observed, the NH law is a good candidate to 388 model the wall behavior. If not, the wall is then strain-hardening and GH law should serve as a good 389 approximation.

  404and their contour should be acquired automatically, as done byMinetti et al. (2014) or Saadat et al.

  405(2020), and post-treated automatically as explained in this paper. tent of serum albumin microcapsules using trinitrobenzenesulfonic acid: effect of variations in 449 polycondensation pH. Int. J. Pharmaceut. 96, 85-90.

  The membrane capillary number Ca s = µV /G s , where V is the flow characteristic velocity,

	110
	111	• The ratio between dilation and shear modulus K s /G s .
	112	We solve this fluid-structure problem by coupling the Boundary Integral Method (BIM) to calculate
	113	the flow field, to the Finite Element Method (FEM) to calculate the force exerted by the membrane on
	114	the fluids (Walter et al., 2010; Hu et al., 2012). Triangular P 1 elements are used to discretize all the
	115	boundaries. There are 5120 P 1 elements and 2562 nodes on the capsule membrane, corresponding to a
	116	characteristic element size ∆h c /l = 0.07. At each time step, the boundary integral equation (9) is solved

109

•

Risso & Carin, 2004), atomic force indentation(Fery & Weinkamer, 2007; de Loubens et al., 2014),

capsules in distilled water, centrifugating the suspension, and resuspending the pellet in clean distilled

Funding Statement

407

We gratefully acknowledge funding from the China Scholarship Council (PhD scholarship of X.Y.

408

Wang) and from the European Research Council (ERC) under the European Union's Horizon 2020

Data Availability Statement

418

Raw data are available from the corresponding author (A.V.S.).

least 3 hours, which is the maximum duration of an experiment, after which the capsules are discarded.

Identification of wall elasticity by flowing microcapsules in a microfluidic cylindrical capillary 230

The microfluidic flow system, shown in Figure 7a, consists of a straight 28-mm-long cylindrical capillary 231 tube with an internal diameter 2l = 75 µm (Capillary tube 1), embedded in another tube (Capillary 232 tube 2), which is immersed in polydimethylsiloxane (PDMS Sylgard 184, Dow Corning) to eliminate 233 optical distortions (Lefebvre et al., 2008). Just prior to an experiment, 500 µl of filtered capsule pellet 234 is suspended in 12 ml glycerol (Sigma). The capsule suspension, which has a viscosity of µ = 0.92 235 Pa.s at 20 • C, is injected into the microchannel by means of a pressure controller (EZ-Flow, Fluigent).

236

Pressure values range from 800 mbar to 1500 mbar, which provide capsule velocities from 0.8 to 6 237 mm/s. Image acquisitions of individual capsules flowing in the tube are performed with a fast camera 238 (Fastcam MINI AX50, Photron) at frequencies f ranging from 2000 to 6000 Hz and an exposition time 239 1/ f . The camera is mounted on a DMI8 microscope (Leica) with a x40 magnification and 0.6 numerical 240 aperture objective.

241

Recordings are performed at least 5 mm downstream of the inlet to ensure that the capsule has reached L 2 (Figure 9). Note that the pictures are not as sharp as those obtained with the microfluidic set-up, due 285 to inferior performance of the camera included in the device and to the fact that it is challenging to keep 286 the capsule steady. The fuzziness of the profile leads to an error of ±20% on D 12 . Correspondingly, it 287 is unreasonable to try to analyze capsules with D 12 < 0.35.

288

The inverse analysis is straightforward, because the deformation of the capsule depends on only 289 one parameter, Ca s . For a given law and shear rate γ, the measured semi-axes L 1 and L 2 yield the with each law, is also shown.

308

The values of G s obtained with NH law are approximately constant with a mean value G s = 309 0.043±0.004 N/m. This indicates that the NH law is a good candidate to model the ovalbumin membrane 310 of the capsules. The results obtained with GH (ν s = 0.5) law are in the same range as the results for 311 NH law for small deformation (Λ = 1.06), as expected. However, the values of G s tend to decrease with 312 increasing deformation: this means that the strain-hardening GH law is not fit to model the membrane 313 behavior under large deformation, since the parameter G s must be decreased as deformation increases.

314

The larger dispersion of the NH values of G s compared to that of the GH ones is linked to the fact that 315 the values of Ca s are larger for the GH analysis than for the NH one.

316

Furthermore, it is possible to verify if, indeed, the capsule membrane is shear-softening. This is done 317 by increasing the flow strength until a continuous elongation regime is reached. The set-up described 318 in Figure 7a did not allow for high enough flow velocity to reach this regime. However, as a proof of 319 concept, we have flowed the same capsules in a slightly different microfluidic system consisting of a values of a/l as those used for the NH or GH (ν s = 0.5) fits: the size ratio has to be increased by 10 to GH law with values of ν s < 0.5 is not very appropriate to model this type of capsules.

333

When we analyze the microrheometric measurements, it is not possible to give a trend of the values 334 of G s with Λ because of the fairly large error on D 12 . We have measured 25 capsules with a radius value of the shear modulus depends on the law: it is found to be G s = 0.039 ± 0.01 N/m for NH law, 338 G s = 0.021 ± 0.007 N/m for GH (ν s = 0.5) and G s = 0.033 ± 0.01 N/m for GH (ν s = 0.2), all with 339 a standard deviation of ±25%. This large deviation is mostly linked to the error in the measurement of 340 D 12 . Another source of error is also due to the fact that the inverse analysis uses deformation curves 341 obtained for a viscosity ratio equal to unity between the internal and external liquids, whereas this ratio 342 is much smaller than 1 in the experiments. However, Foessel et al. (2011) showed that the influence of 343 this viscosity ratio is very small and does not modify significantly the relationship between D 12 and 344 Ca s , up to D 12 ≃ 0.5. This is why we have discarded results with deformation larger than 0.5.

345

Altogether, the microrheometric G s values, shown as shaded areas in Figure 10, overlap well with 346 the results obtained with the microfluidic tube for large deformation. This is clear for the NH law, for 347 which G s is found to have the nearly constant value 0.043±0.004 N/m by microfluidics or 0.039±0.01 348 N/m by microrheometry. In the case of GH (ν s = 0.5) law, this conclusion applies for the range of the observation of flowing capsules in a cylindrical capillary tube and an inverse analysis of the deformed 358 profiles. The latter requires a full numerical model of the fluid-structure interaction, that accounts for spherical capsule with a membrane governed by a neo-Hookean or general Hooke's law with different 361 surface Poisson ratios. We also detail how the inverse analysis can be automated to provide information 362 on the type of elastic constitutive law that governs the capsule wall material together with the value of the 363 corresponding elastic parameters. This is possible because the confinement imposed by the microfluidic 364 configuration allows for large deformation of the capsule membrane. Note that a microfluidic method, 365 based on a similar inverse analysis adapted to the specific case of red blood cells, has been proposed to 366 analyze automatically large cell populations (Saadat et al., 2020). The shape characterization is different from the one presented here, as it had to be adapted to smaller, discoidal particles.

Another microrheological method is used where the capsules are subjected to a simple shear flow 369 in a counter rotating Couette device. The method consists in capturing the deformed profile of those 370 capsules with their centre of mass in the zero velocity plane, which is somewhat tricky to perform. The 371 necessary databases for the inverse analysis are also provided for an initially spherical capsule with a 372 membrane governed by a neo-Hookean or general Hooke's law with different surface Poisson ratios.

373

We validate the two methods by confronting the results obtained with either one on a population of 374 artificial capsules with cross-linked ovalbumin membrane. We test three types of membrane laws, to 375 find for which constant values of G s are obtained: a strain-softening NH law and two strain-hardening 376 GH laws with dilation to shear ratios K s /G s = 3 or 1.5 (ν s = 0.5 or 0.2). The microfluidic method 377 predicts that the membrane shear modulus G s is approximately constant for a NH law: this indicates that 378 this constitutive law is appropriate to model the mechanical behavior of the ovalbumin membrane. In


Ginel Dorleon
email: ginel.dorleon@irit.fr

Imen Megdiche
email: imen.megdiche@irit.fr

Olivier Teste
email: olivier.teste@irit.fr

Absolute Redundancy Analysis Based on Features Selection

Keywords: Computing methodologies → Machine learning; Feature selection Machine Learning, Features Selection, Redundancy Analysis

The goal of feature selection (FS) in machine learning is to find the best subset of features to create efficient models for a learning task. Different FS methods are then used to assess features relevancy. An efficient feature selection method should be able to select relevant and non-redundant features in order to improve learning performance and training efficiency on large data. However in the case of non-independents features, we saw existing features selection methods inappropriately remove redundancy which leads to performance loss. We propose in this article a new criteria for feature redundancy analysis. Using our proposed criteria, we then design an efficient features redundancy analysis method to eliminate redundant features and optimize the performance of a classifier. We experimentally compare the efficiency and performance of our method against other existing methods which may remove redundant features. The results obtained show that our method is effective in maximizing performance while reducing redundancy.

INTRODUCTION

Nowadays, many real world applications [START_REF] Amarasinghe | Critical Analysis of Machine Learning Based Approaches for Fraud Detection in Financial Transactions[END_REF][START_REF] Farahani | Towards Collaborative Machine Learning Driven Healthcare Internet of Things[END_REF][START_REF] Ioannis | Machine learned job recommendation[END_REF][START_REF] Zhiwei (tony) Qin | Deep Reinforcement Learning with Applications in Transportation[END_REF][START_REF] Thakur | An Approach for Detection of Walking Related Falls During Activities of Daily Living[END_REF] deal with so called high-dimensional data. However, high-dimensional data became a major issue in the field of machine learning [START_REF] Reddy | Analysis of Dimensionality Reduction Techniques on Big Data[END_REF] due to its size and the amount of resources required to process it. Learning performance is impacted by high-dimensional dataset [START_REF] Ullah | Dimensionality Reduction Approaches and Evolving Challenges in High Dimensional Data[END_REF]. Naturally, one may believes that more features we get, the more information we get from the features, but that is far from true because it becomes more difficult to extract meaningful conclusions from a dataset as the dimensionality of the data increases. Hence there is a need to resort to dimensionality reduction techniques in order to reduce the size of these data. Feature selection is one among the methods used for dimensionality reduction [START_REF] Ullah | Dimensionality Reduction Approaches and Evolving Challenges in High Dimensional Data[END_REF][START_REF] Venkatesh | A Review of Feature Selection and Its Methods[END_REF]. The goal is therefore to obtain a meaningful subset of relevant and non redundant features that is vital for improving efficiency and reducing overfitting. Generally, it is easier to remove irrelevant features than finding redundant ones. Thus, the difficulty in selecting features now is finding the ones that are redundant. Existing works for features redundancy analysis such as RABFS [START_REF] Wang | A New Method for Redundancy Analysis in Feature Selection[END_REF], mRMR [START_REF] Peng | Feature Selection Based on Mutual Information: Criteria of Max-Dependency, Max-Relevance, and Min-Redundancy[END_REF], FCBF [START_REF] Yu | Efficient Feature Selection via Analysis of Relevance and Redundancy[END_REF] introduced approaches to reduce redundancy. Yet, our study shows that these methods remove inappropriately redundancy because they required user to set a threshold. We saw several problems with these methods based on the definition of a threshold:

• A feature will be redundant depending on the fixed threshold and the user's experience. • The performance of the model will depend on the fixed threshold.

That being said, on the same dataset, users may find different redundant features. This is practically dangerous if there is protected features in the data that we are using. By protected features we mean features that carry special importance and are of priority when making relevant decisions [START_REF] Fang | Achieving Outcome Fairness in Machine Learning Models for Social Decision Problems[END_REF]. Therefore, there is a need for more research on feature redundancy analysis. Our study here focuses on features redundancy analysis and proposes a new method for analyzing features redundancy without the need of defining a threshold.

The rest of this article is as follows: In section 2, we define features relevancy and features redundancy. Section 3 presents the proposed redundancy criterion as well as our redundancy analysis method. Experimental results are analyzed in section 4 and section 5 is our conclusion and perspectives.

FEATURES RELEVANCY AND REDUNDANCY

This section introduces feature redundancy and relevance based on the definition from the literature.

Features Relevancy

In general, features relevance is done by using common features selection methods such as Filter, Wrapper, Embedded or Hybrid [START_REF] Chandrashekar | A Survey on Feature Selection Methods[END_REF][START_REF] Gheyas | Feature subset selection in large dimensionality domains[END_REF]. Other works have introduced notions of ranking the level of features relevance. According to the authors in [START_REF] Salzberg | C4.5: Programs for Machine Learning by J. Ross Quinlan[END_REF], the relevance of a feature can be strong, weak or totally irrelevant. They introduced three categories that are defined below. A feature that has a strong relevance should be considered for the selected subset of features.

One with a weak relevance feature is not really important but it may be used under certain conditions. A totally irrelevant feature is not necessary and should be removed. From these definitions, the authors in [START_REF] Salzberg | C4.5: Programs for Machine Learning by J. Ross Quinlan[END_REF] conclude that, for an optimal result, the subset must contain features with a strong and weak relevance only. There are many works on feature relevancy [START_REF] Chandrashekar | A Survey on Feature Selection Methods[END_REF][START_REF] Gheyas | Feature subset selection in large dimensionality domains[END_REF] with different strategies. However, for feature redundancy, there are not that many effective methods. Thus, research method for redundancy analysis is always of considerable importance. Our objective is to analyze features redundancy and we propose a redundancy criterion in section 3.

Features Redundancy

Here we discuss redundancy in the sense of correlation with respect to the target variable. There is redundancy when there is a high correlation between features [START_REF] John | Irrelevant Features and the Subset Selection Problem[END_REF]. The authors in [START_REF] Wang | A New Method for Redundancy Analysis in Feature Selection[END_REF] believed that redundancy could be strong, moderate or weak. Based on a chosen threshold, the correlation between features will determine if the redundancy is strong, moderate or weak. When the correlation is high, the redundancy is believed to be high and such features are removed. When it is moderate, features are considered as partially redundant and they can be kept or removed. Low correlation means low redundancy. However, the problem with this approach is that the removal of a partially redundant feature based on a fixed threshold may be excessive and may also lead to the loss of useful information for the intended task. This also means that the redundancy is subjective and it varies between users and experiments. Hence we propose a new criterion to evaluate the redundancy between relevant features.

THE PROPOSED REDUNDANCY ANALYSIS METHOD

In this section, we present our proposed redundancy analysis method. We use the Symmetrical Uncertainty (SU) [START_REF] Andrew | Correlation-based feature selection for machine learning[END_REF] as correlation measure to assess redundancy.

Correlation Measure

The correlation measure that we used is based on information gain [START_REF] Elena | Theoretical comparison between the gini index and information gain criteria[END_REF] which for two variables X ,Y is given by:

IG(X , Y ) = H (X ) -H (X |Y ) (1)
Using this measurement, a feature Y is considered to be more correlated to a feature X than a feature Z if and only if: IG(X |Y ) > IG(X |Z ). Information gain uses the notion of entropy to measure the mutual dependence between two variables. The entropy for a random variable X is:

H (X ) = - i P(x i ) log 2 P(x i ) (2)
and between two variables X and Y, it is given by:

H (X |Y ) = j P(y j ) i P(x i |y j ) log 2 P(x i |y j )) (3)
P(x i ): probabilities for all values of X, P(x i |y j ): conditional probabilities between X given the values of Y.

However, the study in [START_REF] Elena | Theoretical comparison between the gini index and information gain criteria[END_REF] showed that features with more values are favored with information gain, thus its normalized version known as Symmetrical Uncertainty (SU) is used. Using equation ( 1), (2), and (3), SU is defined as:

SU (X , Y ) = 2 IG(X , Y ) H (X ) + H (Y ) (4)

Redundancy Criterion

Our proposed redundancy method uses symmetrical uncertainty as correlation measure. Unlike the proposed methods in [START_REF] Peng | Feature Selection Based on Mutual Information: Criteria of Max-Dependency, Max-Relevance, and Min-Redundancy[END_REF][START_REF] Wang | A New Method for Redundancy Analysis in Feature Selection[END_REF][START_REF] Yu | Efficient Feature Selection via Analysis of Relevance and Redundancy[END_REF], we do not have to set a threshold. Using a threshold to analyze a feature redundancy is subjective because the redundancy of that feature depends on that threshold. In our method, we focus on absolute features redundancy. We define our redundancy criterion as follows: two features F j and F i are redundant with respect to a class C (the output variable) if and only if they provide exactly the same amount of information for the output variable. In other words if and only if:

SU (F j , C) = SU (F i , C) (5)
If F j and F i are redundant, the least relevant one needs to be deleted. SU (F j , C) refers to the symmetrical uncertainty between a feature F j and the class C and SU (F i , C) refers to the symmetrical uncertainty between a feature F i and the class C.

Redundancy Analysis Algorithm

The algorithm defined below (Algorithm 1) can be literally translated as follows: from a list F of relevant features resulting from a feature selection method, we choose the most important or relevant feature F j (line 1). Then, the symmetrical uncertainty between F j and the next remaining feature F i in the list F (line 2 to 6) is calculated. If the redundancy criterion is true (line 7), the feature F i is deleted from the list F (line 7) then the next feature F i in F is used (line 8) until all the remaining features in F have been used. Then we start over by varying F j in the list (line 11) and so on until we have considered every remaining feature as F j (line 12). After removing all the redundant ones, we add all the remaining features to the list F', (F' ≤ F). This list, F', containing only relevant and non-redundant attributes, will be used for the desired learning task.

EXPERIMENTAL APPROACH

The diagram below(Figure 1) reflects our experimental approach to perform the redundancy analysis.

Features Importance: we determine the importance of the features using a wrapper feature selection method and then rank the features in order of importance from the most important one to the least. Importantly, this ordered list constitutes the "Ranked Relevant Features". Redundancy Analysis: to obtain the best subset of non-redundant features, we use the "Ranked Relevant Features" list to proceed to the redundancy analysis using the redundancy criterion that we defined in section 3.2 and the algorithm 1.

Classification: the redundancy analysis produces a final reduced list of features, "Selected Non-Redundant Features". This list is used to perform a supervised learning task using SVM [START_REF] Ring | An Approximation of the Gaussian RBF Kernel for Efficient Classification with SVMs[END_REF] and C4.5 [START_REF] Salzberg | C4.5: Programs for Machine Learning by J. Ross Quinlan[END_REF] classifiers. These classifiers were used for comparison purpose with other existing methods.

Experiments

We carry out our experiments in a way so that we can compare our results with other existing methods. The existing methods that can reduce redundancy and to which we compare our results are RABFS, mRMR and FCBF respectively. RABFS [START_REF] Wang | A New Method for Redundancy Analysis in Feature Selection[END_REF] uses maximum information coefficient to establish a threshold and analyze features redundancy and build a subset of features for training. In mRMR [START_REF] Peng | Feature Selection Based on Mutual Information: Criteria of Max-Dependency, Max-Relevance, and Min-Redundancy[END_REF] the aim is to select features with a high relevance with the target and a low redundancy between themselves. FCBF uses symmetrical uncertainty as correlation measure and approximate Markov blanket to remove redundancy [START_REF] Yu | Efficient Feature Selection via Analysis of Relevance and Redundancy[END_REF].

Datasets

To evaluate the performance of our method in finding redundant features and improving the performance of the learning task, 6 datasets including biological and text data from the UCI [START_REF] Dua | UCI Machine Learning Repository[END_REF] were used. In Table 1 below, we give details of those datasets. Those datasets were chosen based on their differences, the number of features varying from 325 to 22283. Plus, this choice will help us to compare the result of our method against other proposed methods that have used the same datasets.

Results

On a classification task, results of our method were compared to others based on the number of selected features and the classification accuracy. We have used SVM with Gaussian kernel [START_REF] Ring | An Approximation of the Gaussian RBF Kernel for Efficient Classification with SVMs[END_REF] and C4.5 [START_REF] Salzberg | C4.5: Programs for Machine Learning by J. Ross Quinlan[END_REF] as classifiers. SVM is a supervised machine learning model that uses classification algorithms for two-group classification problems. It has many obvious advantages in solving large-dimensional. C4.5 is an algorithm used to generate a decision tree that can be used for classification. In tables 2, 3 and 4, we report the results obtained during our experiment including results reported by the other methods. To select our features, we used a wrapper features selection method. Then, with the list of obtained features, we apply our redundancy criterion in order to obtain the list of the best features without redundancy. And finally, we perform a classification task using SVM To assess the effectiveness of our result in term of accuracy, we applied cross validation techniques on each dataset. The results above show that our method performs well. Table 3 and Table 4 show results obtained by the four methods on SVM and C4.5.

Compared to the others methods, we clearly see that our method performed better. In table 3 with SVM, our algorithm has a higher accuracy than other methods on 5 datasets. Only the Prostage-GE dataset, RABFS has a higher accuracy than our method. In table 4 with C4.5, the accuracy of our method is better on all the six datasets than all the other methods.

In Table 2, the other algorithms found fewer features than our proposed method. This can be understood by the fact that the other methods used a Filter strategy by setting a threshold to select the features while we used a wrapper approach.

CONCLUSION

This article presents a redundancy analysis criterion based on symmetrical uncertainty which is a measure of correlation between features. We then design a redundancy analysis algorithm designed according to this criterion. Unless other proposed redundancy methods, our algorithm does not require users to set a threshold. The performance of our method was experimentally compared to other methods such as RABFS, FCBF and mRMR on six different data sets. The comparative results show that our method finds satisfactory results.

Therefore, we intend to conduct further research in the future to incorporate our redundancy criterion into a hybrid feature selection method in order to select both relevant and non-redundant features.

Figure 1 :

 1 Figure 1: Design of our experimental approach

Table 1 :

 1 Experimental Datasets used

	Dataset	Observations Nb of Features
	Colon	62	2000
	ALLAML	71	7129
	PCMAC	1943	3289
	Prostage-GE	102	5966
	GLI-85	85	22283
	lung_small	73	325

Table 2 :

 2 Number of Selected Features by method

	Dataset	Our Method RABFS FCBF mRMR
	Colon	7	3	9	3
	ALLAML	5	3	6	3
	PCMAC	54	28	112	28
	Prostage-GE	21	16	4	16
	GLI-85	13	4	5	4
	lung_small	52	34	112	34

Table 3 :

 3 SVM Classification accuracy by method

	Dataset	Our Method RABFS FCBF mRMR
	Colon	92.03	91.66	90.0 78.57
	ALLAML	97.8	96.07	92.85 97.14
	PCMAC	83.01	80.91	77.51 56.25
	Prostage-GE	93.83	94.0	91.99 94.0
	GLI-85	94.01	92.77	90.69 89.30
	lung_small	88.0	84.82	59.88 84.64
	average	91.44	90.03	87.71 79.42

Table 4 :

 4 C4.5 Classification accuracy by method

	Dataset	Our Method RABFS FCBF mRMR
	Colon	92.04	91.90	75.47 91.78
	ALLAML	96.56	96.07	95.71 94.28
	PCMAC	84.01	82.50	77.81 59.42
	Prostage-GE	91.73	90.09	86.18 84.18
	GLI-85	96.60	95.13	84.58 85.69
	lung_small	89.01	87.76	81.14 78.61
	average	91.65	90.58	83.49 82.33
	and C4.5 so we can compare our results with other existing methods.


Caumon Lorrain
email: lorrain.caumon@laplace.univ-tlse.fr

Georges Zissis

Céline Caumon

Élodie Bécheras

Estelle Guerry

Christelle Infantes

Colours, light & well-being : Characterisation of chromatic phenomena in collective housing

Keywords: Light design, Color design, Visual comfort, Protocol, Accompaniment

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Health and housing threats

The actual pandemic is the sixth one that has hit humanity since the Spanish flu of 1918. According to a ONU report, the frequency and severity of these global epidemics could accelerate in the coming years, due to our lifestyles and the incredible adaptive capacities of viruses, IPBES (2020). In this exceptional health context, we have seen that housing conditions have more than ever impacted our daily lives. As a result, we have become aware that the problems related to the quality and sharing of collective living spaces during a pandemic will be major issues in the future and must require the full attention of real estate professionals.

All the more so as for many reasons, keeping people at home can be accompanied by multiple and varied disabilities, thus affecting the quality of life, Eideliman and Gojard (2008, 89-111), [START_REF] Piccoli | Ethical approach to the issue of confinement of the elderly in the context of the COVID-19 pandemic: Prevention of frailty versus risk of vulnerability[END_REF], ONU (2020). In France, approximately 12 million people are affected by a disability, including 1.5 million with a visual impairment and 850,000 with reduced mobility, INSEE (1999INSEE ( -2001)). Also, age is a factor to be taken into consideration, because in 2050, metropolitan France will have approximately 70 million inhabitants, more than a third of whom will be 60 years old, INSEE (2002). For all these people, the positive and secure perception of the daily environment must become an important issue. Therefore, it becomes necessary to adapt the environment of collective housing to people with different pathologies and their potential consequences on their habits.

Chromatic effects and methods of approach.

With this study, we want to provide reflections on design issues such as designing built, sensitive and inclusive spaces. To do this, we have focused on what inclusiveness means in the creation of the atmosphere of a place through its colour and light factors. For this purpose, we defined that an inclusive atmosphere translates into situations of sensitive and accessible interactions understood as the plural and singular experience that one has of a given place at a given time, influencing our sensations and quality of life. For many years, designers and authorities have been placing people and their plurality at the heart of architectural projects, but if we stick to strict compliance with standards, as people do not respond to any average, many gaps remain.

For example, in the French standards (EN 12464-1 completed by NF X35-103), the only indications are that the age of people must be taken into account to define the lighting levels on work surfaces. In collective dwellings, article 10 of the order of 24 December 2015 imposes minimum characteristics to ensure average horizontal illuminance values measured on the floor along a usual circulation route, taking into account transition zones. It goes without saying then that strict compliance with these standards does not allow us to guarantee the success of an architectural project in the perception of these users, [START_REF] Mudri | Luminous ambience, quantitative/qualitative data and subjective response[END_REF].

Color-Light: a factor of identity and orientation.

In the literature of cognitive sciences and psychology, there is little research on the role of colour in its relationship to space and in particular in the spatial orientation of people. However, we know that a visual environment adapted, [START_REF] Damelincourt | Éclairage d'intérieur et ambiances visuelles[END_REF], to the pathologies of people suffering from disabilities has positive effects, but must respect a certain number of criteria such as a quantity of light, contrasts and an appropriate spatial distribution. We therefore hypothesised that colour in the architectural environment of collective dwellings could support spatial location and orientation, particularly for people with disorientation, who are less receptive to conventional signage systems, Bay et al (2021, pp97-103).

In doing so, this empirical approach will hopefully instil thoughts around colour in communal housing environments. Inherited from hygienic and standardised norms, we note, even today, that few works integrating colour are the object of a voluntary approach. The selection of colours and materials often depends on the tastes of the project manager and the customary validation of the client, but what appears to be a secondary issue is in reality a key point in the assessment of the success of an architectural project. The results of this study will enable the implementation of a creative protocol that will assist property developers in designing visual environments adapted to the needs of all its inhabitants. The main results expected from this study are :

• Improve the analysis and interpretation protocol to define comfortable visual environments.

• Develop tools for simulating lighting ambience in the programme design phase.

• Facilitate the integration of the results of this study by professionals.

MATERIALS AND METHODS

Color-matter, color-light

The protocol presented is based on a combination of chromatic expertise (colour matching) concerning the choice of materials, textures and finishes, favouring colour for its plastic character; and lighting (light characterisation) concerning the quantity and colourful character of the light, giving particular importance to the different colour temperatures. This study focuses mainly on the common spaces and the interior horizontal circulations. This is because the visual ambience of these areas should create a sense of welcome, visual comfort and safety for all users, at all ages, during the day and at night. Therefore, the method used will serve to create coherence and harmony between the exterior landscape treatments and the interior chromatic and lighting treatments in order to create an intuitive and inclusive chain of movement. The method was divided into two stages:

Step 1: Captures

The surveys presented were carried out on 26 June 2019 in Capbreton (Landes, France) over a period of 8 consecutive hours at the site of the future "Bonamour" residence built by the property developer SOBRIM (Basque Country, France).

The first phase consisted of collecting photographs of the site, as the survey of the existing site is an essential phase before any project. Equipped with cameras, this preliminary chromatic analysis was accompanied by a walk around the site. Photographs cannot be used to faithfully reproduce colours on a palette. However, they are indispensable graphic documents for memorising, visualising and disseminating information, Lenclos et al, (1982, 65). Most chromatic studies employ photographic investigations to support the colour surveys. In our case, photography was used in two approaches, one aimed at establishing an inventory of the surrounding urban colours and forms, and the other at colour and light diagnosis in order to judge the appearance of the site under cyclical conditions. This stage was a means of transcribing and analysing the experience of a space.

The second phase consisted of referencing the colours of the site with the help of countertypes. In our study, the colour survey consisted of observing the colours that made up the environment and the architectural elements surrounding the project in order to compare them to reference colour samples. Here, we used the colours of the NCS colour chart. The Natural Color System, is a universal system used for standardised colour communication, based on an intuitive codification designed on human vision. This reference system allows us to communicate about colours in a universal way in various fields of application. This representation also allowed us to retranscribe these chromatic readings in values thanks to the L. a. b system from the CIE XYZ, taking into account the logarithmic response of the eye, but also by the specific characteristics of the coloured surfaces with their luminance index.

The third phase was to carry out a series of measurements to characterise the lighting environment of the site. The evaluation was carried out at three different times of the day (morning at 10:00, early afternoon at 14:00, late afternoon at 17:30) to measure the light amplitude. Also, in order to analyse the light distribution of the space, it was divided into several areas of the site. This series of measurements was carried out with the IRC CL-70F chromaticity meter, allowing us to collect all the values of the light. A video-luminance meter was also used to identify areas that may be sensitive to glare and shadows caused by the future buildings.

Step 2: Creations

The first phase consisted of a study of the existing light, environment, chromatic and architectural identity of the site (see Figure 1).

Figure 1 : Environment Study

Each environment has a unique identity, of which colour and light are part. The mission of the colour designer must necessarily include a diagnosis of the existing environment. This stage defines how we will approach the existing environment and certain elements in relation to the project, but also to the promoter's wishes in terms of the expected aesthetic and functional ambitions. In this phase, we took into account the so-called "permanent" and "cyclical" colours. The "permanent" colours are the basis of any chromatic study. They constitute the stable elements of the place, having a durable character, such as the building materials. They are opposed to "cyclic" colours, which are unstable and subject to innumerable temporal, meteorological and luminous variations, such as the colour of patinas, plants and the sky (etc.).

The second phase consisted of recommending atmospheres adapted to the place, using chromatic ranges, materials and lighting systems that would favour the safety and visual comfort of all the inhabitants. This method consisted of experimentally constructing chromatic ranges by means of the view, proceeding by variation and multiplication of optical combinations until a visual impression was obtained that conformed to the aesthetic expectations of the project. In order to conceive these chromatic ranges, we used the NCS colours previously surveyed on the site, which we then matched with the colour charts of the paint and plaster manufacturers used for this project. Thus, an atmospheric work was conceived around the spirit of the place, the chosen shades are sublimated by the contribution of contrast around several soft and affirmed tonalities inspired by nature and harmonizing perfectly with the vegetal contribution present on the site. These prescriptions led to the creation of three chromatic palettes specific to each building in the project (see figure 2) Inside, the chromatic combinations are composed of five shades, but established on a dominant trichromatic, [START_REF] Déribéré | La couleur dans les activités humaines[END_REF], varying on each level, thus avoiding all visual disturbances caused by a discordant polychromy, and relieving the space of a certain visual monotony recurrent in this type of place. Particular attention was paid to chromatic contrast and luminance values, as contrast sensitivity generally decreases with age and can be even more disturbed when visual pathology is added. Thus, the luminance indices of each recommended colour are between 0.6 and 0.9 for light colours and between 0.2 and 0.45 for dark colours, and finally, a contrast of 70% has been respected between different important supports so that they can be perceived by a visually impaired person, whose sensitivity to contrasts is still operating. Here, light colours are used for large surfaces and dark colours for smaller surfaces or accessories to allow better discrimination of spatial elements. Some of the contrast values are not equal to 70%, but they have been accepted due to a negligible margin of error. The creation of these differentiated harmonies has therefore allowed us to design circulation spaces with chromatic variations for each level, favouring intuitive orientation as well as efficient and comfortable reading of the chain of movement for all inhabitants.

Finally, these harmonies were also accompanied by a lighting design. This was studied so that the quantity and quality of light would meet the needs of all the inhabitants, because at 55 years of age the quantities of light required are 300% higher than at 25 years of age, and this for an equivalent level of visual performance, AFE (2020). For this reason, we recommended an average of 300 lux at the floor level, homogeneous throughout the buildings, using direct and indirect LED lighting with a colour temperature of 3000 Kelvin. Finally, the choice of materials was studied in order to recommend finishes ranging from matt to satin in the entrance halls according to their natural light contribution in order to adapt to each exposure and thus not generate any glare or darkness.

To conclude, the third phase was the creation of a technical execution file for the project management. This file is based on and complements the documents provided by the project architect and includes normative descriptions as well as graphic documents such as colouring diagrams on plans, lighting system layout diagrams, cross-sections, a book of details and signage, as well as a material library to ensure the proper implementation and monitoring of the project.

RESULTS

The different phases of surveys and analyses contributed to demonstrate in a quantitative and normative way how the place could be perceived by the inhabitants, INSEE 2017. The interpretation of these results allowed us to start prescribing efficient lumino-chromatic atmospheres, taking into account the constraints linked to circadian lighting and the location of the buildings. This creation phase, beyond taking into account the standards in force, called upon an experimental construction method, [START_REF] Pfeiffer | L'harmonie des couleurs, cours théorique et pratique[END_REF], taking into account several factors intrinsic to the project:

• -The analysis of the characterisation of the colour and light on the site.

• -The spirit and visual coherence of the place where the project will be located.

• -An efficient chain of movement.

• -Comfort of use and appreciation of the spaces for all inhabitants. The outcome of this protocol was the creation of a construction file and a detail booklet, intended for the project owner in order to transcribe the information collected into technical prescriptions, colouring principles and efficient lighting in the future building. We hypothesise that this expertise in chromatic and luminous characterisation within its future circulation spaces will generate more visual reference points and comfort of use thanks to this protocol..

DISCUSSION

The issue of lighting and colour in collective housing is quite complex, as designers' preferences vary greatly according to both objective and quantifiable conditions (economy, standardisation of practices, specific needs related to people with disabilities, etc.) and socio-cultural and subjective conditions (preference for a particular colour scheme, type of luminaire, type of covering, etc.).

As a result, and in the absence of standards directly related to these semi-private spaces, architects tend to use very neutral, even monotonous, colours and materials, and struggle to install lighting that is sufficiently effective, comfortable and aesthetic in common areas. With the help of this study, we are beginning to awaken designers to the challenges of colour and light. Because together, beyond their simple aesthetic contribution, they make it possible to secure and make efficient the circulations while allowing the inhabitants to plunge into singular universes where the atmosphere becomes a factor of wellbeing and cohesion.

CONCLUSION

In the next ten years, a comparative study will complete the research-creation protocol studied in this article. This comparative study will take into account the values obtained in the old residences and those designed from this protocol, this study will be completed by an interview with the inhabitants questioning them on the perception of the place and basing ourselves on a scale of sensations and anhedonia. This study will enable property developers to adjust and design in a systematic and sustainable way visual ambiences better adapted to human physiological needs and to prove the validity of qualitative approaches in terms of light and colour design within new property programmes.

Figure 2 :

 2 Figure 2 : Chromatic environment creation

ACKNOWLEDGEMENTS

I thank the LAPLACE Laboratory of the Paul Sabatier University in Toulouse, France for making the experiment possible by providing tools. I also thank the company SOBRIM for allowing me to carry out this study and for the interest shown in these results. Finally, I would like to thank them for their willingness to promote and develop their university research within their future real estate programmes thanks to the HARANAM approach..