Dominic Schröder
email: schroeder@ilr.rwth-aachen.de

Thomas Leweke

Ralf Hörnschemeyer

Eike Stumpf

Generation of a wingtip vortex pair using a pressure-side fin

Keywords: Wingtip vortex, Vortex formation, Vortex pair

We present results from a combined experimental and numerical investigation of the flow around a rectangular NACA 0012 wing, whose tip geometry is modified by the addition of a perpendicular fin. The purpose of this modification is to generate a system of two closely-spaced concentrated tip vortices, instead of the familiar single trailing vortex. Experiments were carried out in a water channel, where velocity measurements were made in the near wake of the wing using Stereoscopic Particle Image Velocimetry, in order to determine the characteristics of the tip vortex pair. Various configurations were tested by changing the position, dimensions and angle of attack of the fin. It was found that the fin could generate a strong and concentrated secondary vortex only when placed on the pressure side of the wing. Visualisations of surface streamlines using oil painting in a wind tunnel, as well as numerical simulations of the flow in the wingtip region, show that separation occurs with the fin on the suction side, even at low angles of attack. Both experiments and simulations were used to determine the influence of fin parameter variations on the tip vortex pair, with respect to its circulation ratio and separation distance. Whereas co-rotating vortex pairs of similar circulation could be generated easily, the fin's ability to produce counter-rotating secondary vortices is rather limited. The current results have relevance in the context of reducing the impact of concentrated tip vortices, which for rotor configurations can lead to strong blade-vortex interactions, causing fatigue and aerodynamic noise.

Introduction

The presence of vortices in flow fields containing finite-span lifting surfaces, such as aircraft wings, rotor blades and propellers, is a well-known phenomenon. As a direct physical consequence of the generated lift, the occurence of vortices trailing downstream of a finite wing is inevitable [START_REF] Schlichting | Aerodynamik des Flugzeuges. Zweiter Band[END_REF]. These wake vortices represent a possible threat to following aircraft, inducing a downwash and strong rolling moments, as well as large structural loads on the wing. Rossow [START_REF] Rossow | Lift-generated vortex wakes of subsonic transport aircraft[END_REF], Gerz et al. [START_REF] Gerz | Commercial aircraft wake vortices[END_REF] and Breitsamter [START_REF] Breitsamter | Wake vortex characteristics of transport aircraft[END_REF] present detailed reviews of the research on fixed-wing aircraft wakes. In systems containing rotors, the blade tip vortices form a helical structure, due to the combination of free-stream velocity and rotational motion. Regarding helicopters in certain flight regimes, the interaction of a tip vortex with a following blade is responsible for unwanted noise and structural vibrations. Considering these negative effects of trailing vortices, numerous studies have been carried out to investigate the temporal and spatial evolution of these systems regarding their strength and possible mechanisms to accelerate their decay. Gerz et al. [START_REF] Gerz | Commercial aircraft wake vortices[END_REF] divided the strategies to reduce the wake vortex hazard for fixed-wing aircraft into two categories. The first one approaches the problem by attempting to modify the vortex properties, e.g. by reducing the vorticity peak in the centre and increasing the core diameter (low-vorticity vortex design). One way to achieve this goal is to enhance the spreading of the vorticity field by means of modified wing control surfaces, as described e.g. by Coustols et al. [START_REF] Coustols | Minimised wake: a collaborative research programme on aircraft wake vortices[END_REF]. In the 1970s, another approach to influence the strength of the wingtip vortex was proposed, the modification of the circulation distribution on the wing, since the spanwise loading has a direct impact on the vortex formation process. Rossow [START_REF] Rossow | Theoretical study of lift-generated vortex wakes designed to avoid rollup[END_REF] presented a theoretical study deducing wing loadings resulting in a weaker tip vortex, and Corsiglia et al. [START_REF] Corsiglia | Experimental study of the effect of span loading on aircraft wakes[END_REF] showed a reduction of the induced rolling moment by reshaping the spanwise loading.

Besides the formation of a "modified" vortex, a rapid decay presents the other approach to minimize wake danger. The enforcement of three-dimensional vortex instabilities leads to a quicker decay of the concentrated vortex structure. Jaquin et al. [START_REF] Jacquin | Unsteadiness, instability and turbulence in trailing vortices[END_REF] describe the most eminent instabilities present in aircraft wakes. One way to trigger these instabilities is by interaction with other vortices. Leweke et al. [START_REF] Leweke | Dynamics and instabilities of vortex pairs[END_REF] provide a detailed review of the dynamics and instabilities occurring in vortex pairs, covering both long-and short-wavelength instabilities. An enhancement of these phenomena can be achieved by either active or passive devices. Crouch et al. [START_REF] Crouch | Active-control system for breakup of airplane trailing vortices[END_REF] presented a system of active control surfaces, e.g. ailerons and flaperons. Active Gurney flaps have been studied by Greenblatt et al. [START_REF] Greenblatt | Flap vortex management using active Gurney flaps[END_REF]. Passive elements, such as spoilers and fins, can also be used to modify the wake vortex. A highly turbulent flow zone is created by means of spoiler elements; it influences the roll-up and merging processes, resulting in a reduction of axial peak velocity and viscous core diameter [START_REF] Breitsamter | Wake vortex characteristics of transport aircraft[END_REF]. The impact of a fin mounted on the wing, producing a secondary vortex for wake alleviation, was first investigated by Rossow [START_REF] Rossow | Effect of wing fins on lift-generated wakes[END_REF]. An increased dispersion of the wake caused by the vortex injection was shown theoretically and verified experimentally. Özger et al. [START_REF] Özger | On the structure and attenuation of an aircraft wake[END_REF] presented a similar study, observing a remarkable effect of the injected fin vortex on the wake. However, a detailed analysis concerning the initial vortex properties as a function of the parameters defining the fin geometry was not provided. The knowledge of the initial vortex characteristics would enable a better prediction of the subsequent vortex interactions and the potential for wake alleviation.

In systems consisting of rotating blades, e.g. helicopter rotors or wind turbines, wake alleviation has been an active research topic over the past decades. The reduction or modification of blade-vortex interactions (BVI) as sources of unwanted noise and high structural loads has been of particular interest. Widnall [START_REF] Widnall | Helicopter noise due to blade-vortex interaction[END_REF] provided a theoretical model for the radiated sound level caused by BVI due to fluctuating lift characteristics. Schmitz & Yu [START_REF] Schmitz | Helicopter impulsive noise: Theoretical and experimental status[END_REF] deduced the vortex core diameter as a decisive parameter for noise emission. Concepts for noise reduction based on a simplified model for BVI were provided by Hardin & Lamkin [START_REF] Hardin | Concepts for reduction of blade/vortex interaction noise[END_REF]. Comparable to the fixed wing, Yu [START_REF] Yu | Rotor blade-vortex interaction noise[END_REF] divides BVI reduction methods into active and passive systems. Active systems comprise concepts using higher-harmonic pitch control (HHC) and individual blade control (IBC) and showed promising results in terms of noise and vibration reduction [START_REF] Yu | Rotor blade-vortex interaction noise[END_REF][START_REF] Johnson | Rotorcraft Aeromechanics[END_REF]. The passive concept targets an optimised blade geometry, especially in the tip region, in order to influence the vortex formation and vortex characteristics after the completed roll-up. Various concepts for blade tip geometries and their influence on the vortices have been investigated, aiming at splitting or diffusing the tip vortex [START_REF] Brocklehurst | A review of helicopter rotor blade tip shapes[END_REF]. Yu [START_REF] Yu | Rotor blade-vortex interaction noise[END_REF], Brentner & Farassat [START_REF] Brentner | Modeling aerodynamically generated sound of helicopter rotors[END_REF] and Brocklehurst & Barakos 2 [START_REF] Brocklehurst | A review of helicopter rotor blade tip shapes[END_REF] give detailed reviews on a variety of tip shapes investigated by experimental and numerical methods. The geometry proposed by Brocklehurst & Pike [START_REF] Brocklehurst | Reduction of BVI noise using a vane tip[END_REF] leads to the formation of two distinct vortices instead of a single one. Splitting the vortices results in a noticeable reduction of BVI noise emissions, implying a modification of the vortex structure before it encounters the following blade. An explanation for this phenomenon may be found in the interaction process between the two distinct helical vortices, which can involve three-dimensional instabilities, leading to the eventual merging into a single vortex. Similar to straight vortices, Leweke et al. [START_REF] Leweke | Long-and short-wave instabilities in helical vortices[END_REF] divide the instability mechanisms for helical vortices into two groups, according to the resulting effects. The fist mechanism causes displacements of the whole vortex, with minimal effects on the internal core structure. These perturbations are described as long-wavelength instabilities, since their scale is large compared to the vortex core diameter. Theoretical and experimental studies regarding long-wavelength instabilities in helical vortices can be found in Refs. [START_REF] Okulov | On the stability of multiple helical vortices[END_REF][START_REF] Quaranta | Long-wave instability of a helical vortex[END_REF][START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF].

The other type of instabilities, referred to as short-wavelength instabilities, arises inside the vortex core, with perturbation wavelengths of the order of the core diameter. An analysis by Moore & Saffman [START_REF] Moore | The instability of a straight vortex filament in a strain field[END_REF] deduced the resonance of Kelvin modes by virtue of an external strain field as the origin of the instability. A review of this mechanism, known as elliptic instability since the base flow streamlines are ellipses, is given by Kerswell [START_REF] Kerswell | Elliptical instability[END_REF]. Blanco-Rodríguez & Le Dizès [START_REF] Blanco-Rodríguez | Elliptic instability of a curved batchelor vortex[END_REF] demonstrated that curvature and torsion existing in helical vortex systems act as further sources for elliptic instabilities. An additional short-wavelength instability appears in helical vortex systems, the curvature instability. An analysis of this phenomenon was performed by Fukumoto & Hattori [START_REF] Fukumoto | Three-dimensional distortions of a vortex filament with axial velocity[END_REF] for a vortex ring and extended to helical vortex systems in Refs. [START_REF] Hattori | Short-wave stability of a helical vortex tube: the effect of torsion on the curvature instability[END_REF][START_REF] Hattori | Modal stability analysis of a helical vortex tube with axial flow[END_REF].

In the present study, we focus on the concept of creating two distinct vortices at the tip of a fixed wing. Following an earlier study by Buffo et al. [START_REF] Buffo | Vortex creation and wing-tip geometry dependencies[END_REF], we use the simple geometry of a rectangular wing and propose a method of generating a secondary vortex by adding a perpendicular fin on one side of the wing near the tip. Water channel and wind tunnel experiments, together with numerical simulations, are used to investigate the initial formation of the vortex system for this new wingtip geometry, and to determine the relation between the fin parameters (size, position, orientation) and the properties of the resulting vortex pair. In §2 below, details about the experimental methods and numerical simulations are given. The results are presented in §3, focussing on the qualitative effect of the fin in various positions and the conditions that produce a pair of tip vortices with similar circulation, which represents a favourable configuration for merging processes. Concluding remarks are given in §4.

Experimental and numerical methods

Experimental set-ups

The flow around the novel wingtip geometry was studied experimentally in two facilities located at the Institute of Aero-space Systems. The first is a recirculating water channel, with a closed test section of dimensions 100 cm (length) × 54 cm (width) × 54 cm (height) and a free-stream velocity range up to U = 4 m/s. The inflow velocity field within the test section has a turbulence level of ∼1.5% and is uniform to within less than 2% outside the wall boundary layers. The wing model was mounted vertically on the ceiling of the test section. A motorised crossbeam and rotation axis allowed for adjusting its spatial position and angle of attack (α). The majority of experimental results were obtained in this setup. In addition, oil painting visualisations of surface streamlines were made in a low-speed open-section wind tunnel, using the same wing model (see below). The model itself consists of a rectangular half-wing of semi-span B/2 = 29 cm and chord c = 10 cm, giving a nominal aspect ratio B/c = 5.8. The cross-section has a NACA 0012 profile, and the wingtip is rounded with a body-of-revolution cap. The main wing body is manufactured from anodised aluminium. The tip geometry is interchangeable, it is attached using magnets and dowel pins to guarantee shape accuracy. In order to generate a secondary vortex, the wingtip was modified by adding a perpendicular fin located either on the suction or the pressure side. The fin geometry with its various parameters is shown schematically in Fig. 1. Like the main wing, it has a NACA 0012 cross-section and a rounded tip. Its chord is c f = 8 cm = 0.8 c for all cases investigated in this study. Its position (d), height (h) and angle of attack (α f ) were varied, in order to explore the effect on the trailing vortex system. The various tip configurations tested were manufactured by rapid prototyping (3D printing). The blockage ratio of the model within the water tunnel for the highest investigated angle of attack (α = 12 • ) was 2.3%.

c f α f c c/4 d h B/2
The Reynolds number based on the chord was kept constant at Re = Uc/ν = 100, 000 (ν: kinematic viscosity) in all experiments. This was achieved by adjusting the free-stream velocity as function of the temperature-dependent viscosity of the fluid, i.e. in the range U = 98-102 cm/s for the water channel measurements.

Velocity measurements

The properties of the tip vortex system were determined from measurements of the velocity field in various downstream cross-sections of the flow. These fields were obtained in the water channel by Stereoscopic Particle Image Velocimetry (SPIV), which gives access to the three velocity components in a two-dimensional field of view. The lower and side walls of the test section are made of glass, allowing for the necessary optical access. Fig. 2 presents a schematic view of the measurement setup and the general coordinate system. The flow was seeded with cubic polyamide particles of mean diameter 50 µm and density 1.016 g cm -3 ensuring a good tracking of the fluid motion. The measurement plane was illuminated from below by a doublepulsed laser (Quantel Twins Ultra), with a pulse energy of 120 mJ, operating at an effective wavelength of 532 nm. The optics mounted in front of the laser provided a light sheet of 2-3 mm thickness, minimising the detection probability of unwanted particles located outside measurement plane. Particle images were recorded by two CCD cameras (PCO.2000) with a resolution of 2048 × 2048 pixles, placed on each side of the test section. The cameras were oriented at an angle of approximately 30 • , matching the recommendation of Lawson & Wu [START_REF] Lawson | Three-dimensional particle image velocimetry: experimental error analysis of a digital angular stereoscopic system[END_REF] to minimise measurement errors in both the in-plane and out-of-plane velocity reconstruction. Adapters fulfilling the Scheimpflug criterion and water-filled prisms, as suggested by Prasad and Jensen [START_REF] Prasad | Scheimpflug stereocamera for particle image velocimetry in liquid flows[END_REF], were used to minimise the aberrations due to the change of the optical medium. Two objectives with a focal length of 85 mm and f -number equal to 11 were used to record a 10 cm × 12 cm field of view. To avoid peak-locking errors, the particle diameter on the recorded images were set to approximately 3 pixels by adjusting the focal distance [START_REF] Raffel | Particle Image Velocimetry: A Practical Guide[END_REF].

Calibration, image acquisition, synchronisation of light source and cameras, as well as image processing, were performed using the DaVis 8.4 software developed by LaVision. Calibration was achieved with a dual-plane calibration plate with circular markers (LaVision); the calculated calibration coefficients were within the satisfactory range. It was possible to use a single calibrated plane for all measurements, since the wing model could be traversed in the downstream direction. The double-frame/single-pulse technique was used for image acquisition. For each case, 350 images were recorded at a frequency of 3 Hz. A delay time of 380 µs between two subsequent images resulted in a satisfactory pixel shift and an acceptable loss-of-pairs. The subsequent stereo cross-correlation was a two-stage process, using first an interrogation window size of 64 × 64 pixels with an overlap of 50%, and then a smaller size of 32 × 32 pixels with an overlap of 75%, resulting in a final spatial resolution of 10-12 vectors within the vortex core radius. For both window sizes, 4 calculation passes were carried out. Further data analysis, including vortex identification, the calculation of vortex properties and statistical post-processing, were conducted with in-house Matlab routines.

A first survey was carried out with measurements in 4 planes at equidistant downstream positions (x/c =1-4) behind the trailing edge of the wing. In a second campaign, a reduced number of configurations was investigated in more detail, with an improved field of view and an additional plane at x/c = 6.

Uncertainty analysis

The determination of vortex parameters is influenced by a variety of effects. Detecting the core centers is usually done by localising the maximum of a suitable flow field operator within the velocity field. This method requires valid information about the flow characteristics close to the core regions. However, due to the large centrifugal forces, the regions close to the vortex center are often affected by a lack of seeding particles, causing data voids that represent a drawback for tracer-based measurements of vortices, especially in wind tunnels. Water tunnels, in contrast, provide suitable conditions for the analysis of vortex-dominated flows for comparable Reynolds numbers, due to the reduced tangential velocities in the core regions. All measurements presented in this study exhibit a sufficient seeding density within the vortex cores, allowing the detection of the centers without the need of special filter techniques, e.g. the one proposed by van der Wall & Richard [START_REF] Van Der Wall | Analysis methodology for 3c-piv data of rotary wing vortices[END_REF]. Another aspect which has to be considered is vortex wandering, see e.g. [START_REF] Devenport | The structure and development of a wing-tip vortex[END_REF]. These irregular motion of the vortices between the recorded frames can cause a biased averaged swirl velocity profile, which affects the determination of the core radii and velocity peaks. Wandering is usually addressed by techniques such as conditional averaging [START_REF] Van Der Wall | Analysis methodology for 3c-piv data of rotary wing vortices[END_REF], where the individual vortex centers are aligned before the averaging process. However, this technique is not feasible for our data, since two individual vortices are present within the flow field which both move separately. To identify the effect of wandering within this study, the instantaneous swirl velocity profiles are compared with the profile obtained from the averaged velocity field, an example is given in Fig. 3a) (The corresponding averaged vorticity contourplot of the example is shown in Fig. 10a, the profiles are obtained for the tip vortex). The calculation procedure of the swirl profiles and the center detection method is described in 3.1. The result shows a good agreement between the averaged and the instantaneous profiles with regard to the maximum value and the distance to the center. Deviations of the individual center positions compared to the average are found to be smaller than 1% of the wing chord, in accordance with the findings of Devenport et al. [START_REF] Devenport | The structure and development of a wing-tip vortex[END_REF]. Based on the analysis, the error within the core radius detection is estimated to lie in the range of 5-10%. To evaluate the uncertainty of the determined circulation values, the convergence of the streamwise vorticity component within an exemplary vortex core is shown in Fig. 3(b). Despite the expected high fluctuations within the core region, the vorticity converges to within well below 1% for less than 200 frames. The analysis of the instantaneous circulation values yields an uncertainty for the averaged value of 7-10%.

Visualisations

A closed-circuit low-speed wind tunnel with an open test section and a nozzle diameter of 1.5 m was used for surface streamline visualisations with the oil-painting method. The wing model with a fluorescent coating was positioned at the bottom of the open test section, with the tip pointing upwards. Two high-resolution cameras of 2048 × 2048 pixel resolution were used to capture the streamline formation and final steady-state condition. One camera covered a side view of the wing, recording the suction or the pressure side, depending on the fin position. The other camera was mounted above the model, with a field of view capturing the wingtip region and the outer side of the fin. All visualisations were performed at a Reynolds number of Re = 100, 000.

Only selected configurations, chosen on the basis of previous SPIV results, were tested. Particular attention was paid to the differences in flow behaviour when the fin was positioned on either the suction or the pressure side.

Numerical methods

The numerical simulations in the present study were carried out using the TAU code of DLR [START_REF] Schwamborn | The DLR TAU-code: recent applications in research and industry[END_REF]. This code is an unstructured finite-volume solver for the compressible Reynolds-averaged Navier-Stokes (RANS) equations. Central discretisation schemes are used to compute the spatial derivatives in the RANS equations. To formally achieve second-order accuracy, an artificial matrix dissipation is applied [START_REF] Langer | Investigation and application of point implicit Runge-Kutta methods to inviscid flow problems[END_REF]. The turbulence equations are discretised by a simplified Roe upwind scheme with second-order reconstruction from limited gradients. An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) scheme with a three-step multigrid acceleration is applied to the RANS equations for the integration in pseudo-time. The turbulence equations are integrated on the finest grid levels only. Turbulence modelling is done with the SSG/LRR-ω Reynolds stress model [START_REF] Eisfeld | Advanced turbulence modelling and stress analysis for the DLR-F6 configuration[END_REF], which directly builds on the modelled transport equations for the Reynolds stress tensor. Braun et al. [START_REF] Braun | Numerical simulation of vortex roll-up processes using the SSG/LRR-ω model[END_REF] showed that this model provides good agreement with experimental data when simulating vortices and their formation process. The model is here improved with a recent modification to increase numerical robustness. A transformation of the length-scale equation allows an accelerated convergence even in regions with the finest mesh [START_REF] Eisfeld | Reynolds-stress model computations of the NASA juncture flow experiment[END_REF]. The dimensions of the computational domain are: 50c in the streamwise direction x, 20c in the spanwise direction y and 40c in the "vertical" direction z. No-slip boundary conditions are applied at the wing surfaces. The outer surfaces of the computational domain are implemented with far-field conditions, except for the one containing the wing root, where a symmetry condition is applied. The wing is centered on this symmetry plane.

The hybrid computational grid, consisting of prisms, hexahedrons and structured regions, was generated using the CENTAUR software. 55 structured prismatic layers are utilised in the direction normal to the wing and fin surfaces, in order to resolve the boundary layer region. The thickness of the first prism layer is chosen so that the normalised distance between the surface and the first node is less than unity in the entire domain, which guarantees the resolution of the viscous sublayer everywhere. Structured hexahedron blocks are used in regions where the vortex formation process occurs, in order to resolve the rolled-up vortices with sufficient accuracy and minimise numerical dissipation. A grid step of 10 -3 c is obtained in the structured regions, providing a resolution which is an order of magnitude higher than the one recommended by Dacles-Mariani et al. [START_REF] Dacles-Mariani | On numerical errors and turbulence modeling in tip vortex flow prediction[END_REF]. The grids of all investigated cases have approximately 26 million points. In order to allow comparability to the experimental measurements, the chord-based Reynolds number for all numerical calculations was set to the same value as in the experiments: Re = 100, 000.

Results and discussion

Tip vortex of the bare wing

In this study, the reference configuration (without fin) consists of a rectangular wing of aspect ratio B/c = 5.8, having a symmetric NACA 0012 cross-section profile and rounded tips. Previous experimental studies [START_REF] Chow | Mean and turbulence measurements in the near field of a wingtip vortex[END_REF][START_REF] Giuni | Vortex formation on squared and rounded tip[END_REF] and numerical simulations [START_REF] Jiang | Large-eddy simulation of wing tip vortex in the near field[END_REF][START_REF] Lombard | Implicit large-eddy simulation of a wingtip vortex[END_REF] of this geometry have shown that it generates a single concentrated tip vortex, whose strongly rotating core becomes axisymmetric and almost laminar within about one chord length behind the trailing edge of the wing. Fig. 4 shows examples of streamwise vorticity distributions obtained in the present experiments from SPIV measurements at two downstream positions. At x/c = 1 a high-vorticity vortex core is formed, connected to the low-vorticity vortex sheet shed behind the entire span of the wing. This sheet continues to roll up around the core as it moves downstream.

The vortex structure can be characterised by swirl velocity and circulation profiles. These were obtained by first transforming the velocity components in the cross-sectional y-z plane to a polar coordinate system r-θ around the vortex centre, which is determined with the λ 2 -method proposed by Jeong and Hussain [START_REF] Jeong | On the identification of a vortex[END_REF]. The resulting azimuthal velocity u θ is then averaged on circles of radius r, and integrated along these circles for the circulation. The results for the field measured at x/c = 6 (Fig. 4b) are presented in Fig. 5 two-dimensional inviscid flow, and the swirl velocity by Γ 0 /c. The velocity profiles are similar for all angles of attack, with a maximum of order unity located at a radial distance r m ≈ 0.05c, which defines the core radius. The rescaled circulation profiles are identical up to about twice the core radius (shaded region in Fig. 5b and circle in Fig. 4b). For an untwisted rectangular airfoil in inviscid flow, the spanwise distribution of non-dimensional bound circulation, as well as the radial circulation distribution of the resulting tip vortex which can be deduced from it [START_REF] Donaldson | Calculation of aircraft wake velocity profiles and comparison with experimental measurements[END_REF], depend only on the aspect ratio [START_REF] Trefftz | Prandtlsche Tragflächen-und Propellertheorie[END_REF]. The total circulation for B/c = 5.8 is predicted as 0.82 Γ 0 .

The fact that the profiles in Fig. 5(b) depend also on the angle of attack is due to the non-linearity of the lift curve of the NACA 0012 airfoil for Re = 10 5 . Theoretical calculations using a lift curve based on recent experimental results [START_REF] Ohtake | Nonlinearity of the aerodynamic characteristics of NACA0012 aerofoil at low Reynolds numbers[END_REF][START_REF] Tank | On the possibility (or lack thereof) of agreement between experiment and computation of flows over wings at moderate Reynolds number[END_REF] predict total circulations between 0.94 Γ 0 (for α = 4 • ) and 0.68 Γ 0 (for α = 12 • ), and reproduce well the profiles measured in the present study.

Effect of a tip fin placed on the suction or pressure side

The desired secondary vortex is generated by means of the additional fin placed on either the suction or the pressure side of the wing. It is expected that the fin has a significant impact on the flow behaviour close to the wingtip due to the three-dimensional flow characteristics in this region. Oil flow visualisations provide an insight into the flow near the wing surface, an example is given in Fig. 6. The wing is mounted vertically on an adjustable rotating plate, with gravity directed towards the wing root. Both suction and pressure sides are shown for the reference case without fin (Fig. 6a,b) and a modified configuration with fin (Fig. 6c,d). The flow pattern for the reference case in Fig. 6(a) indicates the presence of a small separation bubble on the suction side close to the leading edge for the investigated flow conditions. The cross flow caused by the pressure difference between the two wing surfaces, and the subsequent vortex formation process, can clearly be identified in the tip region of the bare wing. In comparison, the flow patterns of the modified wing reveal some remarkable effects related to the presence of the fin. The observed flow behaviour is very different when the fin is mounted either on the suction or the pressure side. In the former case (Fig. 6c), a large separation region above the fin's suction side is visible, similar to corner flow separation, inducing a recirculation region adjacent to the trailing edge of the wing. This phenomenon was also observed in preliminary visualisations in the water channel and was expected to have a negative impact on the vortex formation at the fin tip and possible mutual interactions downstream. A decrease of the fin angle down to α f = 6 • does not lead to a reattachment of the flow, giving the impression that the inflow conditions on the suction side are prone to corner flow separation, irrespective of the geometric specifications of the fin. Also, a variation of the spanwise position d yields no notable differences concerning the separation, implying that the influence of the cross flow in the tip region is not decisive for the detected effect. Potential explanations for this flow behaviour include interactions with the separation bubble close to the leading edge and a blocking effect of the main wing, causing non-uniform inflow conditions for the fin.

Several numerical simulations of selected configurations were performed to analyse in more detail the observations obtained from the oil painting visualisations. For comparison, an image equivalent to the oil painting pattern can be generated by the Line Integral Convolution (LIC) method. The result, displayed in Fig. 7 for the same configurations as in Fig. 6, shows good agreement with the experimental observations. The differences between simulation and experiment concerning the flow patterns close to the trailing edge of the wing can be explained by the influence of gravity on the oil film; resulting from the wing positioning in the wind tunnel.

Fig. 8 shows isosurfaces of the streamwise velocity v x , in order to illustrate the size of the separation regions for both fin configurations (for visual clarity, the isosurfaces within the prism layers of the numerical mesh are not displayed). With the fin placed on the suction side (Fig. 8a), a significant flow separation region appears close to the fin root, even at moderate angles of attack. Although the numerical results show that, despite the presence of partly separated flow regions, a secondary vortex is generated at the fin tip (see below), an influence of the separation on the fin vortex formation, which might cause undesired perturbations prior to possible interactions with the wingtip vortex, cannot be ruled out.

The experimental and numerical results indicate that the impact on the surrounding flow field of a fin mounted on the pressure side of the wing is notably smaller. The flow pattern obtained by oil painting (Fig. 6d) shows no evidence of flow separation, similar to the LIC pattern in Fig. 7(d). Contrary to the suction side, the flow around the fin is well attached over the entire wingspan, providing favourable conditions for the formation of a secondary vortex. These impressions from the flow pattern are supported by the numerical results in Fig. 8(b) which show no evidence of separation regions close to the fin. The generation of the primary wing vortex appears not to be influenced by the presence of the fin or the secondary vortex.

Based on these findings it was decided that further SPIV investigations in this study should focus on configurations with the fin mounted on the pressure side of the wing. For this arrangement, a positive fin angle α f (see Fig. 1) results in a co-rotating vortex system, whereas negative fin angles produce a counter-rotating secondary vortex. Considering the effects of the cross flow on the lower surface close to the wingtip, a slight deflection of the free stream approaching the fin occurs, causing a de-or increase of the effective angle of attack, depending on the fin orientation. A numerical parameter study, including a variation of α f for constant d/c = 0.3 and h/c = 0.3, was performed to investigate this hypothesis. For all configurations, a constant angle of attack α = 10 • was chosen.

The result is shown in Fig. 9. Several cuts along the chord display the normalised streamwise vorticity ω to qualitatively illustrate the vortex generation process. The parameter variation reveals that the neutral position of the fin, indicated by the absence of a secondary fin vortex, is located between α f = -4 • and α f = -6 • for the chosen fin configuration. It is expected that the influence of the cross flow decreases for greater values of the fin distance d. As a consequence of this asymmetry in the fin vortex formation, with respect to the fin angle value, it is expected that counter-rotating fin vortices are weaker than co-rotating ones, for the same absolute values of the fin angle. If strong interactions with the wingtip vortex are likely to occur when the fin vortex has a comparable strength, the co-rotating configurations, with positive α f , therefore appear more promising.

a) α f = -10 • b) α f = -8 • c) α f = -6 • d) α f = -4 • e) α f = -2 • f) α f = 0 • g) α f = 2 • h) α f = 4 • i) α f = 6 • j) α f = 10 •

Co-and counter-rotating tip vortex pairs

The experimental investigation of the effect of the fin is again carried out using SPIV measurements in the near wake of the wing. In this section, two representative configurations are analysed in detail. In the first, the wing/fin geometry generates a co-rotating pair of vortices of approximately the same circulation, which is expected to be favorable for the development of vortex interactions and instabilities, as well as merging. The second fin configuration creates a counter-rotating secondary vortex, whose strength is significantly lower than the one of the wingtip vortex, for the reasons discussed above. Figures 10 and11 The co-rotating vortex system is generated by a wing equipped with a fin located on the pressure side at a distance d/c = 0.3 from the tip, and having a height h/c = 0.3 and angle of attack α f = 10 • . Figure 10 reveals that at one chord length behind the trailing edge of the wing (x/c = 1) two concentrated vortices have formed from the wingtip (upper vortex) and fin tip (lower vortex). Both vortices exhibit a stable core structure, and they rotate around each other while propagating downstream, as expected for the co-rotating configuration.

The averaged SPIV velocity fields can again be used to determine the vortex characteristics (radius, circulation), with the procedure described in section 3.1 (Fig. 5). The evolution of the core radii is shown in Fig. 12. For a better comparison with theoretical results, the equivalent Gaussian core size a = r m /1.12 is displayed. The initial radius of the wingtip vortex is practically unchanged by the presence of the fin. The fin vortex has a comparable, slightly smaller size. The downstream evolution of the core radii shows good agreement with the theoretical predictions for two-dimensional viscous Gaussian vortices of similar initial size, which can be deduced from the temporal evolution based on the diffusion of vorticity: a 2 (t) = a 2 (t = 0) + 4νt. The latter are shown as dashed lines in Fig. 12. The apparent laminar viscous growth of the vortex cores suggests the absence of interaction and instability phenomena at this early stage, which would typically lead to a faster core growth. In the observation interval (x/c ≤ 6), the rescaled core radius a/b, where b is the distance between vortex centres, remains well below the critical value of a/b = 0.24 for the onset of merging [START_REF] Leweke | Dynamics and instabilities of vortex pairs[END_REF], so that the formation of a single vortex through this process is only expected much further downstream.

The circulation values for the co-rotating vortex system are plotted in Fig. 13. They were obtained by integrating the streamwise vorticity in a circular area of radius 0.15c around the given vortex centre. The same radius was also used for all other circulation measurements shown in the following, to allow for a better comparison. It is large enough to capture the core vorticity, and at the same time small enough not to include circulation from the low-intensity vorticity sheet shed behind the wing, nor circulation that may be attributed to the other vortex of the pair, i.e. it is less than b/2 for all cases considered. For the chosen co-rotating configuration, the wingtip and and fin vortex circulations are almost identical, and they vary little in the observation interval. It should be noted that the total circulation of the two vortices is about 20% larger than the circulation of the tip vortex without fin and otherwise identical wing parameters. Thus it appears that the additional fin does not only split up the single vortex, but also influences the amount of bound circulation (see also Fig. 16), and therefore the lift and induced drag characteristics of the wing.

The geometric fin parameters for the counter-rotating vortex pair case shown in Fig. 11 are d/c = 0.5, h/c = 0.3 and α f = -12 • . Two vortices of opposite-signed vorticity are generated by this configuration. Despite the high fin angle, the (lower) secondary vortex is notably weaker than the (upper) tip vortex, in agreement with the results from the numerical simulations. Whereas the tip vortex core remains fairly unchanged up to x/c = 6, the core of the fin vortex is being stretched by the strain induced from the much stronger tip vortex. One can see in Fig. 11(e) that it starts getting wrapped around the latter, suggesting that it is likely to get ripped apart later on. This process is reflected in the evolution of the core size in Fig. 14. Contrary to the tip vortex, which again evolves approximately like a two-dimensional laminar vortex, the radius of the fin vortex increases much faster. The measurements of the circulation in Fig. 15 confirm that the strength of the fin vortex is only about 20% of the one of the wingtip vortex. Compared to the reference case, the total circulation is significantly diminished by the addition of the fin. The initial vortex separation is determined by the wingtip/fin geometry; it was found to be close to the distance b 0 between the tips of the trailing edges of the wing and the fin, as illustrated in Fig. 17. The initial core radii of the wing and fin tip vortices depend mainly on the respective chord lengths, which were not varied in this study. For all tested co-rotating configurations, they were found to lie in the range 0.03 ≤ a/c ≤ 0.04 (see Fig. 18). The configurations equipped with fins having negative angles α f generate fin vortices significantly weaker than the corresponding wing vortices, compare Fig. 15. Hence their geometry is stretched and deformed by the presence wing vortex immediately after emerging from the trailing edges, explaining the outliers in Fig. 18. The remainder of this section focusses on circulations Γ w (wingtip vortex) and Γ f (fin vortex), and their ratio, whose variation as function of the geometric parameters is less straightforward. We consider mostly co-rotating configurations, since these are more relevant for possible applications in aeronautics. In these cases, maximum spreading of the vorticity is obtained for circulation ratios Γ f /Γ w close to 1. In the following, a single circulation value is used for each vortex of a given configuration. It is determined by averaging the measurements made in the near wake of the wing up to x/c = 6, as shown e.g. in Figs. 13 and15. Error bars indicate the minimum and maximum values found in this interval. Figure 19 shows the experimentally determined circulation ratios as function of the fin position, for four combinations of wing and fin angles. A slight decrease of the ratio is found in all cases, as the distance to the wingtip increases. As expected, the highest values (approaching Γ f /Γ w = 2) are found for low wing angle and high fin angle. The strength of the fin vortex alone depends little on the fin position, but exhibits a non-trivial variation with the angle-of-attack combinations (Fig. 20). It increases with the fin angle, but also by increasing only the angle of the main wing. The circulation of the tip vortex is roughly proportional to the wing's angle of attack, as expected (Fig. 21), but its value is also significantly influenced by the position of the fin: it increases as the fin moves further away from the tip. These results show that the tip and fin vortices have a mutual influence on each other, and that their strength is not determined independently by the characteristics of the respective wingtip and fin geometries.

The previous results suggest that is it possible to control the circulation ratio Γ f /Γ w by adjusting the fin angle α f , when the fin is placed near the wingtip. Figure 22 displays the relation between both quantities, as determined from the numerical simulations, using the set of configurations shown in Fig. 9. The circulations are here determined in a plane immediately behind the wing trailing edge. For positive angles, the dependency is approximately linear, resulting from the increase of the fin vortex circulation with fin angle (Fig. 20) and the almost unchanged circulation of the wingtip vortex (Fig. 21). Negative fin angles exhibit a different behaviour, with the generated fin vortices being much weaker in comparison. The circulation ratio (absolute value) remains small and increases slightly only at large negative fin angles. As discussed in section 3.2, this asymmetry can probably be linked to the three-dimensionality of the flow in the wingtip region, which modifies the effective angle of attack of the fin. Overall, the result in Fig. 22 confirms the qualitative impressions from Fig. 9.

An increase of the fin height h/c has several effects. It makes the fin geometry less threedimensional and moves the fin tip further away from the wing surface into the free stream. This is expected to lead to an increase of the fin vortex circulation, which is confirmed by the measurements shown in Fig. 23. At the same time, a larger fin further prevents the spanwise cross flow near the main wing surface and therefore disturbs the formation of the tip vortex. Both tendencies lead to a significant increase of the circulation ratio with h/c, as shown in Fig. 24. The effect is enhanced when the fin moves closer to the wingtip. For the configuration with α = 6 • , α f = 10 • and h/c = 0.5, a circulation ratio larger than 3 is found with the fin located at d/c = 0.3.

A smaller set of counter-rotating configurations with different parameter values was also investigated. As already noted in Fig. 22, the (absolute) circulation ratios are generally significantly smaller. In addition, Fig. 25 shows that there is a tendency for the ratio to increase as the fin moves away from the wingtip, which can be related to the diminishing influence of the tip vortex on the flow near the fin for increasing d/c. The effects on the circulation ratio of a variation of the fin height or of the wing angle of attack were found to be qualitatively similar to the ones observed for co-rotating configurations.

Conclusion

Through a combined experimental and numerical study, we have analysed the influence of a perpendicular fin, mounted close to the tip of a rectangular wing, on the generation of the trailing vortex system. This work was motivated by certain rotor blade tip geometries investigated in the past, aimed at splitting the concentrated tip vortex into two distinct vortices, which then undergo a mutual interaction and merging process resulting in a modified final vortex with altered characteristics (core radius, maximum swirl velocity). In the present study, a particular concept of generating two distinct tip vortices is explored for a fixed wing, in order to understand the fundamental mechanisms involved. The vortex splitting is achieved by adding a fin on the wing surface. When the fin is placed on the suction side of the wing, the experimental and numerical visualisations of the near-wall flow reveal a strong tendency for flow separation, which is detrimental to the formation of the secondary fin vortex. Most of the study therefore focussed on configurations with the fin on the pressure side, where no separation occurs. By adjusting the geometrical parameters defining the fin, it was possible to generate a variety of co-and counterrotating vortex systems. These were characterised by the respective vortex circulations and radii, and the separation distance. The three-dimensional characteristics of the flow near the wingtip affects the performance of the fin. The cross flow on the wing surface in this region modifies the effective fin angle, which favours the generation of co-rotating vortices. An extensive parameter study has shown that it is possible to generate vortex systems with circulation ratios close to unity, resulting in an efficient spreading of the tip vortex vorticity. In addition, such pairs of nearly equal circulation are prone to develop strong mutual interactions and merge into a less concentrated final vortex, leading to less severe interactions with other structures (e.g. bladevortex interactions generating noise in the case of a rotor). In the current investigation using a fixed-wing geometry, instabilities and merging of the tip and fin vortices were not observed in the near-wake region considered. In a related study [START_REF] Schröder | Experiments on helical vortex pairs in the wake of a rotor[END_REF][START_REF] Schröder | Experimental investigation of a rotor blade tip vortex pair[END_REF][START_REF] Schröder | Instability and merging of a helical vortex pair in the wake of a rotor[END_REF] involving a rotating wing equipped with a similar fin, designed using the results presented here, a strong three-dimensional short-wave instability, followed by a rapid merging, was found. This interesting new behaviour appears to be related to the difference in the spanwise circulation distributions between fixed and rotating wings. It suggests that the wing tip modification using a fin may hold promise for reducing the level of undesired blade-vortex interactions in rotor flows.

Declaration of competing interest

There are no conflicts of interest to declare.

Fig. 1 .

 1 Fig. 1. Schematic side and end views of the wingtip geometry equipped with a fin.

Fig. 2 .

 2 Fig. 2. (a) Experimental setup for SPIV measurements in the water channel (view from below). (b) Sketch defining the coordinate system.

Fig. 3 .

 3 Fig. 3. (a) Instantaneous swirl velocity profiles of the tip vortex; the black line represents the profile obtained from the averaged velocity field. (b) Convergence ratio of the streamwise vorticity component ω at a point within the tip vortex core.

6 Fig. 4 .

 64 Fig. 4. Streamwise vorticity distribution at two downstream positions behind the bare wing at α = 10 • . The dashed circle in (b) has a diameter of 0.2c.

Fig. 5 .

 5 Fig. 5. Radial velocity and circulation profiles (azimuthal averages) of the tip vortex at x/c = 6, for α in the range 4 • -12 • . The thick lines show the results for α = 10 • .

Fig. 6 .Fig. 7 .

 67 Fig. 6. Oil flow pattern for the reference case and a modified configuration at Re = 100, 000 and α = 10 • . For a better comparison, the pressure sides are mirrored. Fin geometry for (c,d): d/c = 0.5, h/c = 0.3, α f = 10 • , flow is from left to right.

Fig. 8 .

 8 Fig. 8. Illustration of the separation tendency close to the fin root at an angle of attack of α = 10 • for a fin position on (a) the suction and (b) the pressure side of the main wing. Fin geometry: d/c = 0.5, h/c = 0.3, α f = 10 • .

Fig. 9 .

 9 Fig. 9. Vortex formation at the fin and wingtips for different fin angles, illustrating the effect of the cross flow close to the wingtip. The neutral position (no fin vortex) is shifted to α f ≈ -5 • . d/c = 0.3 and h/c = 0.3 for all cases.

6 Fig. 10 . 6 Fig. 11 .

 610611 Fig. 10. Vorticity fields in different planes behind the wing, illustrating the development of a co-rotating vortex system. The fin parameters are: d/c = 0.3, h/c = 0.3, α f = 10 • .

Fig. 12 .

 12 Fig.12. Vortex core radii for the co-rotating system. The dashed lines show the expected viscous evolution for a laminar Gaussian vortex.

  w

Fig. 13 .

 13 Fig. 13. Vortex circulations in the co-rotating system.

Fig. 14 .

 14 Fig. 14. Vortex core radii for the counter-rotating system. Dashed lines: viscous evolution.

Fig. 15 .

 15 Fig. 15. Vortex circulations in the counter-rotating system.

Fig. 17 .

 17 Fig. 17. Vortex separation b, measured at x/c = 1, as function of the geometrical distance b 0 between wing and fin trailing edge tips, for all tested configurations.

Fig. 18 .

 18 Fig. 18. Gaussian core radius a for all configurations.

Fig. 19 .

 19 Fig. 19. Variation of the circulation ratio with fin position, for various combinations of angles of attack. The fin height is h/c = 0.3 for all cases.

Fig. 20 .

 20 Fig. 20. Variation of the fin vortex circulation with fin position, for various combinations of angles of attack. h/c = 0.3.

Fig. 21 .

 21 Fig. 21. Variation of the wingtip vortex circulation with fin position, for various combinations of angles of attack. h/c = 0.3.

Fig. 22 .

 22 Fig. 22. Circulation ratio immediately behind the wing trailing edge as function of the fin angle. Data obtained from numerical simulations for α = 10 • , d/c = 0.3 and h/c = 0.3 (see also Fig. 9).

Fig. 23 .

 23 Fig. 23. Effect of fin height on the fin vortex circulation in co-rotating systems. The fin angle is constant (α f = 10 • ).

Fig. 24 .

 24 Fig. 24. Effect of fin height on the circulation ratio of co-rotating systems. α f = 10 • .

Fig. 25 .

 25 Fig. 25. Effect of fin position on the circulation ratio of counter-rotating systems. The fin height is constant (h/c = 0.3).

Acknowledgements

This work is part of the German-French project TWIN-HELIX, supported by the Deutsche Forschungsgemeinschaft (grant no. 391677260) and the French Agence Nationale de la Recherche (grant no. ANR-17-CE06-0018).

Reference wing

Fig. [START_REF] Hardin | Concepts for reduction of blade/vortex interaction noise[END_REF]. Spanwise circulation distribution for the co-and counter-rotating cases shown in Figs. 10 and11, compared to the reference wing without fin. Figure 16 displays the spanwise distributions of the normalised circulation for the two fin configurations, as well as for the reference wing without fin. They were deduced from the spanwise vorticity field immediately downstream of the trailing edge of the wing, obtained by numerical simulation. The result obtained for the reference wing is in good agreement with the Prandtl model for a finite-span rectangular wing [START_REF] Trefftz | Prandtlsche Tragflächen-und Propellertheorie[END_REF], the small deviation (kink) in the tip region can be explained by the incipient roll-up of the tip vortex. The circulation profiles of the modified configurations reflect well the presence of the additional secondary vortices. They manifest themselves through an additional sharp decrease or increase of the radial distribution, their amount corresponding to the circulations seen in Figs. 13 and15. Further away from the tip region (for y/B < 0.3), the circulation distributions for all cases converge.

For both co-and counter-rotating systems, the influence of the additional fin on the generated lift or drag has not been analysed experimentally within the scope of this work. The circulation distributions obtained from the numerical simulations in Fig. 16 reveal that the fin has an effect on the bound circulation which is directly related to the lift distribution. In addition, the drag characteristics of the wing are likely to be affected by the presence of the fin as well. A more detailed analysis of the effect of the fin on the aerodynamic performance of the wing is planned for future work.

Parameter study

The geometry and position of the fin which generates the secondary tip vortex are determined by the parameters shown in Fig. 1. We now discuss how the variation of these parameters influences the characteristics of the resulting vortex pair, using the results from a series of SPIV measurements. For this analysis, the following parameter values were considered: wing angle α = 6 • , 10 • ; fin angle α f = ±6 • , ±10 • ; fin height h/c = 0.3, 0.5; fin position d/c = 0.2, 0.3, 0.5. The tip vortex pair is characterised by the circulation (Γ) and core size (a) of each vortex, as well as the distance between the vortex centres (b).


Hana Boughrara

Souad Djelalli

Nacerddine Haddaoui

Jean-Noël Staelens

Philippe Supiot

Ulrich Maschke
email: ulrich.maschke@univ-lille.fr

A facile route to improve compatibilization of Low Density PolyEthylene/Poly (ε-caprolactone) blends

Keywords: Polyethylene (PE), poly (ε-caprolactone) (PCL), Ox-biodegradable Polymer, thermo-oxidation, pro-oxidants additives, compatibilizer

Low density Polyethylene (designated hereafter as "PE") is known for its inactivity, durability and resistance to degradation. For this reason adding pro-oxidants as additives in PE matrix could be efficient to elaborate a material designated as Ox-PE, exhibiting chemical reactivity. This modification could lead to an enhancement of compatibility between Ox-PE and other functionalized polymers. This approach has been exploited in this report to elaborate blends of Ox-PE with poly (ε-caprolactone) (PCL), a biodegradable polymer. Fourier Transform InfraRed spectroscopy (FTIR), Scanning Electron Microscopy (SEM) and thermal characterization by DSC, TGA were applied to investigate structural and thermal properties of PE/PCL (75/25 wt%/wt%) blends, compatibilized with 1 Phr and 5 Phr of Ethylene-co-Glycidyl MethAcrylate (EGMA) copolymer or with a Ox-PE/PCL mixture.

Structural observations of the PE75/PCL25 blend by SEM revealed a phase separated morphology indicating incompatibility between PE and PCL. This was also confirmed by FTIR spectroscopy where no changes were noticed concerning the characteristic bands of either PE or PCL. Incorporating EGMA in the PE75/PCL25 blend resulted in reduced particle sizes of the dispersed PCL phase in the PE matrix confirming the reaction of epoxy groups of EGMA with hydroxyl end-groups of PCL at the interface. Regarding the thermal behavior, all PE/PCL blends exhibited an intermediate response between that of PE and PCL homopolymers. Interestingly, a high degree of compatibility was achieved for the Ox-PE75/PCL25 blend, together with a lower thermal stability compared to PE75/PCL25.

Introduction

Despite the strong development of green polymers in recent years, the use of synthetic polymers has doubled due to their successful application in various domains: packaging, automotive components, transportation, medical equipment, electric, electronic and aerospace parts, among others [START_REF] Vanapalli | Singleuse LDPE -Eucalyptus biomass char composite produced from co-pyrolysis has the properties to improve the soil quality[END_REF][START_REF] Vázquez-Morillas | Biodegradation and Ecotoxicity of Polyethylene Films Containing Pro-Oxidant Additive[END_REF]. These materials present good physico-chemical properties such as resistance to corrosion and microbiological attack, insolubility, impermeability towards aqueous media, ensuring their service in different fields [START_REF] Taghavi | Challenges in biodegradation of non-degradable thermoplastic waste: From environmental impact to operational readiness[END_REF].

Among the family of polyolefins, low density polyethylene (designated hereafter as "PE") occupies a significant position because of its large tonnage, and its mechanical, thermal and chemical performances, which have enlarged use of PE in a wide range of industrial applications, especially in packaging and agricultural films. However, after this rush of consumption, end-of-life PE accumulates in nature as waste [START_REF] Johansen | A review of the plastic value chain from a circular economy perspective[END_REF].

Consequently, waste accumulation of PE has become a real risk to biodiversity and a source of environmental pollution [START_REF] Ren | Biodegradation of polyethylene by enterobacter sp. D1 from the guts ofwax moth galleria mellonella[END_REF]. The resistance of PE to degradation and biological attacks is attributed mainly to its high molecular weight, hydrophobicity and lack of functional groups on its main chain [START_REF] Madhu | Physico-mechanical properties and biodegradation of oxo-degradable HDPE/PLA blends[END_REF][START_REF] Al-Salem | Insights into the evaluation of the abiotic and biotic degradation rate of commercial pro-oxidant filled polyethylene (PE) thin films[END_REF]. Indeed, the chemical structure of PE is responsible for its incompatibility with other materials and makes thus the attack by microorganisms difficult, which has a substantial impact on the degradation process [START_REF] Plummer | The post-modification of polyolefins with emerging synthetic methods[END_REF]. As a result, many research groups proposed different approaches to reduce the accumulation of considerable quantities of non-biodegradable PE waste in the environment [START_REF] Karlsson | Influence of thermooxidative degradation on the in situ fate of polyethylene in temperate coastal waters[END_REF]. One possible approach consists to blend PE with biodegradable polymers, which could be a notable alternative since each component can contribute by its favorable properties to make the resultant material more interesting [START_REF] Oksiuta | Mechanical and thermal properties of polylactide (PLA) composites modified with Mg, Fe, and polyethylene (PE) additives[END_REF][START_REF] Bezerra | Compatibility and characterization of Bio-PE/PCL blends[END_REF]. In this context, several studies have focused on PE/aliphatic polyester blends such as poly(lactide) (PLA) and poly(hydroxybutyrate-co-valerate) PHBV [START_REF] Hamad | Biodegradable polymer blends and composites: An overview[END_REF][START_REF] Djellali | Structural, morphological and mechanical characteristics of polyethylene, poly(lactic acid) and poly(ethylene-co-glycidyl methacrylate) blends, Iran[END_REF][START_REF] Djellali | Viscosity and viscoelasticity measurements of low density polyethylene/poly(lactic acid) blends[END_REF][START_REF] Medjdoub | Viscoelastic, thermal and environmental characteristics of poly(lactic acid), linear low-density polyethylene and low-density polyethylene ternary blends and composites[END_REF][START_REF] Podzorova | Degradation of Polylactide-Polyethylene Binary Blends in Soil[END_REF][START_REF] Khan | LDPE:PLA and LDPE:PLA:OMMT polymer composites: Preparation, characterization, and its biodegradation using Bacillus species isolated from dumping yard[END_REF][START_REF] Lekube | Study of mechanical and rheological properties, morphology, and miscibility in polylactid acid blends with thermoplastic polymers[END_REF][START_REF] Burlein | Mechanical and morphological properties of LDPE/ PHB blends filled with castor oil pressed cake[END_REF][START_REF] Sadik | Polyolefins/Poly(3-hydroxybutyrate-co -hydroxyvalerate) blends compatibilization: Morphology, rheological, and mechanical properties[END_REF]. Nevertheless, only few studies are dealing with the PE/Poly-(caprolactone) (PCL) system despite the excellent properties that make PCL an outstanding candidate to be blended with polyolefins to achieve specific mechanical and degradation properties [START_REF] Bezerra | Compatibility and characterization of Bio-PE/PCL blends[END_REF][START_REF] França | Photodegradation mechanisms on poly(ε-caprolactone) (PCL)[END_REF]. PCL is a prominent aliphatic polyester due to its numerous advantages including extraordinary mechanical properties, biocompatibility, hydrophobicity, solubility in several solvents, non-toxicity, and biodegradability [START_REF] Salehi | Characterization of structural, mechanical and nano-mechanical properties of electrospun PGS/PCL fibers[END_REF][START_REF] Nevoralová | Structure Characterization and Biodegradation Rate of Poly(εcaprolactone)/Starch Blends[END_REF]. Nonetheless, when developing polymer blends, the risk of incompatibility between multiphase components represents a critical factor to be considered.

In this context, the most common method for overcoming such a problem is to add compatibilizing agents, such as copolymers containing fragments that are compatible with at least one of the components. Furthermore, interaction between the components at the interface has a significant impact on the morphology of the resulting material, which is a criterion that will determine its final properties [START_REF] Su | Significant toughness improvement in iPP/PLLA/EGMA blend by introducing dicumyl peroxide as the morphology governor[END_REF].

Another interesting way to modify PE structure was recently adopted, based on the incorporation of pro-oxidants or pro-degradants. These additives are usually transition metalion complexes in the form of stearates, which may initiate the oxidation of long PE chains in the presence of UV light (photo-oxidation) or heat (thermo-oxidation) [START_REF] Al-Salem | Insights into the evaluation of the abiotic and biotic degradation rate of commercial pro-oxidant filled polyethylene (PE) thin films[END_REF][START_REF] Bensaad | Effects of calcium stearate as pro-oxidant agent on the natural aging of polypropylene[END_REF][START_REF] Glowik-Lazarczyk | Influence of oxo-degradable pe recyclate addition on the degradation of commercial low density polyethylene (PE-LD)[END_REF][START_REF] Mandal | Thermal degradation kinetics of oxo-degradable PP/PLA blends[END_REF][START_REF] Subramaniam | Enhanced degradation properties of polypropylene integrated with iron and cobalt stearates and its synthetic application[END_REF]. Cobalt stearate (Co 2+ ), Manganese stearate (Mn 2+ ) and Iron stearate (Fe 3+ ) represent the commonly used pro-oxidant additives with polyolefins [START_REF] Roy | Investigating the role of metal oxidation state on the degradation behaviour of LDPE[END_REF][START_REF] Suresh | Influence of thermal oxidation on surface and thermo-mechanical properties of polyethylene[END_REF][START_REF] Abrusci | Comparative effect of metal stearates as pro-oxidant additives on bacterial biodegradation of thermal-and photo-degraded low density polyethylene mulching fi lms[END_REF][START_REF] Pablos | Photodegradation of polyethylenes : Comparative effect of Fe and Ca-stearates as prooxidant additives[END_REF][START_REF] Yu | Enhancement of Pro-Degradant Performance in Polyethylene / Starch Blends as a Function of Distribution[END_REF][START_REF] Fontanella | Comparison of biodegradability of various polypropylene fi lms containing pro-oxidant additives based on Mn , Mn / Fe or Co[END_REF].

Incorporating these compounds facilitates the long PE chain scission leading to the formation of hydrophilic groups, together with a decrease of the molecular weight. The formed fragments, with lower molecular weight and higher hydrophilicity, are more susceptible to be attacked by microorganisms, either in abiotic or biotic environment [START_REF] Sable | Studies on Biodegradability of Cobalt Stearate Filled Polypropylene After Abiotic Treatment[END_REF][START_REF] Gharehdashli | Photodegradation of low-density polyethylene with prooxidant and photocatalyst[END_REF].

In this report, the aforementioned approaches were combined to create a blend that poses little environmental risk when discarded after use. Two types of blends have been prepared: (i) blends based on PE/PCL with and without (Ethylene-co-Glycidyl MethAcrylate) (EGMA) as copolymer, and (ii) blends containing Ox-PE (PE with pro-oxidant) and PCL at a fixed blending ratio of Ox-PE75/PCL25 (wt%/wt%). The physicochemical properties of these blends were assessed using analytical techniques such as Fourier Transform InfraRed spectroscopy (FTIR), Scanning Electron Microscopy (SEM), Differential Scanning Calorimetry (DSC), and Thermo Gravimetric Analysis (TGA).

Experimental

Materials

The low density PE (LDPE 1003/FE/23) was supplied by Total Petrochemicals (Belgium) with a volumetric density of 0.92g/cm 3 , a molecular weight (M w ) of 450,000 g/mol, and a melting point of 111°C. Poly(ε-caprolactone) (PCL) (CAPA 6500) was obtained from Perstorp group (Sweden), possessing a M w ~50,000 g/mol and a melting point about 58-60°C.

The (ethylene glycidyl methacrylate) (EGMA) copolymer (Lotader) was produced by Arkema group (France). The pro-oxidants used in this study, cobalt stearate, manganese stearate, and iron stearate, were synthesized in our Algerian laboratory according to protocols described in [START_REF] Roy | Investigating the role of metal oxidation state on the degradation behaviour of LDPE[END_REF] and [START_REF] Abrusci | Comparative effect of metal stearates as pro-oxidant additives on bacterial biodegradation of thermal-and photo-degraded low density polyethylene mulching fi lms[END_REF].

Sample Preparation

PE-PCL-compatibilizer blends

The homopolymers LDPE, PCL were dried at 40°C for 24h. The PE/PCL blends were prepared with different ratios of PCL ranging from 0 to 100 weight% (wt%). The compatibilizer EGMA was added to the PE75/PCL25 blend at two concentrations 1 and 5 Phr.

The melt blending for all formulations was carried out at 130°C and 40 rpm for 20 min in a Brabender plasticorder® equipment (Duisburg, Germany).

For simplicity reasons, the designation 75/25 PE/PCL will be used instead of writing 75wt%/25wt% PE/PCL. The PE75/PCL25 blend was selected for two reasons, firstly PE should present the major part of the mixture to investigate its degradation, and secondly, observations of sample morphology by SEM of this blend showed a continuous PE phase including dispersed PCL spheres as minority phase. EGMA was chosen as compatibilizer following promising results obtained for a PE/polyester system [START_REF] Sadik | Polyolefins/Poly(3-hydroxybutyrate-co -hydroxyvalerate) blends compatibilization: Morphology, rheological, and mechanical properties[END_REF]. Applying the PE75/PCL25 blend, low concentrations of EGMA are likely to reduce the size of dispersed nodules and promote compatibility at the interface. The EGMA concentrations applied (1 Phr, 5 Phr) were chosen similar to work on polyolefin/polyester blends [START_REF] Pai | Reactive compatibilization of poly(lactic acid)/polyethylene octene copolymer blends with ethylene-glycidyl methacrylate copolymer[END_REF].

Table 1 describes designation and composition of samples used in this study.

PE/pro-oxidant mixtures

PE was blended with 0.9 Phr of the synthesized pro-oxidants containing 0.3% cobalt stearate, 0.3% of manganese stearate and 0.3% of iron stearate. The melt blending of ingredients was performed in the Brabender plastograph at 140°C and 40 rpm for 10 min. The use of a masterbatch [START_REF] Fontanella | Comparison of biodegradability of various polypropylene fi lms containing pro-oxidant additives based on Mn , Mn / Fe or Co[END_REF], containing the pro-oxidants, presents the advantage to obtain high efficiency compared to the employment of individual pro-oxidants which risk to yield an antagonism effect. The choice of the masterbatch concentration (0.9 Phr) was based on a study of the evolution of the carbonyl level [START_REF] Suresh | Influence of thermal oxidation on surface and thermo-mechanical properties of polyethylene[END_REF], followed by FTIR during 10 days of thermooxidation, to detect oxidation products generated by the degradation of PE.

The extrudate of PE/pro-oxidants (Ox-PE) was placed in an air-circulating oven at 70°C for a period of 10 days in order to catalyze the pro-oxidant and accelerate the thermo-oxidation reaction, which is composed of three stages, initiation, propagation and termination [START_REF] Chatterjee | Enzyme-mediated biodegradation of heat treated commercial polyethylene by Staphylococcal species[END_REF]. In the first stage, the pro-oxidants undergo thermal decomposition, forming unstable free radicals which subsequently react with hydrogens from PE chains. At the propagation stage, alkyl radicals formed during the previous stage react with atmospheric oxygen to create peroxide radicals, which combine with hydrogens from PE chains leading to the formation of hydroperoxides and macroradicals. These hydroperoxides decompose thermally, which leads to the formation of new radicals which make it possible to create other oxidation products (alcohols, ketones, carboxylic acids, etc.). The propagation reactions stop when the generated radicals react with each other to give stable species, insensitive to oxidation.

Ox-PE/PCL blends

Blends containing 75wt% of Ox-PE and 25wt% of PCL (Ox-PE75/PCL25) were prepared in the Brabender plastograph at 130°C and 40rpm for 10 min. Thick films (1 mm) were prepared from the different formulations using a hydraulic press at a temperature of 160°C. FTIR spectra of polymer films were obtained in Attenuated Total Reflection-mode at room temperature in the interval of 500-4000 cm -1 using a Perkin Elmer Frontier model with a spectral resolution of 4 cm -1 applying 32 scans.

Scanning Electron Microscopy

Fractured surface morphologies of polymer films were observed with a FEI Tecnai 200 kV SEM applying an accelerating voltage of 15 kV and using energy dispersion X-ray analysis.

The sample surfaces were coated with a carbon layer to avoid electrostatic charging during analysis.

Differential Scanning Calorimetry

DSC measurements of PE, PCL and the elaborated blends were carried out on a DSC 8000 instrument (Perkin Elmer). The samples were prepared by introducing 8 to 10 mg of the polymers into aluminum pans. Three successive heating and cooling cycles were conducted under nitrogen flow, applying a ramp rate of 10°C/min in the range of temperatures from -70°C to 160°C. Only thermograms of the second heating cycles were taken into account for data analysis. The crystallinity degree (Xc) of samples was calculated using the following equation ( 1):

X C (%) = (ΔH m / W × ΔH 0m )*100 (1)
where ΔH m represents the measured fusion enthalpy, ΔH 0m is the fusion enthalpy of 100% crystalline polymers in the blends (PE: 293.1 J/g [START_REF] Moo-Tun | Thermo-oxidative aging of low density polyethylene blown films in presence of cellulose nanocrystals and a pro-oxidant additive[END_REF] and PCL : 139.5 J/g [START_REF] Jing | Shape memory thermoplastic polyurethane (TPU)/poly(ε-caprolactone) (PCL) blends as self-knotting sutures[END_REF]), and W stands for the weight fraction of PE and PCL.

Thermogravimetric analysis

TGA and Differential Thermal Analysis (DTA) were performed on a Pyris 1 TGA device (Perkin Elmer) with a resolution of 1μg. Heating of the sample was carried out from 25°C to 700°C with a rate of 10°C/min under nitrogen atmosphere, and a flow rate of 20 mL/min. The spectra of binary PE/PCL blends as function of composition (Figure 1a) were found to be similar to that of neat PCL. The different characteristic bands of PCL are present in the spectra of the blends, and they are independent of PCL concentration. Figure 1b represents an enlarged view of Figure 1a between 1650 cm -1 and 680 cm -1 . The doublet at 1473-1463 cm -1 , corresponding to symmetric and asymmetric C-H stretching of PE, decreases and merges to form a large band for PCL-containing blends. Moreover, the two bands situated around 730 cm -1 show inversion of their intensities after incorporation of PCL.

Results and Discussion

Structural analysis

These results indicate the presence of certain interactions between PE and PCL chains.

Similar results were obtained by Blázquez-Blázquez et al. [START_REF] Blázquez-Blázquez | Crystalline Characteristics and Their Influence in the Mechanical Performance in Poly(ε-Caprolactone) / High Density Polyethylene Blends[END_REF].

The FTIR spectra of EGMA and PE75/PCL25, containing 0, 1, and 5Phr of EGMA, are

shown in Figure 2. The EGMA spectrum exhibits absorption bands at 997, 910 and 848 cm -1 associated to the epoxy group, a band at 1730 cm -1 indicating the presence of a C═O group, as well as the characteristic bands of PE [START_REF] Pai | Reactive compatibilization of poly(lactic acid)/polyethylene octene copolymer blends with ethylene-glycidyl methacrylate copolymer[END_REF][START_REF] Loyens | Phase morphology development in reactively compatibilised polyethylene terephthalate/elastomer blends[END_REF]. In contrast, peaks from glycidyl groups (EGMA) (997-848 cm -1 ) are imperceptible in the spectra of PE75/PCL25 with 1 and 5 Phr of EGMA. A new small band appears, corresponding to a hydroxyl group (OH) in the region of 3200 cm -1 , indicating a reaction between the epoxy group of EGMA and hydroxyl end groups of PCL [START_REF] Do Nascimento | Effect of copolymers containing glycidyl methacrylate functional groups on the rheological, mechanical, and morphological properties of poly(ethylene terephthalate)[END_REF][START_REF] Cui | An innovative strategy to regulate bimodal cellular structure in chain extended poly(butylene adipate co terephthalate) foams[END_REF]. The spectrum of Ox-PE75/PCL25 blend, displayed in Figure 3, presents nearly the same bands compared to those of PE. The changes, taking place on the Ox-PE75/ PCL25 spectrum, are especially situated in the range from 1400 to 700 cm -1 . They are associated to CH 2 bending mode and C-O-C stretching. One observes also a reduction of the band at 1720cm -1 , and an increase of the doublet at 2944-2865 cm -1 . Such findings could reflect the strong activity of pro-oxidants to induce thermo-oxidation processes in PE phase [START_REF] Maalihan | Effect of colorant, thickness, and pro-oxidant loading on degradation of low-density polyethylene films during thermal aging[END_REF][START_REF] Benítez | Abiotic degradation of LDPE and LLDPE formulated with a pro-oxidant additive[END_REF][START_REF] Nguyen | Thermal oxidation of polyolefins by mild pro-oxidant additives based on iron carboxylates and lipophilic amines: Degradability in the absence of light and effect on the adhesion to paperboard[END_REF][START_REF] Liu | Accelerating the degradation of polyolefins through additives and blending[END_REF][START_REF] Suresh | Influence of thermal oxidation on surface and thermo-mechanical properties of polyethylene[END_REF], which promote generation of peroxyl and /or alkoxyl radicals, formation of carbonyl groups on PE backbone, leading to chain scission, and formation of oxidation products. These processes are extensively described in literature [START_REF] Chatterjee | Enzyme-mediated biodegradation of heat treated commercial polyethylene by Staphylococcal species[END_REF]. Furthermore, the oxidation products generated along the chains during shear melt blending of Ox-PE75/PCL25, can create successful interaction with PCL chains. Indeed, the apparent reduction of the band intensity at 1721 cm -1 (carbonyl group) (Figure 3) and the disappearance of the bands between 1400 and 700 cm -1 may be a significant proof of interaction between Ox-PE and PCL chains during the melting process, which may result in the formation of new polymer chain arrangements. Following these remarks, an attempt was made to visualize by SEM observations the change of compatibility in these blends.

Analysis of morphology

SEM micrographs of fractured surfaces of the elaborated materials are displayed in Figure 4.

In the case of the PE75/PCL25 blend (Figure 4a), a typical morphology of an immiscible system appears where two separate phases, corresponding to each compound, were observed.

They are distributed in the form of a nodular morphology, consisting of a dispersion of spheres (or nodules) of PCL as the minority phase, in the PE matrix, as majority phase.

Figure 4b and 4c indicate that, due to the diffusion effect introduced by EGMA chains at the interface; addition of EGMA causes a decrease of the size of PCL particles in the immiscible PE75/PCL25 blend. This effect is more pronounced for 5 Phr EGMA than for 1 phr. It can be deduced that EGMA act synergistically to reduce the particle size of the dispersed phase. A relatively uniform particle distribution within the matrix was observed. The same effect has been described in literature for other polymer systems [START_REF] Gardella | PLA maleation: An easy and effective method to modify the properties of PLA/PCL immiscible blends[END_REF][START_REF] Sui | The combined effect of reactive and high-shear extrusion on the phase morphologies and properties of PLA/OBC/EGMA ternary blends[END_REF][START_REF] Xia | Highly toughened poly(lactic acid) blends prepared by reactive blending with a renewable poly(ether block amide) elastomer[END_REF]. The DSC curve of PCL exhibits a melting temperature at around 55°C and a crystallization temperature at 35°C. Furthermore, the thermograms of PE/PCL blends present exo-and endothermic peaks corresponding to fusion and crystallization of the homopolymers. In the heating cycle (Figure 5a), the melting temperature (Tm) of PE increases smoothly with incorporation of PCL from 106°C (PE75/PCL25) to 111°C (PE25/PCL75). The cooling cycles of PE/PCL blends present two crystallization peaks, the first one in the range from -101°C to -104°C, and the second one between -31°C and -34°C, which can be attributed to PE and PCL, respectively. The thermal data of all samples are illustrated in Table 2.

A small increase of the crystallization temperature (Tc) of PE as well as a decrease of Tc of PCL was observed with increasing PCL content in the binary PE/PCL blends. This is due to the fact that PE crystallizes at higher temperatures than PCL. As a consequence, PCL chains could undergo confinement effects into small volumes of lamellar crystallized PE [START_REF] Espinosa | Thermal and mechanical properties of UHMWPE/HDPE/PCL and bioglass filler: Effect of polycaprolactone[END_REF]. The degree of crystallinity (Xc) of both PE and PCL phases in the blends shows slightly decreased values compared to those of the neat homopolymers, thus suggesting a certain compatibility between PCL and PE chains. Different explanations have been proposed in literature to understand this behavior [START_REF] El-Rafey | A study on the physical, mechanical, thermal properties and soil biodegradation of HDPE blended with PBS/HDPE-g-MA[END_REF]. 2). The Xc values of PE75/PCL25/EG1 were found to be similar compared to PE75/PCL25. However, at 5 Phr of EGMA, Xc (PE) strongly decreased, which could be attributed to the interface formation by the reaction between the epoxy ring of EGMA and hydroxyl end groups of PCL during melt-blending. This interface contributed to modify interfacial adhesion between PE and PCL, which is in good agreement with results obtained in the literature [START_REF] Kumar | Effect of glycidyl methacrylate (GMA) on the thermal, mechanical and morphological property of biodegradable PLA/PBAT blend and its nanocomposites[END_REF].

Figures 7a and7b represent DSC thermograms of heating and cooling ramps for PE75/PCL25

and Ox-PE75/PCL25 blends, respectively. The results from thermal data analysis were gathered in Table 2. The thermogram of Ox-PE/PCL (Figure 7a) reveals similar thermal events compared to PE/PCL, accompanied with a small increase of the melting temperature of Ox-PE. During the cooling ramps a shift of the crystallization temperature of Ox-PE and PCL to higher temperatures was observed together with a change of the shape of the crystallization curves of PE. Changes of enthalpy and temperature values for PE and PCL in the Ox-PE/PCL system can be explained by the reorganization of polymers chains and formation of new crystalline phases after incorporating pro-oxidants in the PE phase.

The crystallinity degrees of PE and PCL phases in the blend decreased from 21.7% in PE/PCL to 18.2% in Ox-PE/PCL and from 33.1% in PE/PCL to 21.8% in Ox-PE/PCL, respectively. This reduction of the crystallinity in the PE phase can be explained by the incorporation of pro-oxidants in the PE matrix, which initiate the oxidation process in the polymeric chain and lead to the formation of polar groups [START_REF] Mandal | Thermal degradation kinetics of oxo-degradable PP/PLA blends[END_REF][START_REF] Gharehdashli | Photodegradation of low-density polyethylene with prooxidant and photocatalyst[END_REF][START_REF] Panahi | Investigating the degradability of polyethylene using starch, oxo-material, and polylactic acid under the different environmental conditions[END_REF][START_REF] Sable | Studies on Biodegradability of Cobalt Stearate Filled Polypropylene After Abiotic Treatment[END_REF].

The decrease of crystallinity of the PCL phase in Ox-PE/PCL system is related to the sample morphology. Indeed, the decrease of the size of the dispersed phase in the Ox-PE/PCL blend, compared to the PE/PCL system (Figure 4), provokes a reduction of the crystallinity of the PCL phase. Similar results were reported by several authors for other polymer systems [START_REF] Su | The effects of carbon nanotubes selective location on the structures and properties of polyphenylene sulfide/polyamide 66 fibers[END_REF].

Thermogravimetric analysis

The results of TGA analysis of neat homopolymers and the different blends are illustrated in Figure 8, and the important degradation temperatures are presented in Table 3. T onset is the temperature corresponding to 5% of mass loss, T f corresponds to the temperature of the end of degradation related to a mass loss of 95%, and T dmax stands for the temperature corresponding to the maximum of mass loss. TGA curves of pure PCL and PE showed single decomposition steps with T dmax of 409°C and 496°C, respectively (see Figure 8b). PE starts degradation at around T onset = 411°C and finishes at around T f = 496°C, whereas PCL begins the degradation process at T onset =367°C, ending at T f = 448°C. Figure 8a as well as Table 3 indicates that PE is thermally more stable than PCL, since it degrades at higher temperatures.

Table 3

TGA data of PE, PCL and their blends.

The PE75/PCL25 blends show an intermediate behavior between PE and PCL (Figure 8a) with a decomposition temperature comprised between those of PE and PCL. Indeed, PCL decomposes at a lower temperature than PE. The PE75/PCL25 binary blend exhibits a twostate decomposition process which can be seen in the thermograms where two main peaks appeared at 409°C and 475°C, which can be attributed to the decomposition processes of PCL and PE, respectively. Similarly, two decomposition states were also observed when EGMA was incorporated into the PE75/PCL25 blend (Figure 8), yielding only small changes in T onset and T f compared to PE75/PCL25. This is probably due to enhanced interaction between the epoxy group of EGMA and the hydroxyl group of PCL.

Samples

However, in the case of the Ox-PE75/PCL25 blend, Figure 9a, b and Table 3 show a reduction of T onset of about 20°C compared to the other systems (PE, PCL, PE75/PCL25).

This may be attributed to the catalyst effect of the pro-oxidant and its efficiency to accelerate degradation process of PE [START_REF] Madhu | Physico-mechanical properties and biodegradation of oxo-degradable HDPE/PLA blends[END_REF].

These modifications, occurring in the PE matrix, promote the Ox-PE75/PCL25 system to begin thermal degradation at lower temperatures than the other blends, resulting in a decrease of thermal stability.

Conclusions

In this paper, several approaches have been developed to enhance compatibility between PE and PCL, which can be a solution for the treatment of end-of-life PE waste.

A series of PE/PCL blends were prepared and examined. FTIR and DSC results showed certain interaction between PE and PCL chains. EGMA copolymer was used in an attempt to increase compatibility within PE/PCL blends. Morphology analysis demonstrate that the size of the dispersed phase was slightly decreased in the presence of EGMA which can be explained by the reaction between hydroxyl end groups of PCL and epoxy group of EGMA at the interface. However no significant change in thermal degradation was achieved.

Structure modification of PE was realized by thermo-oxidation in the presence of prooxidants. The crucial point consists in the fact that this thermo-oxidation was performed before PE was mixed with PCL. This is the principal reason for the creation of interaction and thus enhancement of compatibility, yielding a decrease of crystallinity and thermal stability.

The trick of adding pro-oxidants to the PE matrix before blending with PCL ensured that thermo-oxidation took place on the PE chain. This method of elaboration allows developing a new strategy to obtain compatibility in melt blending with PCL or other biodegradable polymers, meeting thus the challenge of preventing pollution in the environment caused by end-of-life PE.

Figure

  Figure1arepresents FTIR spectra of homopolymers PE, PCL and their blends. The spectrum of PE reveals doublets at 2919-2851 cm -1 and 1473-1463 cm -1 , associated to symmetric and asymmetric (CH 2 ) stretching and bending deformations of CH 2 , respectively. A low absorption band at 1376 cm -1 can be attributed to symmetric deformation of methyl groups. A band appearing at 730-719 cm -1 corresponds to rocking deformation of methylene groups (CH 2 )[START_REF] Gulmine | Polyethylene characterization by FTIR[END_REF].In neat PCL, CH 2 groups manifest themselves in several positions: a doublet at 2944-2865 cm -1 corresponding to symmetric and asymmetric (CH 2 ) stretching, and the band at 726 cm -1 can be attributed to CH 2 vibration. The intense peak at 1723 cm -1 can be assigned to the stretching of the carbonyls (C=O) of the ester groups. The different peaks observed at 1470, 1397, 1368 cm -1 are associated to CH 2 bending mode; peaks at 1243, 1108 and 1045 cm -1 can be attributed to C-O-C stretching. Other bands between 1164 cm -1 and 1194 cm -1 are also associated to C-O and O-C-O stretching, respectively[START_REF] Fakhri | Impact of poly(ε-caprolactone) on the thermal, dynamic-mechanical and crystallization behavior of polyvinylidene fluoride/poly(ε-caprolactone) blends in the presence of KI-6 mesoporous particles[END_REF].

Fig. 1 .

 1 Fig. 1. (a) ATR-FTIR spectra of PE, PCL, and their blends; (b) the same spectra in the wavenumber range between 1800 and 700 cm -1 .

Fig. 2 .

 2 Fig. 2. FTIR spectra of EGMA, PE75/PCL25 compatibilized with 1 and 5Phr of EGMA.

Fig. 3 .

 3 Fig. 3. FTIR spectra of PE, PCL, PE75/PCL25 and Ox-PE75/PCL25.

Fig. 4 .Figures 5

 45 Fig. 4. SEM micrographs of the fracture surface of (a) PE75/PCL25, (c) PE75/PCL25EG1, (d) PE75/PCL25EG5 and (d) Ox-PE75/PCL25.

Fig. 5 .

 5 Fig. 5. Thermograms of (a) second heating, (b) cooling curves recorded at a scan rate of 10°C/min for PE, PCL and PE/PCL binary blends.

Fig. 6 .Figure 6 .

 66 Fig. 6. DSC thermograms of (a) heating and (b) cooling ramps for PE75/PCL25 blends in the presence of 1 and 5 Phr of EGMA.

Fig. 7 .

 7 Fig. 7. DSC thermograms of (a) heating and (b) cooling ramps for PE75/PCL25 and Ox-PE75/PCL25 blends.

Fig. 8 .

 8 Fig. 8. a) TGA and b) DTA curves of neat homopolymers and their blends.

Fig. 9 .

 9 Fig. 9. a) TGA and b) DTA curves of PE75/PCL25 and Ox-PE75/PCL25.

Table 1

 1 Composition and designation of the prepared samples

	Composition and	PE (wt %)	PCL (wt %) EGMA (Phr)	Pro-oxidant (Phr)
	designation
	PE	100	0	/	/
	PE75/PCL25	75	25	/	/
	PE50/PCL50	50	50	/	/
	PE25/PCL75	25	75	/	/
	PCL	0	100	/	/
	PE75/PCL25EG1	75	25	1	/
	PE75/PCL25EG5	75	25	5	/
	Ox-PE75/PCL25	75	25	/	0.9

Table 2

 2 Thermal properties of neat LDPE, PCL and their blends obtained from DSC thermograms.

	Sample	Heating cycle

Acknowledgements

The first author (H.B.) received a scholarship under the Profas B+ PhD-program between Algeria and France. Our thanks therefore go first of all to the various actors who participated in the implementation of this program. The authors gratefully acknowledge the support of the Algerian Ministry of Higher Education and Scientific Research (MESRS), the General Directorate of Scientific Research and Technological Development (DGRSDT) of Algeria, the University of Sétif/Algeria, the French Ministry of Higher Education and Research (MENESR), the CNRS, and the University and the CROUS of Lille/France.