Yu Fan

David Helbert

Anne-Sophie Capelle-Laizé

Philippe Carré

Christine Fernandez-Maloigne

Detection of Image Splicing using Illuminant Color Estimation

Keywords:

Digital image forensics is a set of techniques used for digital image forgery detection and is widely used to certify the content or the authenticity of a document. The splicing operation, which crops and pastes one or several regions from separate images, is a common technique used for image forgery. In the literature, most image forgery detection techniques are based on machine learning. Only a few methods take advantage of physical features to detect the tampering. In this paper, we propose a new method to detect image splicing from an analysis of regions of interest in the uv chromaticity space. Their pixels are compared to the Planckian locus and the closest ones, seen as achromatic, are stored in a weighted histogram depicting Gaussian distribution. After a selection of the suitable Gaussians, the illuminant color is estimated. Results on spiced images are presented and discussed.

Introduction

More than 350 million photos have been uploaded every day on Facebook on average, throughout 2013 [START_REF] Facebook | A focus on efficiency[END_REF]. On that same year, due to the popularity of smartphones, more than 660 billion of photos have been taken, which increased to 1.1 trillion in 2016 [START_REF] Richter | Smartphones cause photography boom[END_REF]. There is no doubt that our everyday lives are replete with images coming from numerous media, let it be television, newspaper, news site or social network. Given the rising threat of "fake news", it would be interesting to know the ratio of manipulated images, which is not at all a straightforward matter. According to a 2015 poll, while 76% of press photographers regard image manipulation as a "serious problem", 25% admit that they sometimes alter the content of images, other than by cropping [START_REF] Hadland | The state of news photography: the lives and livelihoods of photojournalists in the digital age[END_REF]. This being only related to the press, we would also have to include all the pictures fraudulently submitted in the information flow and shared all across social medias, which is impossible to estimate. Indeed, digital image forgery is nowadays accessible to the general public through the use of numerous powerful and low-cost image editing software. From this assessment, we can admit that being able to trust the authenticity of any given digital image has become quite difficult [START_REF] Farid | Digital doctoring: Can we trust photographs?[END_REF][START_REF] Parry | Digital manipulation and photographic evidence: defrauding the courts one thousand words at a time[END_REF] while having the means to detect image forgery is now primordial: this is the purview of digital image forensics, a set of techniques used for image forgery detection [START_REF] Farid | Image forgery detection[END_REF][START_REF] Sencar | Overview of state-ofthe-art in digital image forensics[END_REF], that is to say certifying the content or the authenticity of documents and their data [START_REF] Pearson | Image manipulation: Csi: cell biology[END_REF]. Even though the authenticity of an image can be proved by directly embedding a digital watermark into it [START_REF] Cox | Digital watermarking and steganography[END_REF], not all hardware can insert such a watermark before the manipulation of the image. To overcome this difficulty, blind image forensics has been proposed to deal with the image tampering without inserting any security information. It assumes that even if the image forgeries may not leave usual traces that would indicate tampering, they also alter the underlying patterns that are introduced by imaging devices of an original untampered image. A digital image can be tampered in many ways, such as by geometric transformations, color adjustments, copy-moves and so on. One of the most common image manipulation method consists in cropping and pasting one or several regions from the separate images, a technique known as splicing. In this article, we will focus on the detection of images that have been spliced.

Over the past few years, many techniques and methodologies have been proposed to deal with image forgeries linked to image splicing [START_REF] Farid | Image forgery detection[END_REF][START_REF] Mahdian | A bibliography on blind methods for identifying image forgery[END_REF][START_REF] Lin | Recent advances in passive digital image security forensics: A brief review[END_REF]. Previous works can generally be classified into three categories. The first category identifies the manipulated images by detecting the statistical anomalies, for example in the frequency domain [START_REF] Popescu | Statistical tools for digital forensics[END_REF][START_REF] Shi | A natural image model approach to splicing detection[END_REF][START_REF] Chen | Image splicing detection using 2-d phase congruency and statistical moments of characteristic function[END_REF]. Deep learning based forensic methods are proposed to design image splicing and detect image manipulations [START_REF] Bayar | A deep learning approach to universal image manipulation detection using a new convolutional layer[END_REF][START_REF] Rao | A deep learning approach to detection of splicing and copy-move forgeries in images[END_REF]. Many methods in this category are based on algorithms needing preconditions, such as the ones based on a learning strategy, requiring a the construction of a model to generate results. In addition, some of them are weak against anti-forensics techniques that remove the detectable traces found in the images and used by these methods. The second category evaluates the changes in the features introduced by digital data acquisition devices such as cameras, scanners, etc. Most of the methods in this category require information about the source acquisition device in order to compare the inherent patterns extracted from the sample images. Some examples of the inherent patterns are the sensor pattern noise [START_REF] Lukas | Digital camera identification from sensor pattern noise[END_REF], aberrations produced by a lens [START_REF] Johnson | Exposing digital forgeries through chromatic aberration[END_REF] and so on. The physically based techniques of the last category detect the inconsistency of the scene properties. Among those, the illumination condition has been considered as an indicator for forgery detection. The illuminant-based methods are either geometry-based or color-based. The geometry-based methods detect the inconsistencies of the direction of light source between the sample regions on the scene [START_REF] Johnson | Exposing digital forgeries by detecting inconsistencies in lighting[END_REF][START_REF] Kee | Exposing digital forgeries from 3-d lighting environments[END_REF][START_REF] O'brien | Exposing photo manipulation with inconsistent reflections[END_REF][START_REF] De Carvalho | Exposing digital image forgeries by illumination color classification[END_REF], while the color-based ones detect the illuminant color inconsistencies [START_REF] Gholap | Illuminant colour based image forensics[END_REF][START_REF] Riess | Scene illumination as an indicator of image manipulation[END_REF][START_REF] Wu | Image splicing detection using illuminant color inconsistency[END_REF][START_REF] Cozzolino | Image forgery localization through the fusion of camerabased, feature-based and pixel-based techniques[END_REF].

In this paper, we will focus on a color-based method for splicing operation detection. In recent years, a lot of methods have been proposed for illuminant estimation [START_REF] Gijsenij | Computational color constancy: Survey and experiments[END_REF][START_REF] Vidyadharan | Illuminant color inconsistency as a powerful clue for detecting digital image forgery: A survey[END_REF]. However, very few of them are applied to the security field. In addition, most of the methods for illu- minant estimation are based on the Lambertian model [START_REF] Van De Weijer | Edgebased color constancy[END_REF] and some of them estimate the illuminant using the dichromatic reflection model [START_REF] Tan | Color constancy through inverse-intensity chromaticity space[END_REF][START_REF] Francis | Illuminant colour based image forensics using mismatch in human skin highlights[END_REF]. We propose to adapt a method of illuminant estimation for splicing operation detection based on Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF], using the Lambertian model.

The contributions of this work are as it follows: we also improved the way the illuminant colors are estimated by making it more quick and reliable. Secondly, we added a practical way to analyze the illuminant estimation to detect potential tampering.

A collection of images was created by using a Nikon D300S camera with two 60mm and 90mm lenses, is composed of 25 high-resolution pictures and is showcased in Section 4. Each set features indoors and outdoors photographs of various scenes depicting sets of objects, humans or simple background sceneries, with a majority of scenes containing specular highlights. Since our method relies on operations made directly on the pixels values of the image, the pictures have been taken in RAW format with a 14-bit depth to preserve their quality by avoiding any compression, then converted to a TIFF format with a 16-bit depth. Multiple objects, persons, animals and plants have been extracted from different scenes and pasted in some others, resulting in a set of twenty sliced pictures involving those different categories of sceneries. The splicing operations were done using Adobe Photoshop CS6.

The paper is organized as follows. In Section 2, we summarize the related work in the field of color constancy and image splicing detection with the illuminant color. Section 3 explains the physical principles used to estimate the illuminant color based on the dichromatic reflection model and the Lambertian model. In Section 4, we provide a step-by-step explanation of the method we are proposing to detect image forgery in addition to numerous experiments on spliced pictures to test their performances. The conclusion is given in the last section.

Related work

As mentioned previously, the illuminant color inconsistency is used to detect image splicing in many proposed methods. The earliest method applying the illuminant color analysis in image forensics has been proposed by Gholap and Bora [START_REF] Gholap | Illuminant colour based image forensics[END_REF]. The authors estimate the chromaticity of the illuminant color of different objects based on the dichromatic reflectance model and try to detect the changes in the model. Later on, Francis and Gholap [START_REF] Francis | Illuminant colour based image forensics using mismatch in human skin highlights[END_REF] proposed a method to help dealing with the detection of the illuminant when encountering pictures that features human skin. However, this method turns out to be especially sensitive to the skin highlight regions. To avoid these constraints, Wu and Fang [START_REF] Wu | Image splicing detection using illuminant color inconsistency[END_REF] estimate the illuminant color on each overlapping block under the Lambertian assumption, i.e., purely diffuse reflectance. For this, low-level statistics-based algorithms of illuminant estimation have been adapted for the specific image block. The angular error between the estimates of the blocks and those of some reference blocks is measured for the final decision of tampering. However, the method is practically limited by manual selection of reference blocks, thus the inappropriate reference blocks probably produce the inaccurate detection results.

Riess and Angelopouou [START_REF] Riess | Scene illumination as an indicator of image manipulation[END_REF] have proposed a physicalbased method for local illuminant estimation, based on inverse-intensity chromaticity space. Both the illuminant and distance maps are used to identify image authenticity. Although this method can perform on rough highlight regions, manual interaction is needed to select the dominant illuminants. Furthermore, the authors do not provide any numerical criterion for splicing detection. Recently, De Carvalho and Riess [START_REF] De Carvalho | Exposing digital image forgeries by illumination color classification[END_REF] have developed a learning process of the illuminant colors for the detection of spliced images of people. The illuminant estimates for faces are performed using statistics-based [START_REF] Van De Weijer | Edgebased color constancy[END_REF] and physics-based [START_REF] Riess | Scene illumination as an indicator of image manipulation[END_REF] methods. These estimates are then used to automatically make tampering decision through a novel machinelearning approach. The proposed method requires only a small amount of human interactions and produces satisfactory results, but it has not shown any effectiveness on other types of images e.g., images containing plants, or animals.

In the field of color constancy, extensive methods have been presented [START_REF] Gijsenij | Computational color constancy: Survey and experiments[END_REF]. Indeed, most illuminant color estimators typically assume globally uniform illumination. In other words, the spectral distribution of one light source is uniform across the scene and therefore the illuminant color is constant all over the image. However, in practice, many real-world images consist of more than one illuminant and thus often exhibit a mixture of different light sources. In order to use the illumination as an indicator of image splicing, we require multiple and local illuminant estimation. However, very few methods explicitly focus on this direction. In early research, color constancy for multiple illuminants has been proposed by Kuang and Xiong [START_REF] Kuang | Color constancy for multiilluminants high-dynamic-range scenes[END_REF]. They used the modified local auto white-balance algorithm to solve the local illuminant for High-Dynamic-Range images. The illuminant estimation per pixel is performed through color information of its neighboring pixels, weighted by the spatial distance, luminance intensity difference and chromaticity. Later, Bleier and Riess have proposed a method [START_REF] Bleier | Color constancy and non-uniform illumination: Can existing algorithms work?[END_REF] to determine multiple light sources using local illuminant estimation for super pixels which originates from the segmentation on the image. The common algorithms are applied to each super pixel independently. The final accurate illuminant per super pixel is determined using either the average of all combined estimates or machine learning regression. Gijsenij and Rui [START_REF] Gijsenij | Color constancy for multiple light sources[END_REF] have proposed a general color constancy method for multiple light sources. They apply the existing color constancy algorithms to image patches in order to obtain local illuminant estimates. This method mainly focuses on scenes with two distinct light sources and their combination. The final estimation of two distinct illuminant colors is given either by clustering the illuminant estimates for patches or by incorporating spatial information with segmentation. Recently, Beigpour and Riess have developed a new method [START_REF] Beigpour | Multi-illuminant estimation with conditional random fields[END_REF] to estimate the multiple illuminants and their spatial distribution, using an energy minimization strategy within a Conditional Random Field. They have also proposed two new datasets for multi-illuminant estimation. More recently, Joze and Drew have presented an exemplar-based color constancy method [START_REF] Joze | Exemplar-based color constancy and multiple illumination[END_REF] for multiple illuminants. Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] have proposed a learning-free method based on the Planckian locus for the estimation of several illuminants which we adapted in our second method. The illuminant colors of the scene are obtained by projecting gray pixels on a Planckian locus in a specific chromaticity diagram. Van de Weijer and Gevers [START_REF] Van De Weijer | Edgebased color constancy[END_REF] have presented a framework, namely Grey-Edge, that systematically incorporates the well-known color constancy methods. Finally, given its omnipresence in an increasingly wide and varied range of application in the last years, it should be noted that Bianco and Cusano [START_REF] Bianco | Single and multiple illuminant estimation using convolutional neural networks[END_REF] developed a Convolutional Neural Network specifically designed to provide multiple local illuminant color estimations by working on image patches. Within a similar context, Shi and Loy [START_REF] Shi | Deep specialized network for illuminant estimation[END_REF] developed a Deep Specialized Network separated into two sub-networks: one makes multiple illuminant estimation hypotheses and the other selects one of them. In both of these papers, it is shown that the presented networks either achieve or outperform the state-of-the-art performance. We will now present the different physical models used to estimate illuminants in order to detect spliced regions.

Illuminant color estimation

Color constancy aims to estimate the chromaticity of the illuminant color and then to correct the image to a canonical light source using the diagonal model. The illumination estimation, which is thus the main part of color constancy, is applied in different fields such as image segmentation, image retrieval and object recognition. Furthermore, the illuminant color can also be an indicator of image tampering evidence because of the variation of light sources from two different scenes. The colors of an object observed in the image are determined by its actual color and the color of the light source. Therefore, the objects that are in the same scene but exposed to two different illuminants may appear of different colors.

In the method we are developing, the main task is indeed the estimation of these illuminant colors. We will show below that the different models stated from the formation of a color image can be of use when trying to estimate the illuminant color of a given region in a scene.

Color image formation

A color image taken by a linear device such as a digital camera is expressed as a vector of 3 pixel values (RGB), i.e. p = (p R , p G , p B ) T . These values depend on the surface reflectance for body reflection component S b (λ, x), the spectral power distribution E(λ) i.e. the color of the light source and the device sensitivity function ρ(λ) = (ρ R , ρ G , ρ B ) T . Thus the image color at location x can be modeled as [START_REF] Tominaga | Standard surfacereflectance model and illuminant estimation[END_REF][41]:

p c (x) = ω m b (x)E(λ)S b (λ, x)ρ c (λ)dλ + ω m S (x)E(λ)ρ c (λ)dλ, (1)
where c is a color pixel in (R, G, B), λ and ω being the interval of wavelength of the light and the visible spectrum, respectively. Moreover, as the first part of Equation 1corresponds to the diffuse body or Lambertian reflectance and the second part corresponds to the interface or specular reflectance, m b (x) and m S (x) are the geometric scale factors for these respective types of reflectance, in that order. The surface reflectance S S (λ, x) of the interface component is assumed to be constant as the index of refraction does not significantly vary according to ω. Accordingly, S S (λ, x) does not appear in Equation 1and is included in m S (x).

Dichromatic reflection model

The dichromatic reflection model [START_REF] Shafer | Using color to separate reflection components[END_REF] states that the light reflected from an inhomogeneous object is decomposed into two additive components: the diffuse or body reflection and the specular or interface reflection. The former corresponds to the Lambertian reflectance, while the latter is assumed to be similar to the spectral energy distribution of the incident light. The underlying assumption [START_REF] Tominaga | Standard surfacereflectance model and illuminant estimation[END_REF] for most dichromatic-based methods is that the pixels of an object surface fall on a plan in a RGB color space. Relying on at least two unparalleled plans that correspond to two different color surfaces, the color of the light source is estimated by finding an intersection of these planes. Some methods [START_REF] Gholap | Illuminant colour based image forensics[END_REF][START_REF] Tan | Color constancy through inverse-intensity chromaticity space[END_REF][START_REF] Finlayson | Solving for colour constancy using a constrained dichromatic reflection model[END_REF][START_REF] Lehmann | Color line search for illuminant estimation in real-world scenes[END_REF] for illumination estimation propose to use the bright areas of the image such as highlights, specularities or white surfaces. Both these approaches assume that the color of the pixels in the highlighted regions is identical or similar to that of the light source. Although those dichromaticbased methods can perform well for the objects that show specular highlights, they require the highlight regions segmentation and suffer from the problem of similar object colors.

Lambertian model

Under the Lambertian assumption, the target image only has a diffuse reflection. It means that the Lambertian model ignores the specular reflection. As a result, Equation 1 used in the color image formation becomes:

p c (x) = m(x) ω E(λ)S(λ, x)ρ c (λ)dλ, (2)
where m(x) is the scale factor of the Lambertian surface and does not depend of the wavelength of the light. For a given x, the reflected light color p c (x) can then be modeled as follows:

p r c(x) =   p R p G p B   = ω E(λ)S(λ, x)ρ c (λ)dλ. (3)
Since p c (λ) is unknown and the spectral power distribution E(λ) cannot be recovered from the discrete sensor measures, determining p c is under constraints: it is therefore usual to estimate the illuminant color based on some strong assumptions. We will need two of these assumptions in the next part.

Illuminant color estimation

Illuminant color estimation using dichromatic lines

Gholap and Bora [START_REF] Gholap | Illuminant colour based image forensics[END_REF] have introduced a method to estimate the chromaticity of the illuminant color by using the specular regions of a pair of objects. The estimation is accomplished by finding an intersection point, i.e., the values of the illuminant chromaticity, of two dichromatic lines in the r -g chromaticity space. First, two dichromatic planes corresponding to the two chosen specular regions must be found, as they represent the observations of our color signal by being the linear combination of the diffuse reflection vector and the specular reflection vector [START_REF] Tominaga | Standard surfacereflectance model and illuminant estimation[END_REF]. This is done by the application of principal component analysis, or PCA, on each of their pixels. It is used as a feature extraction method to get a better representation of the RGB values from our set of pixels, in the form of a two-dimensional space. After using an orthogonal transformation, the initial set of data is converted into a set of values of linearly uncorrelated variables which are the principal components of the PCA. We can obtain our two-dimensional feature space by projecting the data onto the plane defined by the first two principal components: they correspond to the eigenvectors with the two most significant eigenvalues, meaning that these components have the largest possible variance and that they are the most informative about our initial set of data. The two planes obtained from applying PCA on the sets of pixels from our regions are mapped in the r -g chromaticity space using the following parameters:

r = R R + G + B , g = G R + G + B . (4)
Any two specular regions of different colors can be used in illumination estimation. This method suffers from several constraints: it needs an initial detection of specular highlights and the picture, including the sliced region, must contain specular highlights, these specularities should not be too small and the spliced regions and original areas ratio should stay balanced.

Illuminant color estimation using Planckian locus

Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] have proposed a learning-free method based on the Planckian locus to estimate the color of several illuminants. The method relies on two physical assumptions. The first one concerns the limit of feasible illuminants: the set of possible light sources is assumed to be modeled by using the Planckian locus of black-body radiators. The second physical assumption concerns the content of the image: it is assumed that there is at least an achromatic/gray surface that contains perfectly reflective pixels in the scene, which means that this achromatic surface is a region that depicts a color identical to the light source. From these assumptions, the illuminant can be calculated with the Planckian model, which states that the spectrum of light source E(T, λ) emitted by a black body in thermal equilibrium at a definite temperature T is given by:

E(T, λ) = c 1 λ -5 e c 2 λT -1 -1 , (5)
where T is the temperature in Kelvin, λ corresponds to the wavelength and c 1 = 3.74183 × 10 16 W m 2 and c 2 = 1.4388 × 10 -2 mK are two constants. Although Equation 5 can be directly used to compute the spectrum of most light sources in the daily life, the results cannot be represented in chromaticity space. In our work, we use Mazin and Delon's [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] numerical approach based on the Planckian locus instead of directly using Equation 5. The Planckian locus is the path followed by the color of a black body in a given chromaticity space when the temperature of the black body changes. The black body is represented by the achromatic surface in the image. Note that not only most natural illuminants but also some typical artificial light sources can be estimated by the Planckian locus [START_REF] Judd | Spectral distribution of typical daylight as a function of correlated color temperature[END_REF]. Figure 3a

    R G B   , (6) x = X X + Y + Z , y = Y X + Y + Z , (7)
with R, G and B the intensity of the red, blue and green channel values of a given pixel in the RGB color space, respectively. The Planckian locus can be computed using also the CIE 1960 color space, also known as MacAdam's uv chromaticity diagram [START_REF] Kelly | Lines of constant correlated color temperature based on macadamâĂŹs (u, υ) uniform chromaticity transformation of the cie diagram[END_REF], which is used in our algorithm. It is shown in Figure 3b. The uv diagram is represented by the two chromaticity coordinates u and v, obtained as follows:

u = 4x 12y -2x + 3 , v = 6y 12y -2x + 3 . (8)
Figure 3b shows the Planckian locus depending on the different color temperatures in the CIE 1960 uv chromaticity diagram. For T , a color temperature in Kelvin located between 1000 K and 15000 K, the following values of u and v project the Planckian locus in the CIE 1960 uv chromaticity diagram: Also, in order to provide a better sampling of these temperatures according to the human perception [START_REF] Priest | A proposed scale for use in specifying the chromaticity of incandescent illuminants and various phases of daylight[END_REF], we decide to use the Micro Reciprocal Degree (MIRED):

T M IRED = 10 6 T , (11)
with T the color temperature in Kelvin and T M IRED its MIRED value in reciprocal megaKelvin (M K -1 ). Different methods for the estimation of the illuminant have been proposed using the Planckian locus, with for example Lehman and Palm [START_REF] Lehmann | Color line search for illuminant estimation in real-world scenes[END_REF] and Finlayson and Schaefer [START_REF] Finlayson | Single surface colour constancy[END_REF] estimating the illumination chromaticity by intersecting the dichromatic line with the Planckian locus. In those cases, the illuminant color can be estimated even if there is only one surface in the scene. However, the image must be segmented into regions of homogeneous color, and these regions have to contain highlight pixels. Additionally, the methods work poorly for yellow and blue illuminated regions whose dichromatic lines have similar orientations to the Planckian locus. From this approach, Storring [START_REF] Storring | Estimation of the illuminant colour from human skin colour[END_REF] proposes a method to estimate the illuminant color from observations of the skin color. It shows good performance on real-world images but requires prior knowledge about the camera parameters. The selection of achromatic pixels is done by projection on the Planckian locus and a voting procedure is used to obtain robust illuminant estimation.

The method of Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] has not a presegmentation processing. Moreover, it performs well for the scene of several illuminants. To estimate the illuminant color of a region, its achromatic pixels are first found by selecting the pixels of the region, projected in the uv chromaticity diagram, that are the closest to the Planckian locus. Then, an histogram of the MIRED temperatures estimated from the achromatic pixels of the region is built. These temperatures correspond to the dominant illuminants in the region: the histogram is considered to be a mixture of Gaussians, with each Gaussian distribution corresponding to one illuminant. We proceed with a small filtering to separate the major Gaussian distributions from the micro-peaks. Finally, an estimation of the illuminant is made by combining the Gaussian distributions that are left and projecting the corresponding temperature to the Planckian locus.

Detection of Image Splicing using Planckian Locus

Proposed method

We propose an adaptation of the method of Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] for image manipulation detection. The goal of this method is to compare estimations of the illuminant color related to different regions of the picture that will be retrieved via manual segmentation. The original paper assumed that a single illuminant is used in the whole scene: since the pictures we are working on are spliced, we chose to bring this method to the security field by making the illuminant estimation local. The way we estimate these illuminants is quicker and more reliable than the original method and we added a final representation of the picture showcasing the estimated illuminant colors to easily spot the possible anomalies in our pictures. Our algorithm is built as it follows:

) 12
with p uv being a pixel of the image projected in the uv chromaticity diagram, L being the Planckian locus and p uvproj the projection of p uv on the Planckian locus. An example of a projection is shown in Figure 5. If the Euclidean distance between the pixel and its projection is less than a given threshold δ experimentally set at δ = 0.0125, the pixel is potentially considered as an achromatic pixel, which means it needs to satisfy the following condition:

||p uv -p uvproj || 2 < δ. ( 13
)
This achromatic pixel lets us retrieve the temperature of its related black body radiator by looking at its position on the Planckian locus.

In Figure 6, the pixels from the different regions are projected on the uv chromaticity diagram. The ones satisfying Equation 13 are represented by red dots while those which don't are represented in black. For the sake of clarity, only 10% of the pixels appear in this graphic. We can already see that the achromatic pixels from region 3 are located in a lower area on the chromaticity diagram than the pixels from the other regions, which corresponds to a higher temperature in the Planckian locus.

Figure 7 highlights the pixels that have been selected. Note that if less than 5% of the pixels of a region are labeled as achromatic, no illuminant color will be estimated. Here, 99.5%, 97.4%, 74.2% and 99.7% of the pixels from respectively region 1, 2, 3 and 4 remain. A few pixels In order to estimate the illuminant chromaticity of the region, we need to build the histogram of all the different temperatures detected from the achromatic pixels we gathered. As explained in Section 3.2.2 with Equation 11, this histogram is built in MIRED. To limit the influence of the darkest pixel, it is also weighted by the power of each pixel luminance value Y found in the CIE 1931 color space, as defined in Equation 6.

To estimate the illuminant, we have to extract the modes of histogram denoting the most frequent MIRED. These temperatures correspond to the dominant illuminants in the scene. Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF] propose to use an a contrario detection method, but operating in this way has a drawback: since it has to make the decision for each interval of histogram, it becomes really complex in the case of local regions of interest. In our method, we decide to first smooth the histogram with a Gaussian filter, which makes the histogram a mixture of Gaussians, each Gaussian distribution being considered as one illuminant.

To detect the different Gaussian distribution, we propose a new step in Mazin and Delon [START_REF] Mazin | Estimation of illuminants from projections on the planckian locus[END_REF]'s method by using an ad hoc procedure. Firstly, we start by recording the color temperature which corresponds to a peak value in the histogram. This temperature value T mean is considered as the mean of its corresponding Gaussian distribution. Secondly, the standard deviation σ is computed by analyzing the distribution values around T mean . Having T mean and σ at hand, we can now approximate a Gaussian distribution. To avoid parasites, we decided that if a given Gaussian distribution G i is to be associated to an illuminant, it needs to satisfy the two rules stated below:

1. The ratio between the peak value of the Gaussian distribution P i and the peak value of the whole histogram P H must be equal or larger than a given threshold δ 1 = 0.05: Pi P H ≥ δ 1

2. The normalized peak value of the Gaussian distribution, which is the ratio between the peak value of the Gaussian distribution P i and the sum of each value h j in the histogram, must be equal or larger than a given threshold δ 2 = 0.01: Pi Figure 8 shows the histogram of our four regions. As said earlier, the achromatic pixels from region 3 seem to be of a higher temperature than the other regions. Note that the histogram is sorted in MIRED: the higher temperatures are on the left side while the lower ones are on the right. Note that we obtained the same results using Gaussian mixture models (GMMs) with the Expectation-Maximization (EM) algorithm but with a more important complexity. Now that the distribution has been validated, we select all the achromatic pixels in the [T mean -σ,T mean +σ] range and approximate their value to estimate the corresponding illuminant. If multiple Gaussian distributions in the region have been detected, the procedure explained above is repeated but a weighted mean is operated to estimate the final illuminant, using the peak values of the Gaussian distributions as weights for the achromatic pixels.

In Figure 9, we can see that regions 1 and 4 illuminants estimations are pretty close to each others but regions 2 and 3 seem more distant. While the object from region 3 does indeed come from an other picture, the object from region 2 comes from the original image: a suitable explanation would be that the object from region 2 is really close to the light source located on the right, whereas the objects from region 1 and 4 are more close to the light source located on the left. Moreover, Figure 9 only gives us information coming from the uv color space. Another point of view could be acquired by converting those colors back to the RGB color space. Since the luminance value, represented by Y , is needed when going from the xyz to the XY Z color space, a new value of Y = 0.8 has been arbitrarily given. Finally, since our the pixels used to estimate our illuminant colors are achromatic, the color seen in the RGB color space will, by definition, have a low saturation. As a consequence, we artificially enhance its color saturation value in the HSV color space before visualizing it, for comparison purposes only:

S E = S + 0.2 * (255 -S) (14)
with S E being the enhanced saturation value and S being the normalized original one. In Figure 10, region 3 definitely stands out by having a greenish color as opposed to the other three regions having an orange color.

Results

To validate our method for image splicing detection, we perform experiments on multiple images that have been taken and manipulated for the purposes of this paper, as explained in Section 1. Some results of detection are showcased below in the following sections and a last section describes and explains the problems that were met during the experiments.

Experiment 1

There is no interaction between each region of interest we can select in an image. The color estimation we get at the end of the algorithm depends only of the selected pixels. Therefore, since the final decision is made by comparing the different colors given by the algorithm, an experiment dedicated to a non-spliced image is unnecessary, as it is equivalent to only analyze the non-spliced regions of a spliced image.

In the first experiment, we will analyze a spliced image taken outdoors and containing an object coming from an image taken indoors. In Figure 11, the camera corresponding to region 4 is the object cropped from an other image. We can also note that region 6 is a gray-colored reflective surface and a red traffic light directly casts a red light on it. In Figure 12, we can see that the red parts of region 6 have been discarded as they are not close to the Planckian locus when projected on the uv chromaticity diagram. Only the white-gray text remains. In Figure 13, we can observe that the illuminant color linked to the spliced region 4 is far away from the rest of the regions.

Finally, Figure 14 gives us an estimation of the illuminant color of each object. Region 4 illuminant color is yellow, regions 1, 2, 3, 5, 7 colors are blueish, while region 6 color is more purple: it may come from the fact that

Experiment 2

We apply our algorithm to the spliced picture we studied in the previous method. This time, we are using new regions of interest, seen in Figure 15 (b). As we can see in F igure 16 (a), only 0.4% of the pixels from region 1 are close enough to the Planckian locus to be considered as achromatic, the other 99.6% being represented in black. This region will therefore not be used in the next steps of the algorithm. The results obtained in Figure 17 and 18 are not satisfying: every remaining object has a different estimated illuminant color. This is explained by the fact that region 2 and 3 depict objects that are coated in an intense color and their achromatic pixels contain more information about their color than the light source they reflect. The regions 1 and 4 which are gray and white are the only ones that can give us an acceptable illuminant color estimation.

Experiment 3

In our third experiment, we will examine a picture featuring people. The original picture has been taken indoors in a closed environment and contains one person. The same person has been photographed outdoors, thus taken with a different light source, then cropped and pasted in the first picture, resulting in Figure 19 (a). 20 properly as regions belonging to the spliced person are located next to regions belonging to the original picture. However, let us take into account that these regions go by pairs or triplets considering their nature: regions 1 and 4 depict the person's face, regions 3 and 7 depict his hand, regions 2 and 5 depict his shirt and region 6 and 8/9 depict his trousers, the first region cited being part of the original picture and the second/third being from the spliced region. We can see that the spliced regions are always under the Planckian locus while the original are always above -or slightly below in the case of region 1. The global illuminant color palette has shifted downward when comparing the spliced regions to the original ones. The spreading of the illumination color estimation belonging to the same picture come from the fact that we try to compare areas of different nature, with some of them, like the skin, having a natural color.

Discussion

Finally, the consequences of the multiple light sources are visible with our approach. As we have seen in Figure 14, when analyzing the final picture given by the algorithm, it is important to take into account the fact that some objects might receive multiple light sources and therefore get an illuminant color rather different from the other objects, even if it has not been spliced.

To estimate the illuminant color, the algorithm tries to find the achromatic pixel contained in the regions based on the second physical assumption we made in Section 3.2.2: there is at least an achromatic surface that contains perfectly reflective pixels in the scene, this surface depicting a color identical to the light source. It first means that the algorithm will not give acceptable results if the studied surfaces do not contain a sufficiently high amount of achromatic pixels. However, an achromatic surface do not necessarily mean that it is the sign of a nearblack-body radiator either. It may simply be the natural color of the object. Even if most of the chromatic pixels are discarded when projected on the Planckian locus, the remaining pixels may not be related to a reflective surface. The consequence is that to get significant results, it is preferable to select regions of interest that correspond to naturally white or gray colored objects. Otherwise, if an picked area is of a high-saturated color, it should be compared to areas of similar design, like a wall with an other wall or a shirt with an other shirt. It is also the reason why when pictures involve people, the algorithm works best if these people possess a similar skin-tone.

Conclusion

In this paper, we introduce a method to detect image splicing operations, a popular image forgery technique consisting in cropping a region from a given image and pasting it onto an other. We have proposed the adaptation of a method based on the Lambertian model, adding a way to locally estimate the illuminant color and easily compare multiple regions of an image.

This learning-free approach gives us good results and is easy to apply, as it does not need a precise segmentation of the regions of interest. However, these regions need not to be bright-colored as it interferes with the illuminant color estimation. Otherwise, colored objects of similar nature can be used for comparison.

When coming across a suspicious image, our method involves an analysis of the inconstancies in an estimation of the scene illuminant color, it also returns a colored image acting as a decision support and either representing a "tamper score" in the form of a heat map or a direct estimation of the illuminant color.

  (a) The first dataset, with pictures both taken indoors and outdoors. (b) Subset of the images used in the sliced pictures.

Figure 1 :

 1 Figure 1: Preview of pictures.

Figure 2 :

 2 Figure 2: (a) Two dichromatic planes p 1 and p 2 in the RGB color space, (b) p 1 and p 2 mapped as two dichromatic lines l 1 and l 2 in the r -g chromaticity space. l 1 and l 2 intersection is highlighted in red.

  depicts the Planckian locus in the CIE (International Commission on Illumination) 1931 xy chromaticity diagram. The black line is a path that goes from deep red at low temperatures through orange, yellowish white, white and finally bluish white at high temperatures. The method we use is based on the following assumption: the various chromaticities of most illuminant colors are very close to the values found in the Planckian locus by studying achromatic pixels. The two chromaticity coordinates x and y are normalization of the tristimulus values XY Z and are obtained from pixels values in the RGB color space by the following transformation matrix given by CIE 1961 when the image origin is unknown: as follows: 0.31000 0.20000 0.17697 0.81240 0.01063 0.00000 0.01000 0.99000

  (a) CIE 1931 xy chromaticity diagram. (b) CIE 1960 uv chromaticity diagram.

Figure 3 :

 3 Figure 3: Planckian locus in the CIE chromaticity diagram.

2 , 2 .

 22 + 1.54118254 × 10 -4 × T + 1.28641212 × 10 -7 × T 2 1 + 8.42420235 × 10 -4 × T + 7.08145163 × 10 -7 × T + 4.22806245 × 10 -5 × T + 4.20481691 × 10 -8 × T 2 1 -2.89741816 × 10 -5 × T + 1.61456053 × 10 -7 × T (10)

1 .

 1 All the pixels from each region of interest are plot in the CIE 1960 uv chromaticity diagram 2. The pixels close to the Planckian locus are labeled as achromatic and are projected on it 3. Their position on the Planckian locus corresponding to a particular temperature value, a weighted histogram is built 4. A Gaussian filter is applied on the histogram, which lets us retrieve the different Gaussian distributions that are represented 5. The most significant Gaussian distribution are kept and pixels from these Gaussians are used to estimate the illuminant color of the region 6. The illuminant color, originally estimated in the uv color space, is also converted to the RGB color space and gets more saturated for viewing purposes 7. The colors are applied on the regions of interest to easily spot the ones that differ We will use the image (a) in Figure 4 where the object from the base presented on Figure 1 (b) has been pasted onto a new image. The chosen regions of interest in (b) correspond to the different objects in the scene we want to compare.

Figure 4 :

 4 Figure 4: (a) Spliced image, (b) Regions of interest.

Figure 5 :

 5 Figure 5: Projection of a pixel on the Planckian locus from the CIE 1960 uv chromaticity diagram.

Figure 6 :

 6 Figure 6: Projection on the Planckian locus from the CIE 1960 uv chromaticity diagram of 10% of the pixels from (a) Region 1, (b) Region 2, (c) Region 3, (d) Region 4.

Figure 7 :

 7 Figure 7: Achromatic pixels in the different regions.

≥ δ 2

 2 with N b the total number of bins in the histogram

Figure 8 :

 8 Figure 8: Histogram of the achromatic pixels in from (a) Region 1, (b) Region 2, (c) Region 3, (d) Region 4 (original histograms in blue, estimations in red).

Figure 9 :

 9 Figure 9: Estimation of the illuminant color in the CIE 1960 uv chromaticity diagram.

Figure 10 :

 10 Figure 10: (a) Spliced image, (b) Estimation of the illuminant color in the RGB color space, with enhanced saturation.

Figure 11 :

 11 Figure 11: (a) Spliced image, (b) Regions of interest.

Figure 12 :

 12 Figure 12: Achromatic pixels in the different regions.

Figure 13 :

 13 Figure 13: Estimation of the illuminant color in the CIE 1960 uv chromaticity diagram.

Figure 14 :

 14 Figure 14: (a) Spliced image, (b) Estimation of the illuminant color in the RGB color space, with enhanced saturation.

Figure 15 :

 15 Figure 15: (a) Spliced image, (b) Regions of interest.

Figure 16 :

 16 Figure 16: Projection on the Planckian locus from the CIE 1960 uv chromaticity diagram of 10% of the pixels from (a) Region 1, (b) Region 2, (c) Region 3, (d) Region 4, (e) Region 5.

Figure 17 :

 17 Figure 17: Estimation of the illuminant color in the CIE 1960 uv chromaticity diagram.

Figure 18 :

 18 Figure 18: (a) Spliced image, (b) Estimation of the illuminant color in the RGB color space, with enhanced saturation.

Figure 19 :

 19 Figure 19: (a) Spliced image, (b) Regions of interest

Figure 20 :

 20 Figure 20: Estimation of the illuminant color in the CIE 1960 uv chromaticity diagram

Figure 21 :

 21 Figure 21: (a) Spliced image, (b) Estimation of the illuminant color in the RGB color space, with enhanced saturation


Nawal Berrada

Samah Hamze

Alexandre Desforges

Jaafar Ghanbaja

Jérôme Gleize

Thierry Maré

Brigitte Vigolo

Patrice Estellé
email: patrice.estelle@univ-rennes1.fr

Surface tension of functionalized MWCNT-based nanofluids in water and commercial propylene-glycol mixture

Keywords: MWCNT, nanofluids, chemical modification, surface tension, effect of concentration and base fluid

Nanofluids which consist of the addition of nanoparticles in a base fluid are envisaged for a large domain of applications. For many of them, the surface tension (ST) behavior of the prepared nanofluids is a key parameter to exploit their thermophysical properties. Due to their remarkable properties, carbon nanotubes (CNTs) are commonly used to develop nanofluids. However, the evolution of the ST of CNT-based nanofluids is still far from being understood and predictable.

In the present work, two base fluids were used: water and a commercial mixture of propyleneglycol/water (around 40:60 wt.%). The impact of the used multi-walled CNT (MWCNT) addition, MWCNT concentration (0.001 and 0.1 wt.%) and temperature variation (273.15-333.15 K) on the density and ST evolution for the two kinds of CNT-based nanofluids is studied. The chemically modified MWCNTs are assumed to bear both localized hydrophilic areas due to grafted functional groups and remaining hydrophobic surfaces. The found difference in ST behavior between the two types of nanofluids is explained in light with the involved interfaces in each nanofluid. ST evolution is found to strongly depend on the CNT surface properties.

Introduction

Nanofluids, a very simple product of the emerging world of nanotechnology, are suspensions of nanoparticles (1-100 nm in size) in conventional base fluids such as water, glycols, or oils. Since their introduction in the early 1990s, they have been the subject of many research works. The nanoparticles are typically made of metals, carbides, oxides, or carbon-based materials. As compared to the pure base fluids, this innovative class of heat transfer fluids exhibits much higher thermophysical properties including increase in thermal conductivity, high single-phase and boiling heat transfer coefficients, and enhanced critical heat flux. Due to their unique properties, nanofluids can be used in various applications including micro-channel cooling within integrated circuits, biomedical therapies and diagnosis, manufacturing procedures, chemical and pharmaceutical processes, engine and electronic device cooling, concentrating solar energy, nuclear reactors, etc… [START_REF] Mahian | Recent advances in modeling and simulation of nanofluid flows-Part I: Fundamentals and theory[END_REF]. In particular, the liquid-gas surface tension plays a major role in applications related to boiling and condensation phenomena, and other processes involving heat transfer [START_REF] Estelle | Current trends in surface tension and wetting behavior of nanofluids[END_REF]. However, how surface tension (ST) may change with particle parameters such as concentration, size and shape, nature of the used nanoparticles, and also with the type of base fluids and surfactant is an emerging topic. Some recent efforts have been devoted towards defining and measuring the surface tension of nanofluids as reviewed in ref. [START_REF] Estelle | Current trends in surface tension and wetting behavior of nanofluids[END_REF].

In addition, as nanoparticles suspended in the base fluid, carbon nanotubes (CNTs) have been widely analysed, but the properties of CNT-based nanofluids such as the contact angle of sessile droplets [START_REF] Hernaiz | The contact angle of nanofluids as thermophysical property[END_REF] and the effective gas-liquid surface tension of these nanofluids have been rarely investigated. Main results from the open literature are described in the following. Xue et al. [START_REF] Xue | The interface effect of carbon nanotube suspension on the thermal performance of a two-phase closed thermosyphon[END_REF] studied the ST of acid-treated CNTs dispersed in water. Experiments were performed from the bubble pressure method for a nanotube volume concentration of 1 vol.%. They showed that the presence of CNTs in water increased the ST of water up to 13.5 % and the ST of nanofluid decreased with rising temperature from 298.15 to 343.15 K. Tanvir and Qiao [START_REF] Tanvir | Surface tension of Nanofluid-type fuels containing suspended nanomaterials[END_REF] exploited the pendant drop method to measure the ST of multi-walled CNTs (MWCNTs) dispersed in water or ethanol. The measurements were done at ambient temperature and the studied weight concentration range was between 0.1 and 10 wt.%. They found that, for ethanol-based nanofluids, the ST decreased slightly up to 2 wt.%, then it was increased with nanoparticle loading. For water-based nanofluids, an increase in ST with the mass content of CNTs was thus reported. Effect of sodium dodecyl benzene sulfonate (SDBS) surfactant addition and chemical treatment of single-walled carbon nanotubes SWCNTs dispersed in water and ST of resulting nanofluids were investigated by Murshed et al. [START_REF] Murshed | An Experimental Study of Surface Tension-Dependent Pool Boiling Characteristics of Carbon Nanotubes-Nanofluids[END_REF] and Kumar and Milanova [START_REF] Kumar | Effect of surface tension on nanotube nanofluids[END_REF] for a concentration of 0.1 vol.%. The authors showed that for SWCNT-based nanofluids, in a low surfactant concentration domain, ST did not vary with surfactant concentration. However, above a critical value of surfactant concentration, ST decreased because of the excess of surfactant in water. Interestingly, decrease in nanofluid ST with surfactant concentration was correlated to an observed increase in heat flux during pool boiling. Study of ST of functionalized MWCNT-based nanofluids was reported by Karthikeyan et al. [START_REF] Karthikeyan | Wetting behavior of multi-walled carbon nanotube nanofluids[END_REF]. Ethanol and water were used as base fluids.

ST properties were obtained at ambient temperature with the pendant drop method. They highlighted that ST of well-stable nanofluids started to increase from a critical concentration value of 500 ppm with ethanol, and did not depend on the MWCNT concentration for water as base fluid. In another work, Soleimani et al. [START_REF] Soleimani | Impact of carbon nanotubes based nanofluid on oil recovery efficiency using core flooding[END_REF] investigated the ST of distilled water-based nanofluids where different concentrations of MWCNTs. From 0.05 to 0.5 wt.% of MWCNTs were dispersed by using sodium dodecyl sulfate (SDS) as a surfactant. They used the pendant drop method for their measurements, and they obtained that the ST increased steadily of up to 0.3 wt.% then it decreased. Ershadi et al. [START_REF] Ershadi | Carbonate and sandstone reservoirs wettability improvement without using surfactants for Chemical Enhanced Oil Recovery (C-EOR)[END_REF] prepared 0.2 wt.% of MWCNT/SiO 2 nanohybridbased nanofluids with water as base fluid. They investigated the effect of nanofluids on the wettability of carbonate and sandstone substrates by measuring interfacial tension and contact angle. Their results showed that the nanofluid could significantly decrease the ST and change the wettability of the rock from oil-wet to water-wet conditions. A decreasing in ST was also obtained by AfzaliTabar et al. [START_REF] Afzalitabar | Preference of multi-walled carbon nanotube (MWCNT) to single-walled carbon nanotube (SWCNT) and activated carbon for preparing silica nanohybrid pickering emulsion for chemical enhanced oil recovery (C-EOR)[END_REF] with MWCNT/SiO 2 , SWCNT/SiO 2 , and activated carbon/SiO 2 dispersed in distilled water. They found a better ability of MWCNT/SiO 2 nano hybrid for decreasing the ST in comparison to the two other samples.

In summary, based on the literature review, it is difficult to predict how ST can change with addition of CNTs. Also, it is not clear whether the ST will increase or decrease with nanotube content with respect to the type of base fluid and what mechanisms are responsible for the observed behaviors. An attempt to give some highlights in this field has motivated the present research. So, the main objective of this work is to determine the effect of CNT addition and temperature on the ST of water-based nanofluids. Functionalized MWCNTs were dispersed in two different heat transfer water-based fluids, pure distilled water and Tyfocor® LS -a commercial fluid composed of propylene-glycol/water (around 40:60 wt.%), up to now only used with nanofluids in solar collector absorber plate with microchannels [START_REF] Oyinlola | Thermal analysis of a solar collector absorber plate with microchannels[END_REF] -respectively. The pendant drop method is used for the ST measurements and two distinct weight concentrations of functionalized MWCNTs are considered, 0.001 and 0.1 wt.%, respectively. In the present study, the complete characterization of the raw and the chemically modified MWCNTs by using thermogravimetric analysis (TGA), transmission electron microscopy (TEM) and Raman spectroscopy is performed. Then, dispersion in the two used base fluids is analyzed by means of optical microscopy and zeta potential techniques. Therefore, the density of base fluids and nanofluids is evaluated. Finally, influence of the nature of the base fluid, the nanotube concentration and the applied temperature on the ST evolution is finally discussed in the light of the involved interfaces in each nanofluid.

Materials and methods

Raw MWCNT sample. The raw MWCNTs (Nanocyl™ NC7000, average inner diameter ~ 9.2 nm, average length: 1.5 µm [START_REF] Estelle | Thermophysical properties and heat transfer performance of carbon nanotubes water-based nanofluids[END_REF] were purchased from Nanocyl S.A. (Belgium). They were synthesized by catalytic chemical vapor deposition (CCVD) by using iron and cobalt as catalysts deposited on an alumina substrate. The raw MWCNTs are referred to as r-MWCNT.

Chemicals. Potassium permanganate (KMnO 4 ) and sodium sulfite (Na2SO3) were obtained from Alfa Aesar (Germany), sodium hydroxide (NaOH) from VWR International (USA), and nitric acid (HNO 3 ) 65 % was acquired from Honeywell Fluka International (USA). Sulfuric acid (H 2 SO 4 ) 95-97 % and hydrochloric acid (HCl) 37 % were both purchased from Sigma Aldrich (Germany).

Chemical treatments. The carried-out purification is a one-pot gas-phase treatment [START_REF] Mercier | Selective removal of metal impurities from single walled carbon nanotube samples[END_REF]. Briefly, the raw MWCNTs (~ 300 mg) were placed in a silica crucible and introduced in a tubular oven.

First, in order to remove air, the sample was vented by the carrier gas, nitrogen. The sample was then heated at 10 K/min up to 1273.15 K under a stream of chlorine at a flow-rate of 200 mL/min. After 2 h at 1273.15 K under chlorine, the MWCNT powder was maintained at 1273.15 K for 2 additional hours under nitrogen before natural cooling.

After this treatment, the purified MWCNTs (referred to p-MWCNT) are ready to be used. p-MWCNT was functionalized using a KMnO 4 /NaOH (1:1) mixture [START_REF] Zhang | Effect of chemical oxidation on the structure of single-walled carbon nanotubes[END_REF]. About 100 mg of purified MWCNTs were put in 60 mL of KMnO 4 0.2 M and 60 mL of NaOH 0.2 M in a round bottom flask equipped with a condenser, and heated with an oil bath until refluxing maintained for 40 min. The solution was then cooled down to room temperature. The excess of KMnO 4 was reduced with 3 g of Na 2 SO 3 in an acid media (35 mL of H 2 SO 4 1 M). Then, the mixture was filtered on a membrane (Merck Millipore, 0.45 µm). Firstly, it was washed with HCl 4 N then with distilled water until neutral pH and dried overnight at 323.15 K. The functionalized MWCNTs thus obtained are denoted f-MWCNT in the following.

Nanofluid preparation. After purification and functionalization of MWCNTs, nanofluids were prepared from the two step-method by dispersing the chosen weight of f-MWCNT in either distilled water (DW) or water-propylene glycol-based solvent namely Tyfocor® LS (referred to Tyfocor in the following (figures and text) for sake of clarity). Two distinct concentrations of f-MWCNT were selected to investigate the effect of nanoparticle content on the ST of nanofluids: 0.1 and 0.001 wt.%. The solutions were sonicated using an ultrasonic probe Vibra cell 75042 during 1 h with a power of 125 W with a pulse mode: 2 sec-ON/1 sec-OFF under controlled temperature.

Characterization techniques.

Thermogravimetric analysis (TGA) was performed with a Setaram Setsys evolution 1750. About 5 mg of MWCNT powder loaded in a platinum crucible was transferred in the chamber where, after a purging stage, temperature was increased from room temperature to 1173.15 K with a ramp of 5 K/min. A 20 mL/min-flow rate of dry air or helium was used as a carrier gas. The metallic impurity content was determined by using the remaining weight after the combustion of the carbon species leading to a rapid decrease in weight.

Transmission electron microscopy (TEM) observations were carried out using a JEM-ARM 200F apparatus at an accelerating voltage of 80 kV. The samples were prepared by dispersing a small amount of CNTs in ethanol using a sonication bath for a few minutes. A drop of the solution was deposited on a holey carbon grid (200 mesh size). Being aware that TEM is a local technique, about 30 images were taken at different areas for each sample to guarantee a statistical analysis.

Raman spectroscopy was carried out by a LabRAM HR 800 micro-Raman spectrometer using a red incident laser (λ= 632.8 nm) and an x50 objective. A drop of the raw or treated MWCNTs dispersed in ethanol was deposited on a glass slide. The recorded number of spectra for each sample was at least 3 and could be higher according to the dispersion of the results. After A Malvern Zetasizer was used to measure the zeta potential of the functionalized MWCNTs dispersed in water.

Density measurements of base fluids and nanofluids were performed with a Rudolph Research Analytical DDM 2910 Automatic Density Meter. Once calibrated by checking the value of air density at 293.15 K, 2 mL of each sample were withdrawn into a syringe and then released in a U-tube until filled. Careful rinsing with ethanol was operated between each measurement. The density measurements were done between 293.15 and 323.15 K every 10 K. In this temperature range, an absolute average deviation AAD = 0.15 % was obtained between experimental data of distilled water and reference data from ref. [START_REF] Sengers | Improved International Formulations for the Viscosity and Thermal-Conductivity of Water Substance[END_REF]. Also, the absolute average deviation AAD is 0.046 % with Tyfocor® LS in comparison to available manufacturer data [17].

The temperature range considered here is linked to the available temperatures of the density measurement apparatus. Consequently, to extend the range of density values for all samples to lower and higher temperatures (from 273.15-283.15 to 333.15 K) than those experimentally measured (from 293.15 to 323.15 K), and also to evaluate ST at these temperatures, the experimental data of density were correlated to equation (1) [START_REF] Cabaleiro | Thermophysical properties of (diphenyl ether plus biphenyl) mixtures for their use as heat transfer fluids[END_REF][START_REF] Vallejo | Potential heat transfer enhancement of functionalized graphene nanoplatelet dispersions in a propylene glycol-water mixture. Thermophysical profile[END_REF].

( ) = (1)
Where is the density in kg.m -3 and T is the temperature in K. The coefficients A i of each sample are gathered in Table 2 along with the respective standard deviation (lower than 0.025 kg.m -3 ).

Finally, ST measurements were performed with a Drop Shape Analyzer DSA-30 from KRÜSS GmBH (Hamburg, Germany) based on the pendant drop technique. Typically, a 15-gauge needle with an outer diameter of 1.835 mm was used to produce drops at controlled flow rate and volume within a temperature chamber. The temperature in the chamber was regulated with a Peltier system and controlled by a PT100 probe. The comprehensive experimental procedure was similar to the one described in ref. [START_REF] Gomez-Villarejo | Experimental analysis of water-based nanofluids using boron nitride nanotubes with improved thermal properties[END_REF]. In the pendant drop configuration, Young-Laplace equation was used for determining ST from the image analysis of the drop shape produced at the end of the needle and the density of the sample. Each ST values reported in the following is the average of at least 10 measurements. ST of DW was measured in the temperature range 283.15-333.15 K (see later in Figure 5). An absolute average deviation AAD = 1.08 % was obtained between experimental data and reference data in this temperature range [START_REF] Vargaftik | International Tables of the Surface-Tension of Water[END_REF].

Results and discussion

Chemical modification of MWCNTs and dispersion in the base fluids

Purity of the treated MWCNTs was quantified by TGA (Figure 1a). The thermogram of the raw MWCNTs shows one weight loss at around 773.15 K assigned to the combustion of carbon species which represents 88 wt.% of the sample and a remaining metallic impurity rate of 12 wt.% in their oxide forms (i.e. Fe 2 O 3 , CoO, Al 2 O 3 ). After the purification treatment, the remaining weight being close to zero, the sample was completely free from metal and the combustion temperature of MWCNTs is shifted to higher temperatures (+ 100 K). As expected, the purified MWCNTs are more stable against combustion than the raw MWCNTs; metallic impurities playing the role of combustion catalyst of CNTs [START_REF] Chiang | Purification and characterization of single-wall carbon nanotubes[END_REF]. Moreover, no mineral impurity pollutes the MWCNTs after functionalization (100 wt.% loss after MWCNT combustion) as it can be sometimes observed after using a KMnO 4 -based treatment [START_REF] Zhang | Functionalization of carbon nanotubes by potassium permanganate assisted with phase transfer catalyst[END_REF]. Figure 2 shows typical TEM images of the MWCNTs before (a and d) and after the two chemical treatments: purification (b and e) and functionalization (c and f) with different magnifications. In the raw MWCNTs, the metal impurity particles (dark particles top right Fig. 2a) are clearly identified and they are no more present is the purified (Fig. 2b) and in the functionalized (Fig. 2c) sample in agreement with the TGA results (Fig. 1a). In higher magnification images, while no damaging on the nanotubes is observable after purification (Fig. 2e), the external MWCNT walls were slightly attacked by the functionalization leaving however untouched the internal walls (Fig. 2f). Raman spectroscopy is a well suitable technique for the structural quality assessment of CNTs because it is very sensitive to the evolution of the sample according to chemical treatments [START_REF] Osswald | Monitoring oxidation of multiwalled carbon nanotubes by Raman spectroscopy[END_REF].

The intensity of the D band (around 1350 cm -1 ) is sensitive to any introduction of defects, for example sp 2 carbon atoms turning sp 3 By assuming that the mass loss of the functionalized MWCNTs at 1173.15 K from TGA (Fig. 1) is due to release of mainly carboxyl acids as expected by the used functionalization method [START_REF] Zhang | Effect of chemical oxidation on the structure of single-walled carbon nanotubes[END_REF],

the functionalization level can be estimated from the following relation equation( 2) [START_REF] Mamane | Chemi-vs physisorption in the radical functionalization of single-walled carbon nanotubes under microwaves[END_REF]:

(

) 2
Where M COOH and M C are the respective molar weights of a carboxyl acid group and a carbon atom; and WL, the weight assigned to the functional group loss from TGA. The weight loss at 1173.15 K is of about 1.49 and 13.37 wt.% for the MWCNTs before and after the chemical treatment, respectively. For f-MWCNT, the weight loss due to detachment of carboxyl groups is of 11.88 wt.%. n determined from ( 1) is about 28. That means that 1 functional group is grafted every 28 carbon atoms or every almost 5 C 6 -rings, in average. The found functionalization level is then relatively low. This seems to indicate that hydrophobic domains are probably still present on the MWCNT surface. Indeed, even if the internal walls remain untouched after the applied chemical treatment, this kind of applied oxidation is known to preferentially occur at the defect sites and the extremities of the MWCNTs leading to a non-homogeneous positioning of the functional groups on the MWCNT surface [START_REF] Devaux | Covalent Functionalization of HiPco Single-Walled Carbon Nanotubes: Differences in the Oxidizing Action of H2SO4 and HNO3 during a Soft Oxidation Process[END_REF][START_REF] Hirsch | Functionalization of single-walled carbon nanotubes[END_REF]. At the nanometer scale, some areas (cylindrical parts of nanotubes) are certainly more hydrophobic and other areas (MWCNT extremities) more hydrophilic; these latter playing the major role for the CNT dispersion within both DW and Tyfocor.

Optical microscopy images shown in Figure 4 evidence that both prepared nanofluids (in DW, This agrees well also with the value of the zeta potential of f-MWCNT in DW measured at -42 mV indicating a good dispersion and stability [START_REF] Ghadimi | A review of nanofluid stability properties and characterization in stationary conditions[END_REF][START_REF] Lee | Effective viscosities and thermal conductivities of aqueous nanofluids containing of Al2O3 low volume concentrations nanoparticles[END_REF]. It should be mentioned that zeta potential distribution for dispersion in Tyfocor is too large certainly due to the presence of the charged additives in this commercial mixture leading to a non-reliable value.

Density of base fluids and nanofluids

The experimental density values of the used base fluids and nanofluids are gathered in Table 1. First at all, it is observed in Figure 5 that ST of DW decreases with temperature, as expected, and the found values are in good agreement with literature data [START_REF] Vargaftik | International Tables of the Surface-Tension of Water[END_REF] as explained in section 2. As shown in Figure 6, ST of Tyfocor is lower than that of DW due to the presence of propylene glycol. Tyfocor ST decreases as well with temperature. No comparison can be made with literature data since this property is reported for the first time with this commercial heat transfer fluid. It is also observed from both figures that reduction rate in ST with temperature is greater for DW. While the densities of nanofluids slightly increases with nanotubes content in comparison to the density of base fluids, as shown before in section 3.2, it appears that ST of nanofluids evolves in different manner following the base fluid and changes are more pronounced, as explained below.

In this

Figure 5 also shows the evolution of ST as a function of temperature and concentration for f-MWCNT/DW-based nanofluids. The ST of these nanofluids is lowered in average by 1.83 and 3.96 % as the concentration of f-MWCNT increases from 0.001 to 0.1 wt.%, respectively. The observed trend is consistent with results previously reported in [START_REF] Tanvir | Surface tension of Nanofluid-type fuels containing suspended nanomaterials[END_REF], as well as with other carbon structures such as graphene oxide and reduced graphene oxide dispersed in water [START_REF] Cabaleiro | Dynamic Viscosity and Surface Tension of Stable Graphene Oxide and Reduced Graphene Oxide Aqueous Nanofluids[END_REF]. As previously mentioned, f-MWCNT is well dispersed in DW due to the grafted functional groups and the functionalized MWCNTs also bear hydrophobic zones which affinity with air/water interface is expected to increase, leading to the observed ST reduction with MWCNT concentration. For the nanofluids prepared with Tyfocor as base fluid, contrary to what is it observed with DW, increase in f-MWCNT concentration induces an increase in ST: ST is of 7.48 and 10.41 % at 273.15 K and 8.87 and 19.43 % at 333.15 K for MWCNT concentration of 0.001 and 0.1 wt.%, respectively (Fig. 6). We hypothesize that covering of the remaining hydrophobic surface of MWCNTs by the polymer chains of propylene glycol could increase affinity between MWCNTs and Tyfocor leading to the observed increase in ST [START_REF] Balamurugan | Interaction of Carbon Nanotube with Ethylene Glycol-Water Binary Mixture: A Molecular Dynamics and Density Functional Theory Investigation[END_REF][START_REF] Mary | Mechanistic Investigations of Viscosity and Thermal Conductivity Enhancement in Multi-Walled Carbon Nanotubes-Propylene Glycol Nanofluids[END_REF]. Indeed, alcohols are well known to play the role of surfactants or co-surfactants, useful to help hydrophobic nanoparticles or colloids to be dispersed in water [START_REF] Kralova | Surfactants Used in Food Industry: A Review[END_REF]. Affinity of f-MWCNTs with Tyfocor is consequently better with DW in agreement with optical observations (Fig. 4). For Tyfocor-based nanofluids, f-MWCNT understandably remain within the bulk liquid, and only a few are transported to the interfacial region due to Brownian motion. The attraction between the nanotubes and propylene glycol contained in Tyfocor reduces the intermolecular spacing resulting in an increase of the ST. This also leads to a raise in ST when the MWCNT content increases. Finally, as reported in literature [START_REF] Estelle | Current trends in surface tension and wetting behavior of nanofluids[END_REF], the ST of all the prepared nanofluids decreases with the raise of temperature whatever the base fluid used.

Conclusions

In this study, MWCNT-based nanofluids were prepared with distilled water and propyleneglycol/water (Tyfocor) without using surfactant. The MWCNTs were chemically oxidized with Behavior of the ST of the nanofluids measured by the pendant drop method was analyzed and discussed as a function of the MWCNT weight loading, temperature and the base fluid used. To

  subtraction of the baseline, the height of the D band was divided by that of the G band to calculate the I D /I G intensity ratio. The error bars were determined from the standard deviation to the calculated I D /I G average. Optical microscopy was performed by an optical microscope Olympus TH4-200 BXS1 using an x10 objective. For the observations, a drop of a MWCNT solution was deposited on a glass slide recovered by a coverslip (22 mm x 22 mm).

Figure 1b shows the

  Figure1bshows the weight losses from TGA in helium of the raw, purified and the two

Figure 1 .

 1 Figure 1. Thermograms recorded of r-MWCNT (blue curve), p-MWCNT (green curve), f-

Figure 2 .

 2 Figure 2. Typical TEM bright field micrographs of the MWCNT samples. a) and d) r-MWCNT;

  hybridization through functionalization. Meanwhile, the G band (around 1590 cm -1 ) is representative of the graphitic carbon sp 2 network. Compared to the raw MWCNTs (I D /I G = 1.87 ± 0.04), the purified MWCNTs show a decrease of the I D /I G (1.59 ± 0.08) meaning that no additional defect has been introduced during our purification treatment. I D /I G is increased for f-MWCNT up to I D /I G = 2.32 ± 0.01. I D /I G is thus significantly increased from 1.59 to 2.32 through functionalization giving a clear evidence of presence of functional groups at the MWCNT surface.

Figure 3 .

 3 Figure 3. I D /I G ratios of r-MWCNT (blue), p-MWCNT (green) and f-MWCNT (orange). The

Fig. 4a and

  Fig. 4a and Tyfocor, Fig. 4b) with 0.1 wt.% of f-MWCNT appear very homogeneous. Only very

Figure 4 .

 4 Figure 4. Optical microscope images of dispersed f-MWCNT (0.1 wt.%) in DW (a) and in

3. 3

 3 Surface tension of base fluids and nanofluids Measurements of ST of base fluids and nanofluids at two weight concentrations 0.001 and 0.1 wt.%, for a temperature range of 283.15-333.15 K for the DW-based nanofluids and 273.15-333.15 K for the Tyfocor-based nanofluids, are reported in figures 5 and 6, respectively. The error bars were determined from the standard deviation to the average value of ST.

Figure 5 .

 5 Figure 5. Surface tension of the f-MWCNT nanofluids with DW as base fluidinfluence of

Figure 6 .

 6 Figure 6. Surface tension of the prepared f-MWCNT nanofluids with Tyfocor as base fluid -Influence

KMnO 4 .

 4 A comprehensive characterization of the raw and the chemically modified MWCNTs by using thermogravimetric analysis (TGA), transmission electron microscopy (TEM) and Raman spectroscopy was performed evidencing the achievement of the functionalization process. The used MWCNT concentration were 0.001 and 0.1 wt.%. The densities of nanofluids are slightly modified by the MWCNT concentration in comparison to the densities of base fluids.

Table 1 .

 1 Table are also reported the computed density values obtained from equation (1) for temperatures lower than 273.15 K and higher than 323.15 K. As mentioned previously, the coefficients A i for each sample and the respective standard deviations from equation (1) in the temperature range 273.15-323.15 K are included in Table2. The density of both base fluids and the corresponding nanofluids decreases as the temperature increases with a similar trend; the Tyfocor density being higher than that of water due to the presence of propylene-glycol.Moreover, the density of nanofluids with the lowest content in MWCNTs (0.001 wt%) is logically very close (almost similar) to that of the respective base fluid by taking into account the measurement uncertainty. For both base fluids, it is observed that the density for 0.1 wt.% of MWCNTs is slightly higher than that of the respective base fluid. An average increase in density of 0.05 % in the temperature range 273.15-323.15 K is noticed for the water-based nanofluid.With Tyfocor as base fluid, the average rise of density in the same temperature range is around 0.08 %. Experimental densities and computed densities (in bold) from equation (1) of the used base fluids and the nanofluids with different MWCNT mass fractions and temperatures

	a)	a)	b)	b)

1045.405 1045.405 1046.395 283.15 999.975 999.975 1000.6 1040.025 1040.025 1040.975

	A 2 / kg.m -3 .K -2	-0.00375	-0.00375	-0.0035	-0.00175	-0.00175	-0.00175
	St. Dev. / kg.m -3	0.022361	0.022362	0.024443	0.022361	0.022361	0.022363
	Regression Coefficient R²	0.999995641 0.99999564 0.999930577 0.99999879 0.99999879 0.99999881
	293.15	998.1	998.1	998.6	1034.3	1034.3	1035.2
	303.15	995.5	995.5	996	1028.2	1028.2	1029.1
	313.15	992.1	992.1	992.5	1021.8	1021.8	1022.6
	323.15	988.1	988.1	988.5	1015.1	1015.1	1015.8
	333.15	983.125 983.125 983.7 1007.875 1007.875 1008.625
	Table 2. Fitting parameters A i and standard deviations (St. Dev.) from equation (1) for the base
	fluids and nanofluids at different mass fraction
			Water as base fluid		Tyfocor as base fluid
	MWCNT mass content / wt.%	0	0.001	0.1		0	0.001	0.1
	A 0 / kg.m -3	741.6537156 741.653716 766.1447213 1057.01046 1057.01046 1059.09306
	A 1 / kg.m -3 .K -1	1.974125	1.974125	1.81905	0.435525	0.435525	0.431525

the best of our knowledge, the ST of MWCNT/Tyfocor-based nanofluids was investigated for the first time in the present study. As expected, a decrease in ST with temperature was observed for both kinds of nanofluids. Our results show an opposite tendency regarding ST with MWCNT concentration for the two used base fluids: a reduction in ST was obtained with distilled water as base fluid and a significant increase in ST was observed with Tyfocor. This phenomenon was explained by the surface properties and the possible induced interactions within each nanofluid, i.e. functionalized MWCNT/distilled water and functionalized MWCNT/Tyfocor nanofluids.

Conflicts of interest

There are no conflicts to declare

Aknowledgements:

The authors thank Mr. P. Franchetti and Mr. L. Aranda for their help for TGA and Raman spectroscopy experiments, respectively. The authors are grateful to Dr. F. Michaux for his help for zeta potential measurements. The authors thank the University of Lorraine for its financial support especially for Miss. N. Berrada's Doctoral Fellowship. Dr. Patrice Estellé acknowledges the European Union through the European Regional Development Fund (ERDF), the Ministry of Higher Education and Research, the French region of Brittany and Rennes Métropole for the financial support of surface tension experimental device.