Ningzhen Wang

Eric Maire

Xiang Chen
email: xchen@tsinghua.edu.cn

Jérôme Adrien

Yanxiang Li

Yasin Amani

Lei Hu

Ying Cheng

Compressive performance and deformation mechanism of the dynamic gas injection aluminum foams

Keywords: aluminum foam, gas injection method, mechanical properties, in-situ compression, deformation mechanism

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Introduction

Closed-cell aluminum foams are a kind of foam structure with closed cellular pores inside the aluminum or aluminum alloy [START_REF] Banhart | Light-Metal Foams-History of Innovation and Technological Challenges[END_REF]. They have attracted some attention due to their light weight, good energy absorption, noise reduction and electromagnetic shielding performances [START_REF] Banhart | Manufacture, characterisation and application of cellular metals and metal foams[END_REF]. There are three different zones in the stress-strain compressive curves of aluminum foams: linear elastic region, stress plateau region (plastic deforming) and densification region [START_REF] Gibson | Cellular solids: structure and properties[END_REF]. The area under the stress-strain curve corresponds to the energy that aluminum foams can absorb. Because the stress remains almost constant with increasing strain in the plateau stage, aluminum foams can absorb a lot of energy in the deformation process [START_REF] Andrews | Compressive and tensile behaviour of aluminum foams[END_REF][START_REF] Jang | Microstructure and mechanical properties of ALPORAS closed-cell aluminium foam[END_REF][START_REF] Idris | Mechanical behaviour and energy absorption of closed-cell aluminium foam panels in uniaxial compression[END_REF][START_REF] Yuan | Effects of cell wall property on compressive performance of aluminum foams[END_REF]. In the case of closed-cell aluminum foams, the entrapped gas inside the cells also plays an important role in the dynamic compression, which extends their application in impact and explosion-proof domains [START_REF] Mukai | Compressive response of a closed-cell aluminum foam at high strain rate[END_REF][START_REF] Raj | Comparison of quasi-static and dynamic compression behavior of closed-cell aluminum foam[END_REF]. Good energy absorption properties of closed-cell aluminum foams make them have wide applications in automotive, aerospace and military industries. [START_REF] Banhart | Manufacture, characterisation and application of cellular metals and metal foams[END_REF][START_REF] Lefebvre | Porous Metals and Metallic Foams: Current Status and Recent Developments[END_REF]. Mechanical properties of aluminum foams are influenced by their relative density [START_REF] Raj | Comparison of quasi-static and dynamic compression behavior of closed-cell aluminum foam[END_REF][START_REF] Chen | Modeling of Macro-deformation Behavior of Thin-Walled Aluminum Foam by Gas Injection Method[END_REF], matrix [START_REF] Shi | Foaming Process and Properties of 6063 Aluminum Foams by Melt Foaming Method[END_REF][START_REF] Yu | The influence of pure Al and hypoeutectic Al-Si alloy base materials on the cell structures of aluminum foams produced by gas injection foaming process[END_REF], the microstructure of the cell walls [START_REF] Markaki | The effect of cell wall microstructure on the deformation and fracture of aluminium-based foams[END_REF], cell shapes [START_REF] Kadkhodapour | Micro-macro investigation of deformation and failure in closed-cell aluminum foams[END_REF] and cell size [START_REF] Chen | Effects of cell size and cell wall thickness variations on the strength of closed-cell foams[END_REF]. These factors are largely related to the preparation methods of closed-cell aluminum foams [START_REF] Sugimura | On the mechanical performance of closed cell Al alloy foams[END_REF][START_REF] Li | Comparison of aluminium foams produced by melt foaming and gas injection processes[END_REF][START_REF] Simone | Aluminum foams produced by liquid-state processes[END_REF][START_REF] Elmoutaouakkil | 2D and 3D characterization of metal foams using X-ray tomography[END_REF].

Gas injection is one of the main methods to produce closed-cell aluminum foams [START_REF] Banhart | Light-Metal Foams-History of Innovation and Technological Challenges[END_REF]. The process involves injecting gas directly into the molten aluminum or aluminum alloy containing ceramic particles [START_REF] Leitlmeier | Development of a Foaming Process for Particulate Reinforced Aluminum Melts[END_REF][START_REF] Jin | Method of producing lightweight foamed metal[END_REF]. Compared to the widely used melt foaming method (Alporas) in the industry [START_REF] Banhart | Light-Metal Foams-History of Innovation and Technological Challenges[END_REF], gas injection method has the advantage of permitting continuous production. [START_REF] Li | Comparison of aluminium foams produced by melt foaming and gas injection processes[END_REF]. An aluminum foam prepared by gas injection method has some key microstructural features, such as an oxide film in the cell walls caused by the oxidizing gas [START_REF] Zhou | The stability of aluminum foams at accumulation and condensation stages in gas injection foaming process[END_REF], the A356 matrix which is usually used [START_REF] Fan | Properties of aluminum foam prepared by gas injection method[END_REF], and ceramic particles which are necessary for the bubbles stability [START_REF] Babcsá N | Foamability of Particle Reinforced Aluminum Melt[END_REF]. These features can affect the cell structures and cell wall microstructures of aluminum foams, and certainly affect the compressive performance [START_REF] Markaki | The effect of cell wall microstructure on the deformation and fracture of aluminium-based foams[END_REF]. Therefore, it is necessary to study the compressive performance of aluminum foams prepared by gas injection method.

Static gas injection method means the gas injection needle was in static condition during the preparation process for uniform cells [START_REF] Yuan | Effects of cell wall property on compressive performance of aluminum foams[END_REF][START_REF] Chen | Modeling of Macro-deformation Behavior of Thin-Walled Aluminum Foam by Gas Injection Method[END_REF]. In order to reduce the size of bubbles and then improve the mechanical properties of gas injection aluminum foams, some dynamic methods were applied in the gas injector, such as the rotating or reciprocating of the gas injector developed by Cymat [START_REF] Jin | Method of producing lightweight foamed metal[END_REF][START_REF] Sang | Process for producing shaped slabs of particle stabilized foamed metal[END_REF], ultrasonic oscillation used by Aluhab [START_REF] Babcsá N | ALUHAB -The superior aluminum foam[END_REF], mechanical vibration generated by a stepper motor [START_REF] Garcí A-Moreno | Sub-mm sized bubbles injected into metallic melts[END_REF] and the high-speed horizontal oscillation [START_REF] Wang | The cell size reduction of aluminum foam with dynamic gas injection based on the improved foamable melt[END_REF]. The mechanical properties of some gas injection aluminum foams have been reported, such as the static gas injection aluminum foam [START_REF] Chen | Modeling of Macro-deformation Behavior of Thin-Walled Aluminum Foam by Gas Injection Method[END_REF][START_REF] Zhang | Compressive properties of aluminum foams by gas injection method[END_REF], Aluhab prepared by ultrasonic oscillation method [START_REF] Babcsá N | Pilot Production and Properties of ALUHAB Aluminium Foams[END_REF] and aluminum foam prepared by rotating gas injector [START_REF] Wang | Cell structure and compressive behavior of an aluminum foam[END_REF]. There have also been some research about Cymat aluminum foams, but their cell size uniformity was not satisfactory [START_REF] Kader | Macro and micro collapse mechanisms of closed-cell aluminium foams during quasi-static compression[END_REF][START_REF] Islam | In-situ quasistatic compression and microstructural characterization of aluminium foams of different cell topology[END_REF]. Dynamic gas injection method assisted with high-speed horizontal oscillation could significantly reduce the cell size and improve the cell quality [START_REF] Wang | The cell size reduction of aluminum foam with dynamic gas injection based on the improved foamable melt[END_REF], so the compressive performance and deformation mechanism of this dynamic gas injection aluminum foam deserve to be studied in detail.

The energy absorption performance of the aluminum foam is related to the failure modes of cells [START_REF] Mu | Deformation mechanisms of closed-cell aluminum foam in compression[END_REF]. The modes usually contain the formation of plastic hinges, tearing, fracture and buckling of cell membranes [START_REF] Kadkhodapour | Micro-macro investigation of deformation and failure in closed-cell aluminum foams[END_REF][START_REF] Mu | Deformation mechanisms of closed-cell aluminum foam in compression[END_REF]. At present, methods for characterizing cell deformation mainly include photographs of the deformation process [START_REF] Zhang | Compressive properties of aluminum foams by gas injection method[END_REF], scanning electron microscope (SEM) [START_REF] Song | Fracture mechanisms and size effects of brittle metallic foams: In situ compression tests inside SEM[END_REF], and X-ray tomography [START_REF] Kader | Macro and micro collapse mechanisms of closed-cell aluminium foams during quasi-static compression[END_REF][START_REF] Jeon | Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography[END_REF][START_REF] Petit | Two-scale study of the fracture of an aluminum foam by X-ray tomography and finite element modeling[END_REF]. Cell deformation is difficult to be observed clearly by the pictures in compression due to the resolution limit [START_REF] Zhang | Compressive properties of aluminum foams by gas injection method[END_REF]. The effective test zone of SEM method is usually small [START_REF] Song | Fracture mechanisms and size effects of brittle metallic foams: In situ compression tests inside SEM[END_REF]. More importantly, the two methods mentioned above could only show the deformation of cells in the outer surface of the sample. In fact, the deformation of each cell can be affected by the surrounding cells, and the deformation of cells in outer surface is not that representative due to fewer constraints compared to the internal cells. Some researchers used finite element simulations based on the model from X-ray tomography to study the cell deformation, but it is hard to consider all factors in the simulation of the compressive process [START_REF] Kader | Macro and micro collapse mechanisms of closed-cell aluminium foams during quasi-static compression[END_REF][START_REF] Jeon | Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography[END_REF]. C. Petit et al. [START_REF] Petit | Two-scale study of the fracture of an aluminum foam by X-ray tomography and finite element modeling[END_REF] used the in-situ test coupled with X-ray tomography in the study of open-cell aluminum foam, and showed that this can be a proper way to characterize the cell deformation. The deformation process of the internal foam structure can be obtained through X-ray tomography during compression test which allows one to study the cell deformation mechanism quantitatively.

In this paper, the compressive performance and deformation characteristics of aluminum foams prepared by dynamic gas injection method assisted with high-speed horizontal oscillation was studied by standard compressive tests, and it was compared with the mechanical properties of aluminum foams prepared by static gas injection method. The cell deformation mechanism of the dynamic gas injection aluminum foams was studied by in-situ compressive tests assisted with X-ray tomography.

Experimental Procedures

Standard compressive test of aluminum foams

In the preparation of aluminum foams used for the compressive test, first the commercial A356 alloy was melted as 700 °C, and Al2O3 particles with the size of 10 μm and the fraction of 10 vol.% were added into the aluminum alloy melt assisted with mechanical stirring. Then, the compressed air was injected into the melt by a gas injection system, bubbles could detach from the gas injection needle and rise to the melt surface. Finally, the solidified foam could be collected from the surface of the melt. In order to reduce the cell size of aluminum foams, a high-speed horizontal oscillation was applied into the gas injection needle, which has been described in detail in the literature [START_REF] Wang | The cell size reduction of aluminum foam with dynamic gas injection based on the improved foamable melt[END_REF], and the dynamic gas injection method mentioned below all refer to this method.

Ten bulk foam samples with porosity between 75 % and 95 % prepared by the dynamic gas injection method were chosen for compressive tests, their porosity distribution is shown in Table 1. In order to facilitate the analysis, the relative density was also used as a variable during the study of mechanical properties of aluminum foams, and the relationship between porosity and relative density is shown in Eq. 1. The cell diameter of the foam samples for compression is in the range of 2-12 mm. Foam samples were cut into a cylindrical or rectangular shape. In order to ensure that every foam has at least 10 cells in each direction, the sample size was mainly determined by the cell size of the aluminum foam. In addition, several aluminum foams prepared by static gas injection method were also compressed for comparison, but the data on the compressive performance of static gas injection aluminum foams mainly comes from literature [START_REF] Chen | Modeling of Macro-deformation Behavior of Thin-Walled Aluminum Foam by Gas Injection Method[END_REF].

     ( 1
)
where Pd is the measured porosity of aluminum foam. ρ * is the overall density of the aluminum foam, which is calculated from the weight and volume of the foam sample. ρs is the density of the matrix material (equal to 2.685g/cm 3 ).

Compressive tests were conducted on a WDW-200E electronic universal testing machine, and the loading rate was 4 mm/min. The strain rate of every foam sample was in quasi-static compressive condition at this loading rate. The load-displacement data during the compression could be obtained after the test, and then the nominal stress σ and nominal strain ε can be calculated by Eqs. ( 2) and (3), respectively.

= F A  (2) 0 = h h   ( 3
)
where F is the load obtained from the compression experiment. A is the loading area of the foam sample. Δh is the deformation of the sample along the compression direction, namely the displacement obtained from the experiment. h0 is the original height of the sample.

A schematic stress-strain curve of aluminum foam during compression is shown in Fig. 1. It can be divided into three stages: elastic deformation stage (Ⅰ), stress plateau stage (Ⅱ) and densification stage (Ⅲ). The energy absorption capacity of an aluminum foam is usually characterized by the densification strain energy WD, and its compressive performance is usually represented by the plateau stress σP. ε0 is the strain corresponding to the first peak stress in the curve. εD is the densification stain, namely the strain at the end of the plateau region. Densification strains of most samples in this paper were determined by the extreme point of the energy absorption efficiency-strain curve, and the detailed calculation process is detailed in [START_REF] Wang | Preparation and Compressive Performance of an A356 Matrix Syntactic Foam[END_REF]. For the aluminum foam with large cells (usually larger than 10 mm), the severe collapse of cell walls will lead to large fluctuation in the stress-strain curve, and then the densification strain determined by the above calculation method will not be accurate. Therefore, densification strains of aluminum foams with large cells were re-determined manually. Then, the densification strain energy and plateau stress of aluminum foams could be calculated by Eqs. ( 4) and ( 5), respectively.

D D 0 ( ) d W       (4) D 0 P D0 ( ) d -          (5)
Fig. 1. A schematic compressive stress-strain curve of an aluminum foam

X-ray tomographic characterization and in-situ compressive test

In order to study the effect of cell parameters on the compressive properties of aluminum foams, some foam samples were scanned by X-ray tomography before being compressed. A laboratory X-ray tomography equipment described in [START_REF] Buffiere | In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics[END_REF] was used in this study. The resolution during the scanning was 50 μm per voxel. Fiji software was used to process the reconstructed 3D images. The pore morphology of the foam sample could be obtained by a home-made plugin called "Param 3D" from the binarized 3D image. In order to avoid the influence of cell connection after binarization, cells were splitted by using "3D watershed split" plugin in Fiji first, and then the morphological parameters of every splitted cell could be obtained by "Param 3D" plugin. The detailed cell characterization process was described in [START_REF] Wang | Comparison of aluminium foams prepared by different methods using X-ray tomography[END_REF].

The X-ray tomography equipment was also used for the in-situ compressive test. One aluminum foam sample with uniform small cells was placed in an aluminum tube with an inner diameter of 15 mm and a wall thickness of 1 mm. This tube is almost transparent to the X-ray. A force sensor was attached to the upper surface of the sample through a grip in the aluminum tube, and the tube containing the sample was connected to a motor. Then, the assembled device was placed on the rotating stage of the X-ray equipment. The detailed description of the compression rig is given in [START_REF] Petit | Two-scale study of the fracture of an aluminum foam by X-ray tomography and finite element modeling[END_REF][START_REF] Buffiere | In Situ Experiments with X ray Tomography: an Attractive Tool for Experimental Mechanics[END_REF]. Due to the limitation of the aluminum tube size, the dimension of the foam sample for in-situ compression are 8 mm in length, 8 mm in width and 10 mm in height. The average cell diameter of the sample is about 1 mm, so there are enough cells along the compression direction. The loading rate of the compression was 0.005 mm/s, so the in-situ compression is in the quasi-static condition. The sample was scanned 19 times throughout the compression process, and the resolution of each scan was 8 μm per voxel. The compressive process was stopped during the X-ray scanning, which takes about half an hour for each scan. In order to observe the initial deformation of cells more clearly, the interval of the first 12 X-ray tomography scans was 60 s, namely the sample was compressed 0.3 mm between two scans. The interval of the subsequent 7 scans was 100 s, namely the sample was compressed 0.5 mm between two scans. After the whole compression process, the load-displacement data during X-ray scanning could be removed according to the load values. Then, the continuous load-displacement curve could be obtained.

Results and discussion

Compressive performance of dynamic gas injection aluminum foams

Fig. 2 shows quasi-static compression stress-strain curves of aluminum foams in Table 1, and the bulk aluminum foams were all prepared by the dynamic gas injection method with high-speed horizontal oscillation. The three-stage characteristics are observed in stress-strain curves of all aluminum foams especially fluctuations in the stress plateau stage. It can also be seen that the level of the plateau stress increases with decreasing porosity. The plateau stress is usually used to represent the mechanical properties of aluminum foams, and it can be increased from 0.3 MPa to 11 MPa when the porosity is reduced from 95 % to 75 %. The dot-dash line in Fig. 2 shows that the densification strain of aluminum foams roughly decreases with decreasing porosity. It is mainly because the reduced porosity leads to the increased volume fraction of the solid phase, and this causes the earlier densification stage during the compression test. Fig. 2. Stress-strain curves of aluminum foams prepared by the dynamic gas injection method Fig. 3(a) shows energy absorption-strain curves of aluminum foams with different porosities before densification stage. It can be seen that the energy absorbed by aluminum foams increases with increasing strain. The energy absorption also increases with decreasing porosity under the same strain, which is consistent with the variation of the plateau stress with porosity. Fig. 3(b) shows the variation of densification strain energy with relative density of aluminum foams. Although the densification strain decreases with the increase of relative density (i.e. the decrease of porosity), the densification strain energy increases with increasing relative density, which is mainly due to the increased plateau stress. Therefore, the aluminum foam with high relative density should be used when huge amount of energy needs to be absorbed. Variation of densification strain energy with relative density of aluminum foams Fig. 4 shows the deformation morphologies of an aluminum foam with the porosity of 85 % during compression as observed by optical macrography from the outside of the sample. Fig. 4(b),(c) and (d) show the layer by layer collapse of cells in the stress plateau stage, and the strain localization. There are some fluctuations in the plateau stage of stress-strain curves of gas injection aluminum foams, as shown in Fig. 2. The fluctuation is the sudden drop of stress caused by the sudden collapse of a certain layer of cells during compression process, which is ultimately due to the brittleness of the aluminum foam. Fig. 4(e) shows that when the compression proceeds around the densification strain, several wide cracks along the axial direction appear in the outer layer of the specimen, which are certainly caused by the brittleness of the foam. When almost all cells are compacted, some cell walls in the outer layer peel off under the influence of these cracks, as shown in Fig. 4(f).

Fig. 4. Deformation morphologies of an aluminum foam during compression

Nominal strains from (a) to (f) are 0 %, 10 %, 20 %, 40 %, 60 %, 80 % According to the previous analysis, the brittle deformation characteristics of aluminum foams prepared by the dynamic gas injection method is obvious. The brittleness is mainly caused by three factors. (1) Due to the addition of ceramic particles (Al2O3) during the preparation process, there are many ceramic particles in the cell walls of aluminum foam [START_REF] Zhou | The stability of aluminum foams at accumulation and condensation stages in gas injection foaming process[END_REF][START_REF] Wang | The cell size reduction of aluminum foam with dynamic gas injection based on the improved foamable melt[END_REF]. There are also oxide films covering the cells walls due to the effect of oxidizing gas source (air) [START_REF] Zhou | The stability of aluminum foams at accumulation and condensation stages in gas injection foaming process[END_REF]. These brittle components will cause the brittleness of cell walls. (2) A356 aluminum alloy has been used as the matrix in the preparation, and the coarse eutectic silicon phase in the alloy contributes to the brittleness of the foam [START_REF] Wang | The cell size reduction of aluminum foam with dynamic gas injection based on the improved foamable melt[END_REF][START_REF] Movahedi | The Temperature Effect on the Compressive Behavior of Closed-Cell Aluminum-Alloy Foams[END_REF]. [START_REF] Gibson | Cellular solids: structure and properties[END_REF] The thickness difference between normal cell wall and Plateau border is relatively bigger in the aluminum foams prepared by gas injection method [START_REF] Wang | Comparison of aluminium foams prepared by different methods using X-ray tomography[END_REF]. Thinner normal cell wall makes the cell easier to collapse during the compression. These three reasons cause the brittleness of gas injection aluminum foams, and then some fluctuations appear in the stress-strain curve.

Effects of preparation methods and cell structures on the compressive performance of gas injection aluminum foams

Fig. 5 shows variation of plateau stress with relative density of aluminum foams prepared by the dynamic gas injection method (GIdyn) and static gas injection method (GIsta) in compression, and some compressive results of aluminum foams prepared by static method have been published in [START_REF] Chen | Modeling of Macro-deformation Behavior of Thin-Walled Aluminum Foam by Gas Injection Method[END_REF]. The axes are scaled logarithmically in Fig. 5 for the better comparison. The application of high-speed horizontal oscillation method could reduce the cell size of aluminum foams, and significantly increase the relative density accordingly, then the mechanical properties of aluminum foams could be increased, as shown in Fig. 5. More importantly, the aluminum foam prepared by dynamic gas injection method has a higher plateau stress than that prepared by static method even at the same relative density. According to Gibson and Ashby's theory [START_REF] Gibson | Cellular solids: structure and properties[END_REF], the relation between the plateau stress and relative density of aluminum foam could be fitted with a power function [START_REF] Mccullough | Uniaxial Stress-Strain Behaviour of Aluminium Alloy Foams[END_REF][START_REF] Banhart | Deformation characteristics of metal foams[END_REF]. Eqs. ( 6) and [START_REF] Yuan | Effects of cell wall property on compressive performance of aluminum foams[END_REF] show the plateau stress-relative density fitting results of aluminum foams prepared by dynamic and static gas injection methods, respectively. It could be seen from Fig. 5 that two points with low relative density for static method do not fit well with the line. It is because cell size is usually large and uneven under low relative density condition, and more internal defects will exist on the cell walls, then the internal defects will lead to the instability of mechanical performance. Fig. 5. Variation of plateau stress with relative density of aluminum foams prepared by different gas injection methods Plateau stresses of different gas injection aluminum foams both increase with the increase of relative density. According to the fitting lines in Fig. 5, the intercept of the fitting line of GIdyn is bigger that of GIsta. Moreover, since the relative density of the aluminum foam is always less than 1, the smaller slope of the fitting line of GIdyn would also cause higher plateau stress. Therefore, the compressive performance of aluminum foams prepared the dynamic method would always higher than that prepared by static method at the same relative density. The movement state of the gas injector is nearly the only difference between the two methods in Fig. 5. It could cause different cell structures and ceramic particles distributions in cell walls, and then lead to different properties of the two kinds of aluminum foams. In terms of cell structure, aluminum foams with smaller cell size could be obtained by dynamic method at the same relative density condition, which is conductive to higher mechanical performance [START_REF] Zhang | Compressive properties of aluminum foams by gas injection method[END_REF]. In terms of performance of cell walls, the rising path of bubbles in the dynamic gas injection system would be longer compared to that in static method, then more ceramic particles probably be absorbed in the cells walls, so higher mechanical performance would be obtained. In summary, due to the better cell wall performance and smaller cell size, the aluminum foam prepared by dynamic gas injection method has better mechanical properties compared to that prepared by static method even at the same relative density.

In order to further study the influencing factors of compressive performance of aluminum foam, three samples with similar porosity (similar relative density) were selected, two were prepared by dynamic gas injection method with high-speed horizontal oscillation and one was prepared by the static method. The X-ray tomography was used to characterize the cell structure of these three samples. Table 2 shows the cell parameters of three foams, and they are named according to their preparation method. Pd is the measured porosity obtained by relative density in Eq. ( 1), PCT is the calculated porosity from 3D tomography images, and d is the average diameter of cells calculated by Fiji software in Table 2. It could be seen that Pd and PCT for the three samples are both around 85 %, their difference lays mainly in the cell size.

Quasi-static compression stress-strain curves of the three aluminum foams are shown in Fig. 6. The fluctuations in the plateau stage of the curves are obvious as expected. The plateau stresses of Dyn-1 Dyn-2 and Sta-1 are 5.1 MPa, 4.4 MPa and 2.9 MPa, as shown in Table 2. The Sta-1 aluminum foam has the lowest plateau stress and the biggest average cell size. However, the average cell size of Dyn-1 is bigger than that of Dyn-2, but Dyn-1 has the highest plateau stress. Therefore, when the porosity is similar, the mechanical performance of aluminum foams is not completely determined by the average cell size. Fig. 6. Stress-strain curves of three gas injection aluminum foams with the porosity of 85 % Fig. 7 shows distributions of equivalent diameter and sphericity of cells in the three aluminum foams illustrated in Fig. 6 and Table 2. The result was based on each individual 3D cell data obtained by Fiji software. Color of the scatter represents the number of cells with corresponding diameter and sphericity in the sample. When colors in the upper part of the color bar are mainly gathered in a certain position, it means the cell size and sphericity distributions of the foam sample are relatively uniform. Actually, the cell characterization results of the three samples have been mentioned in [START_REF] Wang | Comparison of aluminium foams prepared by different methods using X-ray tomography[END_REF], which are listed here for further comparison. It can be seen that most cells in Dyn-1 sample have a diameter of about 4 mm, and the sphericity is concentrated around 0.8. While the diameter of most cells in Dyn-2 sample is between 1.5 ~ 4.5 mm, and the sphericity is mainly distributed in the range between 0.6 ~ 0.8. Therefore, the more uniform cell size and sphericity distributions of Dyn-1 are the main reason for its higher plateau stress. However, Sta-1 sample also shows a uniform cell diameter and sphericity distributions, but its plateau stress is still lower than Dyn-1. This is related to its cell wall performance and larger average cell size caused by static preparation method mentioned previously. Fig. 7. Distributions of equivalent diameter and sphericity of cells in the three aluminum foams with a porosity around 85 %

Analysis of cell deformation by in-situ compressive test of aluminum foam

In order to study the deformation mechanism of the aluminum foam prepared by the dynamic gas injection method, a representative aluminum foam with a dimension of 8 mm × 8 mm × 10 mm was compressed assisted by in-situ observation through X-ray tomography. After obtaining the 3D cell structure of the foam sample by X-ray tomography, the equivalent parameter of every splitted cell in the foam sample could be obtained by home-made plugins in Fiji software. Fig. 8(a) shows the frequency of cell size distribution in the foam sample, and most cell diameters are concentrated in 1 ~ 1.4 mm. The average cell diameter is 1.19 mm, so the cell size of the aluminum foam is relatively uniform. The overall porosity of the sample calculated by the tomography result is 70.9 %. In order to analyze the porosity uniformity in the foam, the 3D volume is divided into a number of 8 μm thick (a voxel) slices along x, y and z directions, and Fig. 8(b) shows the calculated porosity of each slice along the three directions. It can be seen that the porosity of each slice in each direction is almost between 66 % ~ 74 %. Therefore, pores are distributed relatively evenly throughout the foam sample. When there are few structural defects in the aluminum foam, the mechanical properties of small-size and large-size samples are similar [START_REF] Jeon | The effect of structural defects on the compressive behavior of closed-cell Al foam[END_REF]. The uniform cell size and porosity distributions indicate that there are few structural defects in the aluminum foam for in-situ compression. So the mechanical performance of the small size foam (8 mm × 8 mm × 10 mm) could represent the performance of bulk foam samples. 9 shows the quasi-static stress-strain curve of the aluminum foam during in-situ compression, and the densification strain calculated by the energy absorption efficiency-strain curve is also shown in Fig. 9. The three-stage compression feature is also observed in the stress-strain curve. There are also some fluctuations in the stress plateau stage. The amplitude of the fluctuations is gradually decreasing, which is mainly because broken cell walls will enter the interior of the non-deformed cells as the compression proceeds. Table 3 lists the calculated performance parameters of the aluminum foam according to Fig. 9. The plateau stress of the gas injection aluminum foam could reach 22 MPa and the densification strain energy could reach 11 MJ/m 3 when the cell size is reduced to around 1 mm and sufficiently uniform. Compared to the best results in Fig. 2 and3, it can be seen that the mechanical performance is nearly doubled. Therefore, reducing the cell size (usually the relative density will increase accordingly) and improving its uniformity are effective ways to improve the mechanical properties of an aluminum foam. In order to study the failure mechanism of the aluminum foam in cell level, a slice which belongs to the xz plane in the middle of the y direction in the coordinate system in Fig. 10 is selected, and the cell deformation process in this slice is shown in Fig. 11. Because the cell deformation may be affected by the surrounding cells, the deformation of internal cells which are more general were chosen for study. It can be found that there are mainly two failure forms of cell walls: (2) The direct fracture of the cell walls. This failure is usually caused by the inconsistent deformation of cells on both sides of the cell wall, as described by cell walls E and F in Fig. 11. The cell walls fracture under the tensile or shear stress. Fig. 13 shows the deformation process of cell wall E, the length of which is about 0.6 mm. It can be seen that cell wall E directly fractures under the shear stress. The two main failure modes of the cell walls are relatively simple, which is also related to the brittleness of the gas injection aluminum foam. Failures of the cell walls could contribute to the energy absorption of aluminum foams. In addition, the friction between the cell walls after the cells are compacted also contributes to the energy absorption [START_REF] Mu | Deformation mechanisms of closed-cell aluminum foam in compression[END_REF][START_REF] Song | Fracture mechanisms and size effects of brittle metallic foams: In situ compression tests inside SEM[END_REF], as shown in the region G in Fig. 11.

Conclusions

1) The bulk aluminum foams prepared by the dynamic gas injection method with high-speed horizontal oscillation have the porosities of 75 % ~ 95 %, and their plateau stress is in the range of 0.3-11 MPa. The plateau stress and densification strain energy both increase with the increase of relative density (namely the decreasing of porosity). There are some serrated waves in the plateau stage of stress-strain curves, which is mainly caused by the brittleness of aluminum foams prepared by gas injection method. The ceramic particles, oxide films, coarse eutectic silicon phase in the matrix, and the relatively thin normal cell wall contribute to the brittleness of the aluminum foam.

2) The dynamic gas injection method with high-speed horizontal oscillation could greatly reduce the cell size of aluminum foams and increase the relative density, and then the mechanical properties of aluminum foams can be improved. Moreover, due to the better cell wall performance and smaller cell size, the aluminum foam prepared by the dynamic gas injection method has better mechanical properties compared to that prepared by static method even for the same relative density. For aluminum foams with the same preparation process and the similar relative density, the more uniform cell size and sphericity distributions lead to higher mechanical properties of aluminum foams. 3) When the cell size of the aluminum foam prepared by the dynamic gas injection method is reduced to around 1 mm and relatively uniform, the plateau stress of the foam could reach up to 22 MPa, and the densification strain energy could reach 11 MJ/m 3 . The results of the in-situ compressive test show that there are two main failure modes for cell walls of gas injection aluminum foams: the fracture after plastic buckling of the cell walls and the direct fracture of the cell walls.

Fig. 3 .

 3 Fig. 3. (a) Energy absorption-strain curves of aluminum foams with different porosities. (b)Variation of densification strain energy with relative density of aluminum foams

*

Fig. 8 .

 8 Fig. 8. (a) Distribution of the equivalent cell diameter of the foam sample for in-situ compression, (b) Porosity distribution of the foam sample along the three directions

Fig. 9 .

 9 Fig. 9. Stress-strain curve of the aluminum foam during in-situ compression

Fig. 10 .

 10 Fig. 10. The coordinate system used to analyze the morphology of a certain slice

Fig. 11 .

 11 Fig. 11. The cell deformation process in the slice located in the middle of the y-direction

Fig. 12 .

 12 Fig. 12. The failure mode of the cell walls with buckles first and then fracture

Fig. 13 .

 13 Fig. 13. The failure mode of the cell wall with direct fracture

Table 1

 1 Porosities of aluminum foams used for compressive test

	Foam Number	1	2	3	4	5	6	7	8	9	10
	Porosity (%)	75.9 77.8 81.0 82.1 84.3 85.3 88.8 91.7 91.9 95.0
					*
				d P	(1	) 100%
					s

Table 2

 2 Cell parameters and compressive performance of three aluminum foams with similar porosity

	Number	Preparation method	Name	Pd (%)	PCT (%)	d (mm)	σP (MPa)
	1	Dynamic gas injection	Dyn-1	84.3	85.5	3.45	5.1
	2	Dynamic gas injection	Dyn-2	85.3	84.6	2.79	4.4
	3	Static gas injection	Sta-1	85.9	85.2	4.55	2.9

Table 3

 3 The performance parameters of the aluminum foam for in-situ compression

	Parameters	Values	Parameters	Values
	Porosity (%)	70.9	Densification strain (%)	55.6
	Average cell diameter (mm)	1.19	Densification strain energy (MJ/m 3 )	11.1
	First peak stress (MPa)	21.7	Plateau stress (MPa)	21.6

Acknowledgements

This work is supported by the International Cooperation Project of Science and Technology Ministry of China (Grant no. 2013DFR50330). The authors would like to thank the Tsinghua Scholarship for Overseas Graduate Studies.


M Elody Vlieghe

Carole Coufort-Saudejaud

Christine Frances

Alain Lin
email: alain.line@insa-toulouse.fr.

In Situ Characterization of Floc Morphology by Image Analysis in a Turbulent Taylor-Couette Reactor

Keywords: flocculation, aggregate morphology, image analysis, hydrodynamics

Flocculation of bentonite was performed in a turbulent Taylor-Couette reactor under various shear rates. Image processing enabled to determine various morphological characteristics of individual flocs. Not only their mean values but also their distributions were studied under various hydrodynamic conditions. Relevant properties were selected. The temporal evolution of radius of gyration and circularity distributions was monitored during the flocculation process. Although size and shape are obviously correlated, this article points out that their dependency to hydrodynamics is different, showing that flocs of similar sizes produced under different hydrodynamic conditions exhibit different shapes. The sizes are calibrated by the turbulence as the double radius of gyration is close to Kolmogorov microscale, whereas the circularity seems correlated to the rotation speed.

Introduction

The removal of fine particles such as clay from a fluid is an essential part of water treatment. To that end, flocculation processes are used to promote the aggregation of small particles to form flocs that can be more easily removed. The neutralization of surface charges is achieved through the addition of a coagulant and mixing the suspension is required to ensure that the particles encounter one another. The influence of the average shear rate on mean floc size has been widely investigated [START_REF] Spicer | Coagulation and fragmentation: the variation of shear rate and the time lag for attainment of steady state[END_REF][START_REF] Serra | Effect of the shear and volume fraction on the aggregation and breakup of particles[END_REF][START_REF] Biggs | Activated sludge flocculation: on-line determination of floc size and the effect of shear[END_REF][START_REF] Bouyer | Experimental analysis of floc size distributions in a 1-L jar under different hydrodynamics and physicochemical conditions[END_REF] and it is shown that higher shear rates may lead to smaller flocs. Besides, the flow in a mixing tank is highly heterogeneous so the aggregates are subjected to fluctuating stresses during the process that influ-ence significantly the aggregate size distribution. [START_REF] Selomulya | Aggregate properties in relation to aggregation conditions under various applied shear environments[END_REF][START_REF] Coufort | Flocculation related to local hydrodynamics in a Taylor-Couette reactor and in a jar[END_REF][START_REF] Marchisio | Role of turbulent shear rate distribution in aggregation and breakage processes[END_REF][START_REF] Prat | Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics[END_REF] Eventually the floc population at the end of a flocculation process is a result of aggregation and breakup events from which the aggregates may undergo structural changes. [START_REF] Oles | Shear-induced aggregation and breakup of polystyrene latex particles[END_REF] The cohesion of flocs, closely related to their structure, affects their ability to settle down, which is important to ensure a correct separation after the flocculation step, usually performed by sedimentation or filtration. Floc interactions with hydrodynamics are highly affected by porosity, [START_REF] Adler | Streamlines in and around porous particles[END_REF][START_REF] Gmachowski | Aggregate structure and hydrodynamics of aggregated systems[END_REF][START_REF] B€ Abler | Hydrodynamic interactions and orthokinetic collisions of porous aggregates in the Stokes regime[END_REF] therefore, aggregation kinetics is influenced by aggregate structure in terms of collision frequency and efficiency, [START_REF] Kusters | Aggregation kinetics of small particles in agitated vessels[END_REF][START_REF] Sato | Adachi Effect of floc structure on the rate of shear coagulation[END_REF] as well as aggregate breakup. [START_REF] Franc | Strength of aluminium hydroxide flocs[END_REF] Structural changes were shown to occur in flocculation experiments where a first quick growth of floc size was followed by a slow and sometimes subtle decrease to finally reach a steady state (SS). 16- 18 It can be explained by the fact that when flocs become large enough they get subjected to restructuring or breakup, the resulting fragments can aggregate to form denser, thus smaller flocs. This explanation is confirmed by breakup and regrowth experiments. [START_REF] Barbot | Coagulation of bentonite suspension by polyelectrolytes or ferric chloride: floc breakage and reformation[END_REF] However, floc structure observation and quantification is not trivial.

The work of Spicer et al. [START_REF] Spicer | Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks[END_REF] was one of the first studies that analyzed the change of aggregate size and also morphology (as a perimeter-based fractal dimension) during the flocculation of polystyrene particles. They observed a strong dependency of the size and of the fractal dimension to the average shear rate. They found that the porosity first increased during a phase of floc growth, and then decreased as the breakup occurred and the mean size was stabilized. Li et al. [START_REF] Li | The strength and fractal dimension characteristics of alum-kaolin flocs[END_REF] performed flocculation experiments of kaolin with aluminum sulfate under various shear rates in a jar test. They found a very strong correlation between floc characteristics in terms of size, two-dimensional (2-D) fractal dimension, and floc strength (smaller flocs were stronger and denser), all being influenced by the shear rate (the higher the shear rate, the smaller, stronger, and denser the aggregates).

As mentioned above, the floc structure or shape is usually characterized by a fractal dimension. Several definitions for the fractal dimension are found in the literature. They generally take the form of a power law equation Y1X D , where X is a length scale (characteristic radius or perimeter), Y is a higher order dimension (area or volume, equivalently mass or number of primary particles), and D is the fractal dimension or a simple function of the fractal dimension. Under certain conditions, an average mass fractal dimension can be identified from the scattering exponent obtained from light scattering analysis. [START_REF] Sorensen | Light scattering by fractal aggregates: a review[END_REF] This experimental method is intrusive because of sampling, although it can be performed online with a recycling loop [START_REF] Yu | Flocculation of kaolin particles by two typical polyelectrolytes: a comparative study on the kinetics and floc structures[END_REF][START_REF] Soos | Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank[END_REF][START_REF] Harshe | Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates[END_REF] with a risk of flow perturbations and thus floc modifications. [START_REF] Barbot | Coagulation of bentonite suspension by polyelectrolytes or ferric chloride: floc breakage and reformation[END_REF] Another approach to floc characterization is image analysis. Many studies used ex situ destructive methods such as transmission electron microscopy, [START_REF] K€ Oyl€ U | Fractal and projected structure properties of soot aggregates[END_REF] confocal laser scanning microscopy, [START_REF] Soos | Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank[END_REF][START_REF] Harshe | Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates[END_REF][START_REF] Ehrl | Dependence of aggregate strength, structure, and light scattering properties on primary particle size under turbulent conditions in stirred tank[END_REF][START_REF] Thill | Determination of structure of aggregates by confocal scanning laser microscopy[END_REF] or sample analyses coupling a microscope and a CCD camera. [START_REF] Spicer | Coagulation and fragmentation: the variation of shear rate and the time lag for attainment of steady state[END_REF][START_REF] Li | The strength and fractal dimension characteristics of alum-kaolin flocs[END_REF][START_REF] Tang | Fractal morphology and breakage of DLCA and RLCA Aggregates[END_REF][START_REF] Schuetz | A model of the coagulation process with solid particles and flocs in a turbulent flow[END_REF][START_REF] Vahedi | Application of fractal dimensions to study the structure of flocs formed in lime softening process[END_REF] Sometimes an advanced sample preparation is implemented to handle fragile flocs. However, to avoid any risk of aggregate alteration due to sample manipulation or flow modification, in situ measurement methods based on advanced imaging techniques were developed. [START_REF] Chakraborti | Characterization of alum floc by image analysis[END_REF][START_REF] Tolpekin | Aggregation and breakup of colloidal particle aggregates in shear flow, studied with video microscopy[END_REF][START_REF] Rahmani | Evolution of asphaltene floc size distribution in organic solvents under shear[END_REF][START_REF] Nan | Characteristic analysis on morphological evolution of suspended particles in water during dynamic flocculation process[END_REF] In the past decades, some studies used laser sheet lighting. [START_REF] Bouyer | Experimental analysis of floc size distribution and hydrodynamics in a jar-test[END_REF][START_REF] Kilander | Spatial and temporal evolution of floc size distribution in a stirred square tank investigated using PIV and image analysis[END_REF][START_REF] Frappier | Floc cohesive force in reversible aggregation: a Couette laminar flow investigation[END_REF][START_REF] Xiao | PIV characterisation of flocculation dynamics and floc structure in water treatment[END_REF][START_REF] Bubakova | Effect of shear rate on aggregate size and structure in the process of aggregation and at steady state[END_REF] An important feature of these systems is the possibility to acquire a large number of images, besides the images have very few out-of-focus objects that are easily removed during image binarization.

Again, among these studies, those working on aggregate morphology measured average fractal dimensions obtained by correlating aggregate projected area to perimeter (perimeter-based fractal dimension) or characteristic length (2-D fractal dimension). As a matter of fact a large majority of flocculation experiments are restricted to average fractal dimension characterization, failing to represent the morphological diversity within a floc population. Measuring individual morphological properties would make it possible to calculate distributions to better observe and comprehend the mutual influences of aggregate size, aggregate shape, and the surrounding hydrodynamics, and to further describe their evolution through population balance modeling. Some authors studied individual aspect ratios of latex aggregates under various turbulent conditions [START_REF] Soos | Effect of shear rate on aggregate size and morphology investigated under turbulent conditions in stirred tank[END_REF][START_REF] Ehrl | Effect of flow field heterogeneity in coagulators on aggregate size and structure[END_REF] and found that aspect ratio distributions were hardly influenced by the amount of shear or the difference of flow heterogeneities produced by a Taylor-Couette device and a stirred tank. In the past, Gorc-zyca et al. [START_REF] Gorczyca | Image Analysis of alum coagulated mineral suspensions[END_REF] measured distributions of a shape factor of various mineral flocs. They obtained different distributions, well fitted by log-normal laws with large standard deviations. Recently, morphological image analyses have been run in various application fields such as activated sludge, [START_REF] Mesquita | Monitoring of activated sludge settling ability through image analysis: validation on full-scale wastewater treatment plants[END_REF] nanomaterial aggregates, [START_REF] De Temmerman | Quantitative characterization of agglomerates and aggregates of pyrogenic and precipitated amorphous silica nanomaterials by transmission electron microscopy[END_REF] or earthworm casts. [START_REF] Bottinelli | Morphological characterisation of weathered earthworm casts by 2D-image analysis[END_REF] These authors studied a large panel of morphological properties of individual objects and classified these properties according to their ability to describe the system and its different characteristic scales.

This work presents experimental data on bentonite flocculation in a Taylor-Couette reactor under controlled turbulent hydrodynamic conditions. To create large and fragile flocs that can be influenced by hydrodynamic stresses, coagulation by charge neutralization was promoted. To generate hydrodynamic stresses that can interact with flocs, varying operating conditions were chosen in a turbulent regime. The distributions of both size and shape parameters describing floc structure over time is of great importance since posttreatment separation efficiency strongly depends on aggregate size and shape. In the present work, an in situ nonintrusive method was developed to determine floc characteristics under various shear rates. High resolution images of flocs were acquired with a CCD camera in a plane illumated by a laser sheet. Images were analyzed to compute accurate size and shape properties of individual aggregates and their distributions. Average values as well as higher order moments can be derived from these distributions. The flocculation system was monitored during the process until a SS was reached. This work provides an experimental database for understanding and modeling aggregation and breakage phenomena under turbulent conditions. The objectives of the present article are to give a nonexhaustive overview of the variety of morphological floc characteristics that can be obtained by image analysis, to select relevant properties describing the morphological diversity of the floc population involved in this study, and eventually to analyze this diversity with respect to varying hydrodynamic conditions.

Experimental Setup

Materials and device

Bentonite from CECA Chemicals was used for the experiments. The properties of this particular type of clay were well described by Luckham and Rossi. [START_REF] Luckham | The colloidal and rheological properties of bentonite suspensions[END_REF] The dry primary particles measured by laser diffraction granulometry (Master-Sizer2000, Malvern Instruments) have a volume mean diameter of 5 mm. Due to its swelling properties, a 200-mL suspension containing the appropriate quantity to reach the desired mass concentration in the reactor (30 mg L 21 ) was prepared several days before the experiment.

Aluminum sulfate, which is commonly used in water treatment was chosen as a coagulant. To avoid uncertainties due to small quantity measurements, a large volume of solution was prepared in advance, at a concentration determined to obtain a concentration after dilution equal to 3.5 3 10 25 mol L 21 . For each experiment, 5 mL of this solution were sampled with a volumetric pipette, ensuring a constant quality over the experiments. The pH of the suspension after the addition of aluminum sulfate was equal to 4:560:1. Considering the equilibrium constant [START_REF] Duan | Coagulation by hydrolysing metal salts[END_REF] pK Al 31 =AlðOHÞ 21 54:95, the dominant form of aluminum at this pH value is Al [START_REF] Chakraborti | Characterization of alum floc by image analysis[END_REF] , which is favorable for coagulation by charge neutralization.

All the experiments were carried out with demineralized water stored in a large (50-L) tank to keep a constant quality and to avoid bubble formation during the experiments. Experiments were done at room temperature, ranging between 20 and 25 C.

The experiments were performed within a Taylor-Couette apparatus (see Figure 1) composed of an inner cylinder of 10 cm in radius (R 1 ) made of black PVC and an outer cylinder of 11.5 cm in radius (R 2 ) made of transparent plexiglas. The height of the cylinders is H 5 20 cm and the reactor volume is 2 L. The outer cylinder is fixed while the inner one rotates at an adjustable speed N. Hydrodynamics in this reactor were characterized in a previous work [START_REF] Coufort | Flocculation related to local hydrodynamics in a Taylor-Couette reactor and in a jar[END_REF] by particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. The hydrodynamic regime in the Taylor-Couette reactor is characterized by the Taylor number defined as

Ta5 X 2 R 1 R 2 2R 1 ð Þ 3 t 2 (1)
where X (s 21 ) is the angular velocity of the inner cylinder and t (m 2 s 21 ) is the kinematic viscosity of the fluid.

Experimental protocol

Before starting an experiment, the primary suspension was vigorously agitated with a magnetic stirrer during 45 min to break any aggregate formed during the swelling period. Water was poured into the Taylor-Couette vessel and the rotation speed was set to 100 rpm before adding the bentonite suspension. The quick addition of aluminum sulfate was immediately followed by a 3-min phase of aggregation at a high rotation speed (100 rpm). The global shear rate was then equal to 325 s 21 . This short period, assimilated to a coagulation phase, participated to create identical initial conditions before the rotation speed of the inner cylinder was set to the desired value. Aggregation was then carried out at 30, 50, 70, or 90 rpm providing global average shear rate values of 75, 130, 190 or 280 s [START_REF] Sorensen | Light scattering by fractal aggregates: a review[END_REF] , respectively, and Taylor number values of 3:3310 6 ; 9:3310 6 ; 1:8310 [START_REF] Marchisio | Role of turbulent shear rate distribution in aggregation and breakage processes[END_REF] , and 3:0310 [START_REF] Marchisio | Role of turbulent shear rate distribution in aggregation and breakage processes[END_REF] , respectively. The observed hydrodynamic regime corresponds to turbulent Taylor vortex flow.

Image acquisition

Aggregation was monitored by taking floc pictures. A laser sheet (Nd:Yag 532 nm, 30 mJ) was used to illuminate a tangential plane in the gap between the cylinders as shown on Figure 1. A CCD camera (FlowSense EO 16M, 48723 3248 pixels 2 ), synchronized with the laser sheet, acquired grayscale floc pictures with a spatial resolution of 7.3 mm/ pixel. Pictures were taken at a frequency of 4 Hz (low enough to avoid any risk of accounting for the same aggregate on two consecutive pictures). Each acquisition consisted of taking 70 pictures, so the instantaneous results were averaged over 18 s. The time value of a measurement was recorded as the first image was acquired. The acquisition frequency was then limited by the recording time after each acquisition. Thus, the shortest possible time between each measurement was about 2 min. To reduce the amount of data stored this time was extended as the flocculation proceeded.

To quantify floc size and morphology, the image quality is of high importance. Thus, the refraction through the outer cylinder walls was an issue that needed to be treated with care. For this purpose, the Taylor-Couette apparatus was enclosed within a cubical box made of Plexiglas (as is the outer cylinder) and filled with glycerol. Indeed, the refractive index of glycerol (1.47) is close to the refractive index of Plexiglas (1.51), considerably reducing the refraction effect. Besides, the camera was placed so that the optical axis was as perpendicular as feasible to all the interfaces, and positioned so that the length of the image (39 mm) was vertical and the width (26 mm) was horizontal, to minimize the angles of the curved interface.

Image Analysis Protocol Image treatment

To detect and isolate the image regions where the flocs appear, image binarization was performed by applying a gray level threshold. The efforts made to obtain high quality images aimed in particular at reducing as much as possible the need for image treatment. As an example, a 2703180 pixels 2 portion of a raw image is shown on Figure 2a. However, applying a threshold on raw images would produce artificial holes and surface irregularities on the aggregates (see Figure 2b) because the intrinsic heterogeneity of bentonite resulted in a great irregularity of gray levels on the floc images. Thus a circular averaging filter of 1 pixel radius was applied to the raw images (Figure 2a) to slightly smooth these fake irregularities. The effect of this smoothing is shown on Figure 2c. The gray level threshold was then [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] determined by applying Otsu's method [START_REF] Otsu | Threshold selection method from gray-level histograms[END_REF] on each image with the Matlab function graythresh. The principle of this method is to maximize the separability of the classes by optimizing the between-class variance. The resulting binarized image is shown on Figure 2d.

Particle image analysis

Binarized images were analyzed using a Matlab function named regionprops. The outputs directly computed by regionprops are listed in Table 1. However, the estimation of the perimeter has been improved and other characteristic properties have been introduced.

Perimeter. The perimeter value provided by regionprops function measures the cumulated distance between the centers of the pixels belonging to the region and lying on its boundary. This calculation underestimates the aggregate perimeter. It is accurate enough if the region is composed of a great number of pixels, but it can be an issue if aggregates are composed of only a few dozens of pixels. As an example, the perimeter of a square made of 10310 pixels 2 will be estimated as 36 pixels instead of 40, that is, a 10% error. To compensate for this drawback, another estimated perimeter was calculated by building an enlarged region composed by the initial region plus the surrounding pixels, and computing an overestimated perimeter by applying the function regionprops to the enlarged region. Eventually, the perimeter P was estimated as the average of the underestimated and overestimated perimeters.

Radius of gyration. The radius of gyration R g is a characteristic length scale of the (projected) particle that takes into account pixel positions with respect to the centroid. In mechanics, it is defined as the distance to an axis where all the object mass would be concentrated and rotate with the same mass moment of inertia. It can be obtained from the root mean square of the pixel-to-centroid distances

R 2 g 5 1 N p X Np i51 ðx i 2x c Þ 2 1ðy i 2y c Þ 2 h i (2)
where N p denotes the number of pixels on the aggregate, (x i ,y i ) are pixel coordinates, and (x c ,y c ) are centroid coordinates.

Circularity and convexity. To quantify the shape of an aggregate, one can consider several scales and focus on either the overall shape, the presence of concavities, or the surface roughness. Small scale irregularities can have a major impact on the perimeter without significant changes on the area, so parameters involving the aggregate perimeter generally focus more on surface roughness than parameters involving the aggregate area which rather characterize the overall shape. As a complement to the morphological parameters directly provided by Matlab (Table 1), two parameters defined as perimeter ratios were calculated.

The convexity Cv is defined as the ratio of the convex hull perimeter P CH (see Table 1) over the actual perimeter (Eq. 3). As its name suggests, it quantifies how convex the floc image is, that is, it accounts for concavities and boundary roughness (the convexity of a circle as well as of a square is 1). Compared to the solidity defined with area ratio instead of perimeter ratio (see Table 1), the convexity definition focuses more on the surface aspect than on the space distribution of mass Cv 5

P CH P (3)
The circularity Ci is defined as the circle equivalent perimeter divided by the actual perimeter (Eq. 4). It describes how close to a circle the aggregate image is, taking into account the overall shape as well as the boundary roughness (the circularity of a circle is 1, the one of a square is 0.886)

Values of circularity and convexity range between 0 and 1. In practice, values up to 1.1 are obtained for small aggregates because of the lack of accuracy of the perimeter estimation. Without the improvement explained above, values greater than 2 would be obtained.

Image analysis validation

The aim of this work was to provide an experimental database for understanding and modeling aggregation and breakage phenomena under turbulent conditions. It was necessary to acquire a high enough number of flocs (hence of images) to provide accurate data, not only in terms of mean values but also in terms of higher order moments of the measured distributions. The k th order moment of the distribution n(X) is defined and computed as in Eq. 5. The aggregates are first distributed in classes according to the property X taking a finite number of values X i . Y i is the amount (surface fraction, in the case of a surface distribution) of aggregates belonging to the class

X i ; X i11 ½ m k 5 ð 1 0 ðXÞX k dX5n X i ð X i11 Xi nðXÞX k dX X i Y i X k11 i11 2X k11 i À Á k11 ð Þ X i11 2X i ð Þ (5)
Moreover, the acquisition frequency of 4 Hz limited the time resolution. A compromise was made considering 70 images per acquisition, implying an acquisition time of 18 s, meaning that the measured properties are averaged over 18 s, which is small compared to the time scale of the flocculation process (3-4 h). Figure 3 shows the moments of the surface distributions of floc area vs. the number of analyzed images, as well as the corresponding number of flocs. For the sake of readability, the moments are normalized as

m k =m k 1 .
With 70 images, that is, 1.5 3 10 5 flocs, the convergence is satisfactory. Note that better convergence results are obtained on area distributions at lower shear rates, as well as on perimeter distributions, and on area and perimeter number distributions.

To verify the experimental repeatability, the same experiment was carried out twice at each rotation speed. The area and perimeter distributions obtained at SS are shown, respectively, on Figures 4a and4b, since these two parameters are the main basic data from which other relevant properties are derived. The repeatability is good although not perfect, especially concerning the area distribution at the lowest shear rate. According to [19], the experimental protocol consisting in injecting the coagulant after the suspension setting up could lead to reproducibility issues. Besides, the setting up of the initial condition is a delicate and determining step, which is confirmed by the fact that the slight gap between the two distributions obtained at 75 s 21 appeared from the first measurements (so it can be attributed to initial condition fluctuations). However, the similarity of the distributions shown on Figure 4 is fully satisfactory, as are the time evolutions.

Results and Discussion

The results are presented as surface distributions rather than number distributions which attach a relative importance to the smallest aggregates, which constitute a small amount of the overall mass and are less accurately characterized by our imaging system. To ensure a relevant morphological characterization, only aggregate images composed of 10 pixels or more were taken into account, thus the smallest aggregates analyzed have a CED of 26 mm, the minimum R g and L detected are, respectively, 9 and 28 mm. These aggregates are composed of very few primary particles and will be named primary aggregates.

Change of the mean floc characteristics

As suggested by Figure 4, the surface distributions of the floc properties remain monomodal all along the experiments. Therefore, the time evolution of the mean values of the floc characteristics was first considered. The time reference is the change from 100 rpm to the desired rotation speed. One can distinguish between properties characterizing either size or shape.

Size properties. The changes of the mean values of the circle equivalent diameter CED, the radius of gyration R g , and the major axis length L vs. time are reported on Figure 5. To be compared with the other two lengths, twice the radius of gyration is reported (see Figure 5c).

These characteristic length scales tend to higher values when the shear rate is lower. Moreover, they evolve in very similar ways. Whatever the shear rate, the sizes tend to grow during the first minutes and then slowly decrease in time because of breakage and restructuring. After 3-4 h, a SS is reached for all the experiments. At the highest shear rate, one cannot distinguish a growth phase but only a decrease. The extent of the restructuring phenomenon can be com-pared by dividing the maximum size measured, defining the point of maximum growth (MG) referred to below, by the size reached at the SS (similarly to what was done by Franc ¸ois [START_REF] Franc | Strength of aluminium hydroxide flocs[END_REF] concerning floc strength and breakage experiments). The maximum size measured is thus an estimation of the maximum size reached. The ratio of the SS size over the maximum size (either CED, R g , or L) is about 70% and does not depend on the average shear rate.

These three length scales evolve very similarly. Another view of the results is proposed on Figure 6, where the mean length scales at SS are plotted vs. the corresponding mean perimeters. The various length scales P, CED, L, and R g are obviously related to each other, suggesting that studying only one of them would provide sufficient information about the size evolution. The choice of a relevant size property will be presented below. If the projected images of the aggregates were disks, the following two equations would be verified: CED 5 L and 2R g 5CED = ffiffi ffi 2 p

. Here L mean is generally much higher than CED mean , and 2R gmean is very close to CED mean . This is a first evidence that the shapes are not circular, thus the aggregates are not spherical. The analysis of shape properties is thus relevant.

Shape properties.

As mentioned in the introduction of this article, the floc shape is often characterized by a fractal dimension. The information provided by the image analysis allows calculating a 2-D fractal dimension Df defined by the relation A / L Df . This 2-D fractal dimension would be equal to 2 in the case of a circle. Df is obtained by performing a linear regression on the scatter graph obtained by plotting log(A) vs. log(L). The result is an average fractal dimension that characterizes the entire floc population and that can be computed at each time. Note that, contrary to the shape properties defined above, which were measured on flocs composed of more than 10 pixels, Df was determined on a scatter graph containing the data for all the flocs. Indeed, applying a filter on the size would come down to cutting out a part of the scatter graph following a straight line, thus biasing the result of the linear regression. The values obtained were all close to Df 5 1.8 and did not vary with time nor with the hydrodynamic conditions. Therefore, the information provided by this result remains global and seems to be weakly discriminant.

The change of the mean values of the shape properties aspect ratio AR, solidity S, convexity Cv, and circularity Ci vs. time are shown on Figure 7. The aspect ratio (7a) and the solidity (7b) do not seem to be correlated with the shear conditions. The values of AR mean and S mean increase at the beginning of the experiments, especially at the lower shear rate and become constant after 1 h, while the sizes are still increasing. The values of AR mean are all about 0.65. As previously observed by Ehrl et al., [START_REF] Ehrl | Effect of flow field heterogeneity in coagulators on aggregate size and structure[END_REF] the global shape is not much affected by hydrodynamics and the aspect ratio is probably not relevant enough to discriminate between different morphologies. One can notice that an ellipse having a ratio of minor axis length over major axis length equal to 0.65 would verify 2R g 50:6L, which is consistent with the values of R gmean and L mean obtained (Figures 5c and5a). The values of S mean lie between 0.8 and 0.85. The convex area and the actual area are close, indicating the absence of large concavities. AR and S both characterize floc shape at large scales. They both increase only at the early stage of floc growth. A possible explanation is that the first flocs, composed of very few primary aggregates, are more likely to present elongated or curved shapes with relatively low AR and S. After a short time, flocs are composed of higher numbers of primary aggregates that allow less elongated shapes to be formed and large concavities to disappear. On the opposite, the convexity (7c) and the circularity (7d) evolve as long as the sizes do. First a decrease occurs, in a period concomitant with the growth phase observed on Figure 5. Then Cv mean and Ci mean increase and eventually stabilize. Their evolution is in concordance with the size evolution, confirming the change of floc structure during the flocculation. First, the growth phase produces coarse flocs with irregular shapes, then the restructuring occurs and the shapes become smoother and rounder. At any time, Cv mean and Ci mean values are lower at lower shear rates, indicating a strong correlation of the floc shape with hydrodynamics. However, since the floc sizes are also strongly depending on hydrodynamics, the question of size-independent effects of hydrodynamics on the floc shape is still open at this point.

On Figure 8, the mean shape properties at SS are plotted vs.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4pA mean p =P mean . As expected from the previous obser-vations, the aspect ratio and the solidity do not vary significantly. On the contrary, it is interesting to see that the convexity and the circularity follow exactly the same trend. These properties both characterize floc shape at smaller scales (in comparison with AR and S). The convexity compares the convex perimeter to the actual perimeter of the projected floc image, so it characterizes the roughness of the floc surface. The circularity compares the circle equivalent perimeter to the actual perimeter so it characterizes both the overall shape and the surface roughness. Given that the overall shape (AR) has been shown not to change significantly, in this case Cv and Ci account for similar shape characteristics. Furthermore, the parameter ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4pA mean p =P mean is expressed as a circularity involving mean area and mean perimeter. It can be seen that decreasing the rotation speed, the mean circularity points deviate from the first bisector, indicating that the population of flocs present a larger variety of shapes.

Time evolution of R g and Ci distributions

To move further on the result analysis, the next part will focus on the floc property distributions. To that end, it is convenient to reduce the number of properties of interest. An overview of the various properties showed that some of them provide redundant information, whereas some properties seem less relevant than others. To properly choose one size variable and one shape variable to monitor, principal component analysis (PCA) was used (see Appendix A). The PCA performed over all aggregate properties confirmed that it is relevant to distinguish between size properties and shape properties. For this reason, PCA was then performed over two groups thus defined. The radius of gyration was selected as a relevant size property and the circularity was selected as a relevant shape property.

On the following, the results are thus discussed on the base of the radius of gyration and circularity, which were shown sufficient to describe the system.

The time evolutions of R g (resp. Ci) distributions obtained under four different turbulent regimes are plotted on Figure 9 (resp. 10). On each graph, the initial distribution is the one obtained after a period of 3 min during which the rotation speed was equal to 100 rpm and the global shear rate was Focusing first on the initial population, the high-shear mixing phase produced a population of aggregates having radius of gyration spread between 10 and 200 mm, the smallest sizes belonging to primary aggregates composed of very few particles. The initial circularity distribution ranges between 0.35 and 0.95, indicating that the initial agglomerates have various nonspherical shapes.

At 75 s 21 (30 rpm), the growth phase produced a wide distribution of R g (Figure 9a). Large flocs are formed and the small sizes that were largely represented on the initial distribution practically disappear, resulting in a positive and relatively high value of the skewness. The large excess kurtosis indicates that the peak value is largely represented but so are the extreme values. During a second phase, the R g distribution slowly translates backward. The largest flocs formed during the growth phase disappear but the small aggregates do not reappear, indicating floc restructuring. The distribution gets sharper with lower standard deviation, skewness, and kurtosis. At higher shear rates (Figures 9b-d), a clear difference in the evolution of the radius of gyration distribution is noticed. The smallest population of aggregates is always present, either because they do not aggregate, or because of floc breakage. This is characterized by lower values of the positive skewness. Still, a quick growth occurs but it is less significant as the shear rate increases, to the advantage of breakage and restructuring phenomena, to such an extent that the highest shear rate produces a floc population much smaller than the initial one. The absolute values of the standard deviation decrease when the shear rate increases but the normalized values are all comparable (the shapes of the distributions are similar around different mean values), with values slightly decreasing between the growth phase and the SS.

Regarding the circularity distributions (Figure 10), two different distribution shapes are observed after the growth phases at the two lowest shear rates and the two highest. The distributions after the growth phases at 75 and 130 s 21 are close to symmetrical (low skewness in Table 2) and exhibit wide peaks and thin tails, as indicated by the large values of negative excess kurtosis in Table 2. At 75 s 21 , the growth phase produced a population of less circular flocs, with large circularity values (above 0.85) vanishing, corroborating the assumption that the highest circularity values belong to the smallest aggregates.

At higher shear rates (Figures 10c,d), the circularity distributions after the growth phase are less wide, asymmetric (relatively large negative values of the skewness in Table 2) and the peaks are sharper (lower values of excess kurtosis in Table 2).

During the breakage and restructuring phase, the same trend is observed at all the shear rates. The left tails of the distributions are shifted to the right, that is, the lowest nonempty class becomes empty, while the right tail fills up, that is, the highest nonempty class remains the same and is more represented. This produces asymmetric SS distributions with increased values of negative skewnesses (Table 2).

Whatever the shear rate, the growth phase produces a large variety of floc sizes and shapes (the lower the shear rate, the larger the distribution). The longest phase is constituted by a slow and smooth decrease in size together with an increase in Ci values, indicating restructuring. Only the lower SS allowed to flocculate practically all the smallest aggregates (remind that particles composed of less than 10 pixels are not considered and that the surface distributions naturally attribute less importance to the smallest aggregates) while they remain largely represented at the higher shear rates.

Influence of hydrodynamics

To clarify and quantify the influence of hydrodynamics on the radius of gyration and the aggregate circularity, the mean values obtained at the SS were represented on Figure 11. The final mean values of R g are compared with Kolmogorov microscale g on Figure 11a, whereas the final mean values of Ci are plotted vs. the rotation speed N. The g values used on Figure 11a are modes (which have a more physical sense than mean values) of g distributions. [START_REF] Coufort | Flocculation related to local hydrodynamics in a Taylor-Couette reactor and in a jar[END_REF] It is clear from Figure 11a that the sizes (especially the largest sizes, since surface distributions are considered) are calibrated by the microscales of turbulence, while the circularity (11b) evolves linearly with the rotation speed of the inner cylinder. Thus, both size and shape are strongly affected by hydrodynamics, but through different flow characteristics.

Furthermore, a fraction of the SS floc population obtained at G 5 75 s [START_REF] Sorensen | Light scattering by fractal aggregates: a review[END_REF] was selected with the criterion R g < 100 mm. The size distribution of these small flocs formed at 75 s 21 is comparable to the one obtained at 280 s 21 , so if the circularity was only correlated to the size, the Ci distribution of the small flocs formed at 75 s 21 would also be comparable to the one obtained at 280 s 21 . Figure 12 compares the circularity distribution of this fraction of small flocs formed at 75 s 21 to the ones obtained for the entire population at 75 and 280 s 21 . It is clear that the Ci distribution of small flocs formed at 75 s 21 is very different from the ones obtained at 280 s 21 . Flocs of comparable sizes formed under different shear rates exhibit dissimilar circularity distributions. Moreover, the Ci distribution of small flocs formed at 75 s 21 overlaps the ones obtained for the entire population formed at 75 s 21 , except for some high values slightly more represented in the case of the small flocs. The morphological diversity observed for the entire population is just as well represented by the smallest flocs. It means that the observed difference in aggregate circularity distributions obtained under different hydrodynamic conditions is not only due to different sizes. Hydrodynamics indeed has a size-independent influence on floc shape.

Conclusions

Bentonite flocculation experiments were performed under four turbulent conditions in a Taylor-Couette reactor to study floc size and morphology. High resolution images were acquired in a plane illuminated by a laser sheet, to precisely characterize the variety of floc sizes and shapes. For each measurement, a large number of images (70) were analyzed to provide converged distributions of floc properties. The flocculation was monitored at the highest feasible frequency (every few minutes) over a long enough period of time (3-4 h) to reach a SS. It was shown that the various size properties are correlated despite the shape diversity. On the opposite, different shape properties characterize different scales of floc morphology and not all of them are discriminant. In this particular system, the overall shape was not relevant to describe the flocs. The circularity was chosen to be studied. This shape property accounts for the overall shape of a floc as well as the roughness of its boundary. During the flocculation, two phases could be detected: a first rapid phase of growth during which the size increases and the circularity decreases (the higher the shear rate, the stronger this trend), and a second slow phase, usually interpreted as breakage and restructuring, during which the size decreases and the circularity increases. The surface distributions of radius of gyration and circularity were analyzed at the end of the growth phase and at the SS. The parallel evolution of the shape of the distributions showed that high values of circularity are due to small flocs and low values of circularity are related to the presence of large flocs. However, the SS mean values of R g and Ci are not related to the same hydrodynamic characteristics. The sizes are calibrated by the turbulence as double the radius of gyration is close to Kolmogorov microscale, whereas the circularity seems correlated to the rotation speed. This database will be used to develop population balance modeling.

Literature Cited

Appendix: Principal component analysis applied to floc morphological properties PCA was performed on the floc properties. The standardized data set was arranged in a matrix M of size N3p where N is the number of measured variables and p is the number of flocs (in one set of 70 images). The correlation matrix is computed as R51=NM T M. Its eigenvalues are the principal components (PC) and the associated eigenvectors are the coordinates in the space of the original variables. The correlation coefficient of the ith PC and the jth variable is defined by Eq. A1, where V i is the ith eigenvector. A graphical interpretation of the PC is obtained by plotting the circle of correlation, where the abscissa and ordinate of each point are the correlation coefficients between one aggregate property and, respectively, the first and the second PC

rðPC i ; jÞ5 ffiffiffiffiffiffiffi ffi PC i p V i ðjÞ (A1)
The PCA was performed on several dataset obtained at different times under different shear rates and the trend was always the same. One example is illustrated on the following. The results of the PCA performed on the floc properties area (A), perimeter (P), circle equivalent diameter (CED), major axis (L), radius of gyration (R g ), aspect ratio (AR), solidity (S), circularity (Ci), and convexity (Cv) are summarized on Figure A1. The cumulated variance plotted on Figure A1a shows that the first two PC contain 90% of the system variance. The circle of correlation for the first two PC is plotted on Figure A1b. Two groups of measured variables are clearly identified. On the one hand, the length scales CED, L and R g gather together with the two basic measured properties P and A to from the group of size properties.

In particular, the points representing the three length scales CED, L, and R g are extremely close to the perimeter point, meaning that these measured variables are strongly correlated; conversely, are the shape properties AR, S, Ci, and Cv. The aspect ratio AR is isolated and it could be regarded as not included in the group.

To select one property from each of the two groups thus defined, PCA was performed on each one of them. Figure A2 shows the PCA results on the size properties. According to Figure A2a, the first PC represents close to 97% of the variance contained in the group of size properties. Figure A2a confirms that the length scales are strongly correlated. Depending on the dataset studied, P or R g is the property the most correlated to the first PC. Since it is more convenient to work with a characteristic size, in the generally accepted sense, than with a perimeter, the radius of gyration is chosen as a characteristic length scale to be used in the description of the floc population (CED and L would also be appropriate because of almost equally high correlation coefficients). Among the shape group, Figure A3 shows that the first PC represents 73% of the variance. On Figure A3b, AR is isolated from S, Ci, and Cv. Ci is the property the most related to the first PC. For this reason, we propose the circularity as a relevant shape property to be studied.

Manuscript received Dec. 9, 2013, and revision received Jan. 31, 2014.

Figure 1 .

 1 Figure 1. Experimental setup.

Figure 2 .

 2 Figure 2. Image processing.

Figure 3 .

 3 Figure 3. Area distribution normalized moments and number of flocs analyzed vs. the number of images.

Figure 4 .

 4 Figure 4. Steady state (SS) surface distributions of aggregate area obtained for eight experiments at fourfour different shear rates.

Figure 5 .

 5 Figure 5. Mean values of size properties vs. time.

Figure 6 .

 6 Figure 6. Comparison of the SS mean values of size properties obtained under different turbulent conditions.

Figure 7 .

 7 Figure 7. Mean values of shape properties vs. time.

Figure 8 .

 8 Figure 8. Comparison of the SS mean values of shape properties obtained under different turbulent conditions.

Figure 9 .

 9 Figure 9. R g surface distributions over time.

Figure 10 .

 10 Figure 10. Ci surface distributions over time.

Figure 11 .

 11 Figure 11. SS mean values of R g and Ci compared to hydrodynamic characteristics.

Figure 12 .

 12 Figure 12. SS Ci surface distribution at G 5 75 s 21 , small flocs compared to the entire population.

NotationA

  = area, mm 2 A CH = convex area, mm 2 AR = aspect ratio, -CED = circle equivalent diameter, mm Ci = circularity, -Cv = convexity, -Df = two-dimensional fractal dimension, -G = global shear rate, s 21 L = major axis length, mm l = minor axis length, mm m k = kth order moment, [X unit] k n(X) = (surface) density function of X, [X unit] 21 N = rotation speed rpm N p = number of pixels, -P = perimeter, mm P CH = convex perimeter, mm R 1 = inner cylinder radius, m R 2 = outer cylinder radius, m R g = radius of gyration, mm s = skewness, -S = solidity, -Ta = Taylor number,x c , y c = centroid coordinates, mm x i , y i = pixel coordinates, mm X = any floc property, or mm or mm 2 X i , X i11 = borders of class i, [X unit] X mean = surface mean of property X, [X unit] Y i = (surface) fraction of the population in class i, -Greek letters g = Kolmogorov microscale, mm j = kurtosis,t = kinematic viscosity, m 2 s 21 r = standard deviation, [X unit] X = angular velocity, s 21

Figure A2 .

 A2 Figure A2. Results of the PCA performed on size properties A, P, CED, R g , and L.

Figure A1 .

 A1 Figure A1. Results of the PCA performed on nine aggregate properties.

Figure A3 .

 A3 Figure A3. Results of the PCA performed on shape properties AR, S, Ci, and Cv.

Table 1 .

 1 Aggregate Image Properties Directly Computed by regionprops (Lengths in Pixel Units are Converted Before Use)

	Property	Notation		Definition
	Area	A	Cumulated pixel area
	Perimeter Circle equivalent diameter	P CED	Cumulated distance between boundary pixels Diameter of the circle of area: CED 5 ffiffiffiffiffiffiffiffiffiffi ffi 4A=p p
	Centroid coordinates	x c ,y c	Mass center coordinates (average coordinates)
			ðx c ; y c Þ5 1 A	X A ðx i ; y i Þ
				i
	Convex hull area and perimeter	A CH ; P CH	Properties of the smallest convex region that
			contains the projected particle
	Solidity	S	Ratio of the actual area over the convex
			hull area: S5A=A CH
	Major and minor axes	L,l	Axes of the second-order moments equivalent ellipse
	Aspect ratio	AR	AR 5 l=L

Table 2 .

 2 R g and Ci Distribution Characteristics

	R g