Marco Scala
email: marco.scala@ifpen.fr

Lionel Gamet
email: lionel.gamet@ifp.fr

Louis-Marie Malbec

Huai-Zhi Li

Hydrodynamics of gas-liquid

Keywords: CAD Computer-Aided Design PIV Particle Image Velocimetry SMX Kind Hydrodynamics, Sulzer static mixer SMX TM, Multiphase flow, G-L dispersions, Process intensification, Particle image velocimetry (PIV)

performance and thus to open new industrial applications involving gas-liquid flows such as striping and purification of liquids by a gas.

List of symbols

Symbol

Units Description

d

List of abbreviations

Abbreviation Description

Introduction

In chemical industrial processes, the mixing and blending of fluids is a common and widely used operation. One of the main objectives of this process is to increase the interfacial area between the phases to improve mass and heat transfer in order to facilitate heterogeneous chemical reactions. Stirred tanks and bubbles columns are largely utilized as reactors to achieve the mixing and blending tasks [START_REF] Sánchez Pérez | Shear rate in stirred tank and bubble column bioreactors[END_REF]. Certain developments and studies in mixing have revealed that similar results can be achieved by using alternative devices such as static mixers [START_REF] Thakur | Static Mixers in the Process Industries-A Review[END_REF]. The static mixers consist of a series of elements. Each of them is designed to split and recombine the flow [START_REF] Heyouni | Hydrodynamics and mass transfer in gasliquid flow through static mixers[END_REF].

Over the last two decades, the research on static mixers gained renewed interest due to an increasing demand for efficient mixing devices in the industry. Compared to stirred tanks, the static mixers do not have any mobile part and present good mixing performance for a reduced energy consumption [START_REF] Thakur | Static Mixers in the Process Industries-A Review[END_REF]. Furthermore, they present low maintenance cost and easy installation (Madhuranthakam et al. 2009b).

In recent decades, the growing number of studies led to the birth of more and more geometries to cover a wide range of industrial applications. Several designs of static mixers are available nowadays. A classification based on the internal structure of the basic element allows us to assemble them into five mains categories: open design with helical elements, open design containing blades, multilayers design, corrugated plates design and closed design in which the elements have helical or blade shapes [START_REF] Thakur | Static Mixers in the Process Industries-A Review[END_REF].

Much of the current literature on static mixers pays attention to the examination of mixing capacity of liquid/liquid dispersions and related applications. For instance, several authors have estimated the mixing performances for several mixer geometries by injecting polymers, by injecting dye fluids, by performing CFD simulations, or by using Laser Induced Fluorescence technique in the static mixers [START_REF] Pahl | Static Mixers and Their Applications[END_REF][START_REF] Rauline | Numerical investigation of the performance of several static mixers[END_REF][START_REF] Lemenand | Droplets formation in turbulent mixing of two immiscible fluids in a new type of static mixer[END_REF][START_REF] Meijer | On the performance of static mixers: A quantitative comparison[END_REF][START_REF] Das | Laminar liquid-liquid dispersion in the SMX static mixer[END_REF][START_REF] Ghanem | Static mixers. Mechanisms, applications, and characterization methods -A review[END_REF][START_REF] Montante | Blending of miscible liquids with different densities and viscosities in static mixers[END_REF]. Other authors investigated the static mixers using the PIV mainly in single phase or liquid-liquid flows in recent years [START_REF] Voulgaropoulos | Optical measurements in evolving dispersed pipe flows[END_REF][START_REF] Alekseev | Experimental investigations of velocity fields in packed bed static mixers[END_REF]. To the best of our knowledge, the high frequency PIV has never been employed in gas-liquid flows in previous works.

A considerable number of studies have sought to determine the most suitable device conformation for each industrial application [START_REF] Hobbs | Optimization of a static mixer using dynamical systems techniques[END_REF][START_REF] Byrde | Optimization of a Kenics static mixer for non-creeping flow conditions[END_REF][START_REF] Rauline | A Comparative Assessment of the Performance of the Kenics and SMX Static Mixers[END_REF][START_REF] Ugwu | Improvement of mass transfer characteristics and productivities of inclined tubular photobioreactors by installation of internal static mixers[END_REF][START_REF] Regner | Effects of geometry and flow rate on secondary flow and the mixing process in static mixers-a numerical study[END_REF][START_REF] Meijer | On the performance of static mixers: A quantitative comparison[END_REF][START_REF] Paglianti | A mechanistic model for pressure drops in corrugated plates static mixers[END_REF][START_REF] Park | Effect of static mixer geometry on flow mixing and pressure drop in marine SCR applications[END_REF]). In gas/liquid dispersions, an open geometry with blades is usually recommended and employed [START_REF] Thakur | Static Mixers in the Process Industries-A Review[END_REF]Madhuranthakam et al. 2009a). In recent decades, there has been an increasing amount of literature and studies on gas/liquid dispersions using static mixers [START_REF] Chisti | Mass transfer in external-loop airlift bioreactors using static mixers[END_REF][START_REF] Paul | Handbook of industrial mixing[END_REF][START_REF] Taweel | Using in-line static mixers to intensify gas-liquid mass transfer processes[END_REF][START_REF] Fradette | Gas/liquid dispersions with a SMX static mixer in the laminar regime[END_REF][START_REF] Keshav | Liquid phase residence time distribution for gas-liquid flow in Kenics static mixer[END_REF]Madhuranthakam et al. 2009a;[START_REF] Tizaoui | The modelling of ozone mass transfer in static mixers using Back Flow Cell Model[END_REF]. In view of all that has been mentioned so far, one may suppose that the SMX TM Sulzer static mixer is highly adapted for this dispersion, since this mixing device is structured with oblique open blades. The present study examines the interaction between two different phases of a gas-liquid dispersion and the SMX in a laminar flow regime. Local turbulent perturbations cannot be excluded.

As a starting point of the investigation, the organic liquid is kept stationary and its motion is induced by gas bubbles rising through it. Among classical gas-liquid contactors, the liquid phase is usually stagnant in bubble columns while it can be either stagnant or mobile in structured packings [START_REF] Engel | Fluid Dynamics of Packings for Gas-Liquid Contactors[END_REF][START_REF] Wild | Some Aspects of the Hydrodynamics of Bubble Columns[END_REF][START_REF] Luo | Effect of Channel Opening Angle on the Performance of Structured Packings[END_REF]. The static mixers are quite similar to packings. Even if the liquid motion was effectively considered in this work, the negligible effect compared to a stagnant liquid allowed to focus on the case of a stagnant liquid. The major objective of this work is to apply sophisticated methods to analyze the behavior of the SMX TM Sulzer static mixer in these conditions. Furthermore, the stagnant liquid allowed either to perform the analysis with fewer errors or to serve as a reference for further investigation with a flowing liquid.

The initial objective of this study is to address the feasibility of using static mixers for G/L applications in chemical engineering, like for liquid stripping or for treatment of gases. The results gained in this study will be further harnessed to develop a model of G/L interfacial exchange in the SMX TM Sulzer static mixer as well as a bubble breakup and coalescence model. The present paper characterizes the hydrodynamics of the SMX by using two optical methods: the Particle Image Velocimetry (PIV) and the Backlight Shadowgraph Technique (BST). The above techniques were commonly employed to investigate the hydrodynamics of multiphase flows [START_REF] Chen | Particle Image Velocimetry for Characterizing the Flow Structure in Three-dimensional Gas-Liquid-Solid Fluidized Beds[END_REF][START_REF] Delnoij | Ensemble correlation PIV applied to bubble plumes rising in a bubble column[END_REF][START_REF] Delnoij | Measurement of gasliquid two-phase flow in bubble columns using ensemble correlation PIV[END_REF]Deen et al. 2002a;Deen et al. 2002b;[START_REF] Boyer | Measuring techniques in gas-liquid and gasliquid-solid reactors[END_REF][START_REF] Zaruba | Experimental study on bubble motion in a rectangular bubble column using high-speed video observations[END_REF][START_REF] Deen | On image pre-processing for PIV of single-and two-phase flows over reflecting objects[END_REF]Willems et al. 2010;[START_REF] Sathe | Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows[END_REF][START_REF] Sobieszuk | Hydrodynamics and Mass Transfer in Gas-Liquid Flows in Microreactors[END_REF][START_REF] Sathe | Characterization of turbulence in rectangular bubble column[END_REF][START_REF] Ayati | Combined simultaneous twophase PIV and interface elevation measurements in stratified gas/liquid pipe flow[END_REF][START_REF] Laupsien | Bubble Plume Oscillations in Viscous Fluids[END_REF]). Most of the previous studies used these optical techniques for studying bubble columns, microreactors and gas-liquid-solid fluidized beds. For instance, Deen et al.

(2010) introduced innovative PIV pre-processing technique for single and two phases flows. [START_REF] Willems | Use of Particle Imaging Velocimetry to measure liquid velocity profiles in liquid and liquid/gas flows through spacer filled channels[END_REF] used PIV in liquid and gas/liquid flows through spacer filled channels.

In the present study, we applied similar techniques to quantify the flow pattern inside the SMX static mixer. The main objective of this work is to present an innovative experimental investigation of gas-liquid flows in the static mixers. Furthermore, the main advantages and drawbacks of the Backlight Shadowgraph Technique (BST) and Particle Image Velocimetry (PIV) were reported. The gas hold-up in different operating conditions is also estimated. This is an important parameter as it is related to the interfacial area between the phases. The effect of the SMX mixing elements on the velocity flow field is quantified.

As mentioned above, experiments with liquid circulation, both counter-current and cocurrent, were nevertheless carried out to verify the congruence of results. The findings highlighted no relevant difference when the liquid flows in the laminar regime, namely Re < 15 [START_REF] Li | Pressure Drop of Newtonian and Non-Newtonian Fluids Across a Sulzer SMX Static Mixer[END_REF]). The bubbles distributions, mean bubble diameters and velocities remained almost unchanged. The highest deviations observed of these last two parameters were lower than 2%.With respect to bubbly flows in a bubble column without internals, a static mixer in a column opens new applications for gas-liquid flows and also presents more challenging issues as packing optical obstruction for the PIV technique. To our best knowledge, there is no work reported yet in the literature within a transparent static mixer thanks to the recent technique of 3D printing.

Experimental setup

Fluids used in the experiments

For the present research, the normal-heptane was chosen as continuous phase. This liquid compound represents an optimal compromise between similar physical properties to some industrial feed (gasoline, for instance) and safety issues in the laboratories. Furthermore, the n-heptane's chemical inertness ensures the reproducibility of the experiments. For the gas phase, nitrogen was selected to be the dispersed phase because it is a non-reactive and stable compound. Taken together, both fluids guaranteed a high number of re-uses of the same solution. The n-heptane has a density of 684 kg/m 3 and a viscosity of 4.10 x 10 -4 Pa s. The surface tension between the nitrogen and the n-heptane is 0.020 N/m. Three different flow rates were examined: 1 L/h, 2.5 L/h and 5 L/h. The corresponding superficial velocities were 1.35 mm/s, 3.37 mm/s and 6.74 mm/s.

Set-up

The investigation methodologies, namely PIV and shadowgraph technique, require a clear optical access to the system. This conducted us to use transparent materials. The cylindrical column, made of glass, was placed inside a box of squared section in order to reduce image distortion. This external jacket was filled with n-heptane as well. Thanks to the above strategy, optical distortion was completely avoided. The degree of image distortion was checked by inserting a ruler inside the column and by verifying the calibration between the real sizes and the sizes collected by the camera lens.

The behavior of the bubble column, namely the empty column without the SMX mixer inside, was analyzed as well. Data gathered from the bubble column revealed to be useful for a comparison with SMX static mixers. The column has a diameter of 16.2 mm and its height is 450 mm. The SMX TM Sulzer geometry was employed in all the experimental analyses performed. The static mixers are constituted by an elementary unit, usually called element, which is repeated and rotated along the main axis. The number of mixer elements depends on the application of the device. Moreover, the number of mixer elements characterizes the device and has a considerable influence on its behavior [START_REF] Settles | Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media[END_REF].

Fig. 1 depicts one of the mixer structures used during the experiments. The device reported has 10 mixing elements. Mixers with 5 and 15 elements were examined as well. As presented in Fig. 1, each element is rotated by 90 degrees with respect to the previous one. Moreover, the elements are made by a series of inclined blades to 45 degrees from the axis. The standard SMX Sulzer presents some geometric constraints such as the unitary ratio of the element length over its diameter. was possible to make fully transparent plastic SMX mixers. The Accura ClearVue™ refractive index is 1.5 whereas that of n-heptane is 1.39. These values proved to be close enough to ensure satisfactory transparency for the optical visualization (cf. Fig. 9). These mixers present the same element dimensions, as shown in Fig. 1. The width (resp. thickness) of a single crossbar is 1.98 mm (resp. 1 mm). The length and diameter of an element is 15.8 mm. The ratio between diameter and length of an element is thus 1, which conforms to the standard SMX definition [START_REF] Liu | Design modifications to SMX static mixer for improving mixing[END_REF][START_REF] Settles | Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media[END_REF]). The 5, 10, 15 elements devices have an overall length of 79, 158 and 237 mm respectively. The distance between the top of the gas injector and the mixer was kept constant at 100 mm during all the tests. This space was largely enough for bubbles to reach their steady state rising velocity.

The nitrogen flow rate was controlled through an electronic valve connected to a flow regulator. The flow controller employed (Brooks Instrument Flow Controller) is accurate as the maximum potential error during the flow regulations is lower than 2%. The effect of two different nozzle diameters was analyzed, namely 0.25 mm and 1 mm. The nitrogen inlet pressure was settled and maintained to 2 bars using a pressure regulator valve.

Measurement techniques

The measurement methods adopted were the Backlight Shadowgraph Technique (BST)

and the particle image velocimetry (PIV). The objective was to estimate the gas hold-up, the bubbles' sizes, shapes, paths and rising velocities inside the static mixer. The liquid velocity fields were quantified as well through the high-speed PIV. To estimate the gas hold-up, a series of images was collected with a very low frequency, namely 5 Hz. The first frame of the series was acquired without gas. This first frame measured the initial state of the liquid level.

Then, by injecting the gas, images with a higher liquid level were recorded. The presence of nitrogen bubbles within the system increases the overall liquid volume. This volume difference was estimated by comparing the first image with the others. The software imageJ® was employed to make the calibration and to estimate the increment of the liquid level.

The Particle Image Velocimetry

Particle Image Velocimetry (PIV) is an optical and non-intrusive methodology to measure instantaneous flow velocities [START_REF] Link | Validation of a Discrete Particle Model in a 2D Spout-Fluid Bed Using Non-Intrusive Optical Measuring Techniques[END_REF]). This technique is based on image processing of two consecutive frames acquired at a known time interval [START_REF] Sathe | Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows[END_REF]). The PIV is commonly employed to examine liquid flow or gas-liquid flow [START_REF] Sathe | Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows[END_REF]) even with relatively high gas holdup (Deen et al. 2002b;[START_REF] Liu | Study of Bubble Induced Flow Structure using PIV[END_REF][START_REF] Kováts | Characterizing fluid dynamics in a bubble column aimed for the determination of reactive mass transfer[END_REF]. In our PIV measurements, a method similar to that described in [START_REF] Deen | Comparison of PIV and LDA Measurement Methods Applied to the Gas-Liquid Flow in a Bubble Column[END_REF] and [START_REF] Funfschilling | Flow of non-Newtonian fluids around bubbles. PIV measurements and birefringence visualisation[END_REF] was used. In multiphase flows, the PIV shows certain limitations [START_REF] Raffel | Particle Image Velocimetry. A Practical Guide[END_REF][START_REF] Funfschilling | Flow of non-Newtonian fluids around bubbles. PIV measurements and birefringence visualisation[END_REF]). Among them, the major limitations encountered in this study were the sedimentation of the seeding particles, and the shadows created by SMX and bubbles. Lastly, the light diffraction on the phase boundaries, SMX and column walls required the use of a specific strategy. The above limitations were partially resolved by employing suitable fluorescent seeding particles. The seeding particles used are fluorescently labelled polystyrene particles (PS-FluoRed). The tracer formation process generates polymer particles with optimal properties such as high monodispersity, spherical shape, brilliant fluorescence and minimized dye leaching into the surrounding medium. These spherical particles have a diameter of 25.07 μm with a standard deviation of 0.20 μm, their density is 1.05 g/cm 3 , and their refractive index is 1.59. Furthermore, they have the property to absorb the laser light with a wavelength of 532 nm and to emit it with a wavelength of 607 nm. This specific property allowed us to use a filter to remove all of the reflected and scattered laser light from the static mixer, the column, and the bubbles. This filter allowed only the light with wavelength between 595 nm and 615 nm to reach the camera lens. The above strategy improved the quality of the investigation significantly. One major drawback of this tracer is its sedimentation velocity of up to 0.3 mm/s estimated with the Stokes law (G. Stokes 1850).

This value was confirmed by the PIV results as well. The corresponding Stokes' relaxation time is 89 µs for these seeding particles and can be considered suitable enough for the time scale during the PIV experiments.

The sedimentation drove us to remove the solution from the column at the end of each experiment. The solution containing the particles was then collected in a dedicated agitation system that ensured its homogeneity. This approach guaranteed reliable results and repeatability of experiments. The PIV images were acquired through a high-speed and highresolution camera, namely the FASTCAM SA-Z with 12-bit dynamic range and a resolution of 1 024 x 1 024 pixels. This camera is equipped with a highly light-sensitive image sensor (monochrome ISO 50,000). The high power diode pumped Nd:YAG Laser was employed in the PIV investigation. This is a dual oscillator head with a high repetition rate and an average power of 120 W. Two different frequencies were used to perform data acquisition. The instantaneous flow velocities were acquired at 100 Hz. The laser time pulse ranged from 2 ms to 8 ms (from 500 Hz to 125 Hz) with a view to achieve the optimal displacement of the particles between the two consecutive frames required for the velocity field computation. The laser and the camera were connected via TTL inputs/outputs with a high efficiency synchronizer. The laser emits high-energy, monochromatic light with a wavelength of 532 nm. For each configuration, namely with different gas superficial velocities, mixer length and diameter of the injector, 7 500 flow fields were acquired in total and processed to obtain the averaged flow field. The 7 500 fields were collected through 5 different repetition tests, each corresponding to 1 500 flow fields. For each test, the solution containing the seeding particles was removed from the column and stirred for at least 2 minutes before reuse.

The pulsed light was converted into a laser sheet by using a series of curved mirrors and lenses. The laser sheet was focused in the middle section of the column, along the axial direction, and the lighted seeding particles located on this plane were then acquired by the camera. The laser sheet can be considered two-dimensional because of its small thickness in the orthogonal direction. The plane position and thickness in both sides of the jacket were checked daily and kept constant. The calibration, the distance between the camera lens and the column, and the relative position of both devices were controlled as well. To increase the quality and the resolution of acquisitions, the SMX mixers' elements were examined in groups of five. This decision represents a fair compromise between image quality and the number of elements visualized on each image. Data were collected and analyzed by DaVis-LaVision® software. These PIV images were subdivided into small interrogation windows.

The seeding particles' displacement within these windows were measured by crosscorrelation of two consecutive frames. The velocity fields were calculated from the time interval between the frames (Δt) and the measured displacement. The adaptive PIV scheme was selected in order to achieve the suitable image treatment. The multi-pass option permitted to decrease progressively the investigation window size. The window ranged from 64 x 64 pixels to 8 x 8 pixels. The noise was removed by applying a Gaussian filter. The Davis posttreatment algorithm and image-filtering allowed proper phase discrimination: the bubbles were completely removed by the PIV raw images if they were located on the laser plane.

The shadowgraph

In addition to the PIV applied to the continuous liquid phase, the shadowgraph was implemented to achieve an accurate estimation of bubbles' sizes and velocities as a tracking technique for the dispersed phase. This method of analysis is frequently used to investigate dispersed systems characterized by high contrast between the phases [START_REF] Settles | Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media[END_REF]. The images acquisition setup used in the experiments is analogous to the one described by [START_REF] Laupsien | Bubble Plume Oscillations in Viscous Fluids[END_REF]. The technique is based on the shadows created by bubbles rising in the stagnant n-heptane. A EFFILUX LED panel was mounted behind the column as a light source. The distance between the panel and the column was 0.7 m. The monochrome LED panel ensured a homogeneous lighting and provided a high illumination density (max 4000lm). Particular care was given to the LED panel position, optimized to prevent any shadowing and reflection phenomena. Well-outlined shadows were created by the bubbles.

The recording of these shadows was obtained by a high-speed camera located in front of the column. The same camera as for the PIV was employed. The lens was changed, and the filtering system removed. As previously mentioned, the cylindrical column produces a lens effect totally cancelled out by the surrounding square jacket filled with n-heptane. It is worth noting that the refractive indices of heptane, glass and the plastic material of the mixers are close to each other. The mixer and the column are thus almost invisible from outside the cubic box.

Photron-FASTCAM® enabled full control of the camera parameters, such as the frame acquisition rate, the image resolution, and the exposition time. The acquired images had a resolution of 256 x 1024 pixels, corresponding to 25 x 100 mm (about 10.2 pixel/mm).

Although the camera employed was capable of acquiring up to one million frames per second, a frequency of 500 fps was considered suitable for the shadowgraph investigation. In fact, this acquisition frequency permitted to obtain an optimal mean bubble displacement between two consecutive frames, corresponding to 0.1 -0.2 mm. Monitoring displacements below this range requires a higher acquisition frequency, leading to an increase of the amount of data recorded and it complicates post-processing. Higher frequency tests were conducted and led to the same results.

As for the PIV experiments, the shadowgraph tests of the SMX were conducted by splitting the elements into groups of five elements to achieve an optimal image resolution. To increase the reliability of the PIV and shadowgraph imaging technique, each experiment was repeated five times with five-minute intervals between them. An algorithm for the post-treatment of the images was implemented in Halcon®. As the first step of the post-treatment, the background of the images was isolated and removed from each frame and the contrast between the liquid and gaseous phase was artificially increased. A threshold permitted us to isolate the bubbles. A region number was assigned to each bubble. Subsequently, the Halcon®'operator elliptic_axis was chosen to estimate the bubbles' size and position. The operator elliptic_axis estimates the radii R a and R b and the orientation of the ellipse having the same aspect ratio of the input region. The optical_flow_mg operator with the FDRIG algorithm was employed to compute the optical flow between two images [START_REF] Brox | High Accuracy Optical Flow Estimation Based on a Theory for Warping[END_REF]).

This optical flow represents the movement between two consecutive images and allowed the estimation of the bubbles' velocities. The Halcon® algorithm is able to determine bubbles' velocities, formation frequency, position and shape.

Results and discussion

Gas hold-up

The gas hold-up experiments were conducted using both the plastic SMX mixers and the empty bubble column. Increments of the n-heptane level were measured once nitrogen bubbles were generated in the system. The initial liquid level (h i ) and the expanded liquid level after gas injection (h f ) were measured by analyzing the image sequences. Measure errors in locating the liquid head cannot be prevented because of its fluctuation. In fact, bubbles burst at the heptane surface and induced oscillations. To compensate for these perturbations, several images were acquired to average the liquid level. In order to assess reliable values of hold-up, repeated calibration was performed to obtain scale factor from pixel to mm. At least 50 images were averaged to estimate the mean increment of liquid level. This number of frames was considered acceptable to estimate suitable mean values of the liquid level. The hold-up value revealed, in fact, to be unchanged by increasing the number of frames acquired.

Experiments smaller injector leads to smaller bubbles, then lower terminal velocities, higher residence time and then a higher hold-up of nitrogen. This was found to be true except for the higher superficial gas velocity. This uncommon behavior is mainly due to a transition of the bubbles' formation regime towards a jet regime.

Different considerations can be deducted from the data collected by employing the SMX mixers. The hold-up values resulting from the smaller nozzle (dn = 0.25 mm) and lowest superficial gas velocity (V s =1.35 mm/s) appear to be almost constant. A possible explanation for this peculiar behavior might arise from bubbles' sizes in these conditions. The small bubbles generated can potentially rise into the mixer more swiftly, without interacting with each other, except in the first elements of the device. The coalescence and breakup phenomena are restricted in these circumstances. Looking at all the other cases examined, we notice that the gas holdup increases with the number of elements. The larger nozzle diameter appears to increase the gas hold-up significantly, for all superficial gas velocities (see Fig. 2).

Besides, the effect of the nozzle size on the gas hold-up cannot be neglected even by employing 15 elements. Nevertheless, an equilibrium between coalescence and breakup phenomena cannot be excluded particularly in the last elements of the mixer. These observations are further discussed in the next section.

Particle Image Velocimetry results

The PIV technique was employed to examine the liquid velocity fields in two configurations: the empty column and the column with the SMX. As reported in section 2.3.

Measurement techniques, 7 500 frames were acquired to enhance the accuracy of the results.

The data obtained from the empty column led to the expected results. The velocity fields collected are well delineated: an up-flow was detected near the bubbles rising through the stagnant n-heptane, while a down-flow was measured near the column walls. This is confirmed by both the instantaneous and averaged liquid flow fields. Fig. 3 illustrates some velocity fields obtained by the PIV performed in the column without the SMX. The motion of the liquid phase due to a bubble passage can be identified by looking scrupulously at the picture on the right of Fig. 4, where the bubbles' shapes are reported as well. For instance, an up-flow was observed in proximity of the three rightmost bubbles.

Some velocity fields, however, may not match the expected mid cutting plane pattern through a bubble as in the case of the leftmost bubbles. This is due to the fact that the cutting plane of Fig. 4 is shifted along the third direction with respect to the bubbles' mid centerline plane.

Flow patterns become more complicated to interpret for larger gas superficial velocities due to the presence of numerous bubbles. Indeed, the lower superficial gas velocity employed, namely 1.35 mm/s, allowed to isolate the bubbles. The main liquid flows were located in the zone of bubbles' passage. Up-flows were generally observed in the bubbles' proximity, in front of a bubble and in its wake, when looking in a median cutting plane of the bubble.

Down-flows were usually encountered in the lateral sides of the bubbles' paths. We observed a reduction of the velocities, due to lower bubbles velocities inside the mixer. The bubbles velocities are approximately 2 or 3 times smaller inside the mixer. The PIV results suggest that the bubbles rise in the wake left by the previous ones. This behavior implies some preferential paths in the SMX static mixer. It is worth mentioning that in Fig. 5 the flow field is quite scarce in the upper part of the static mixer (r.h.s) due to the presence of several bubbles in this zone (l.h.s). The gas-liquid interfaces of bubbles reflect the laser, making the tracking of seeding particles difficult.

The high acquisition frequency allowed to detect rapid phenomena like bubble deformation and break-up. On the other hand, the findings in this study are subject to some limitations.

Firstly, the PIV technique is only 2D planar. Furthermore, it was not possible to collect data in the regions close to the SMX elements' bars and in the regions characterized by high values of local hold-up. In fact, the quality of PIV results decreases with the amount of bubbles. The presence of bubbles creates black zones and shadows. In these areas, it was often complicated to measure the flow field. This is a well-known problem of the PIV measurements in multiphase flows [START_REF] Funfschilling | Flow of non-Newtonian fluids around bubbles. PIV measurements and birefringence visualisation[END_REF]. The DaVis-LaVision® software permitted a preprocessing of the raw PIV images capable to remove the bubbles interference and to enhance the light emitted by the particles, namely by filtering and normalizing the pixels intensity. This approach allowed us to partially solve the problem related to the local increment of the gas hold-up. The results from the empty column and the SMX mixer were further compared in order to reveal the effect of the mixing device. We split the velocity vector into two components along the horizontal (Vx) and upward vertical (Vy) directions in order to simplify the following discussions. The horizontal (Vx) and vertical (Vy) liquid velocities' probability distributions found for V s =3.37 mm/s are reported in Fig. 6 and Fig. 7. The possible interference of the particles' sedimentation velocity was removed from the data by subtracting the sedimentation velocity from the vertical components (Vy). The vertical liquid velocities decreased significantly in favor of horizontal velocities in the SMX mixer. The maximum magnitude of the liquid velocities detected inside the static mixer were between 10 cm/s (V s =1.35 mm/s) and 15 cm/s (V s =3.37 mm/s). However, the percentages of high velocities were much lower when the mixer is used than in an empty bubble column. As expected, velocities in the empty bubble column were found to be inherently related to the bubble rising velocities, with maxima of approximately 20 cm/s.

Velocities higher than 0.15 m/s and lower than -0.15 m/s were neglected. However, they represent less than the 0.1 % (resp. 0.05%) for the empty column.

The histogram of vertical velocity component on the right is more spread than the horizontal components histogram, which means that higher axial velocity components (Vy)

were obtained. The probability distribution of the horizontal component (Vx) of the velocities is fully symmetric. Fig. 7 depicts the distribution of liquid velocities found inside the 10 elements mixer. We noted several differences compared to the empty column. They can be explained partly by the particular geometry of the SMX. The 45° bars divert the bubbles' paths, thus causing changes in the velocities of the liquid phase.

Shadowgraph results

The relatively low surface tension between the two phases makes the shadowgraph investigation more interesting because of the higher amount of coalescence and break-up events. To assess the shape and rising velocity of the bubbles, the backlight shadowgraph technique was employed. The number of events collected and examined, ranging from 70 000 to 100 000, was considered large enough to estimate the mean properties of the system [START_REF] Buffo | Experimental determination of size distributions. Analyzing proper sample sizes[END_REF]. The bubble diameter was estimated by applying the hypothesis that bubbles are shaped as ellipsoids [START_REF] Grund | Gas-Liquid mass transfer in a bubble column with organic liquids[END_REF][START_REF] Lage | Experimental determination of bubble size distributions in bubble columns: prediction of mean bubble diameter and gas hold up[END_REF][START_REF] Bouaifi | A comparative study of gas holdup, bubble size, interfacial area and mass transfer coefficients in stirred gas-liquid reactors and bubble columns[END_REF][START_REF] Kazakis | Experimental study of bubble formation at metal porous spargers: Effect of liquid properties and sparger characteristics on the initial bubble size distribution[END_REF]. Based on this assumption, an equivalent bubble diameter can be estimated. This diameter is defined as the diameter of the sphere whose volume is equivalent to the ellipsoidal bubble volume [START_REF] Lage | Experimental determination of bubble size distributions in bubble columns: prediction of mean bubble diameter and gas hold up[END_REF]. This hypothesis was later verified.

The amount of gas contained throughout the system with and without static mixers was recomputed by summing up the volumes of all the bubbles. These integrated values were found comparable with the experimental values reported in the section 3.1. Gas hold-up. The maximal deviation observed is lower than 5%. This dissimilarity could be attributed to the ellipsoidal assumption made about bubbles shapes. The satisfactory comparison between these two different methods reveals the accuracy of the images post-treatment algorithm implemented in Halcon® and Matlab®. The Halcon® treatment has proven to be robust and efficient as it was able to detect more than 95% of the bubbles.

A first set of images was collected to examine the characteristics of bubbles flowing in the empty column. When comparing the bubbles' shapes and velocities in the empty column with the ones detected before the SMX, no significant difference was identified. This suggests that the mixer does not affect the bubble shape and velocity in the upstream region. This observation remains valid in regions far from the SMX, roughly larger than two-cylinder diameters. Fig. 8 provides the density probability distributions of the bubbles' diameter for certain operating conditions in the simple column without a mixing device and at the outlet of the SMX.

From the first plot illustrated in Fig. 8 (a), it can be seen that the distribution obtained using the bigger nozzle is quite narrow around the Sauter diameter. The distribution resulting from dn=0.25 mm and V s =3.37 mm/s presents a different trend, with a secondary peak corresponding to small bubbles (de about 0.8 mm). This is explained by a different detachment regime for the bubbles. It was not possible to predict bubbles' characteristics for the higher gas superficial velocity due to overlaps of bubbles that prevent estimating their diameter.

The equivalent bubble diameters were also measured after the outlet of the static mixers.

As shown in Fig. 8, the bubble distributions changed considerably at the mixer exit of the Zigzag and/or spiral bubble paths were often observed in the experiments. A statistical analysis of the probability to find bubbles throughout the system was performed by analysing the instantaneous images. The results obtained on the column without SMX revealed that the probability of finding a bubble in the centre of the column is higher than near the walls. These results are consistent with those of other studies [START_REF] Saffman | On the rise of small air bubbles in water[END_REF][START_REF] Clift | Bubbles, drop and particles[END_REF][START_REF] Lunde | Shape Oscillations of Rising Bubbles[END_REF]). An identical analysis was performed for the 5, 10 and 15 elements SMX.

Since other SMX lengths lead to similar data, Fig. 9 shows only the 10 elements results.

Compared to the bubble column, the instantaneous and mean probabilities of finding bubbles inside the mixing device are higher. The static mixer is decreasing the bubbles velocities and is therefore increasing their residence time. Another observation emerges from the images of Fig. 9: the bubbles rise in the SMX by following preferential paths. These preferential paths are mainly close to the mixer-inclined bars. Furthermore, zones with a null probability (lower than 0.5%) of finding bubbles can be distinguished (white regions). Down-flows were confirmed in these zones by the PIV technique.

Discussion and validation of optical methods

Both the PIV and the shadowgraph results provide new insight into the two-phase flow pattern inside the static mixer. As shown in Fig. 10, the PIV findings match those observed in the shadowgraph. Up-flows were observed in high probability zones of bubbles passages. On the other hand, down-flows were recorded in low probability areas. The first element of the static mixer was considered appropriate to make this comparison because of its lower measurement errors. operating conditions are available in the literature [START_REF] Harmathy | Velocity of large drops and bubbles in media of infinite or restricted extent[END_REF][START_REF] Mendelson | The prediction of bubble terminal velocities from wave theory[END_REF][START_REF] Wallis | The terminal speed of single drops or bubbles in an infinite medium[END_REF][START_REF] Tomiyama | Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions[END_REF][START_REF] Raymond | A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids[END_REF][START_REF] Tomiyama | Single bubbles in stagnant liquids and in linear shear flows[END_REF][START_REF] Tomiyama | Single bubbles in stagnant liquids and in linear shear flows[END_REF] proposed a correlation that allows the calculation of the terminal velocity for a distorted oblate spheroidal bubble:

𝑉 sin √1 𝐸 𝐸√1 𝐸 1 𝐸 𝜌 𝜌 𝑔𝑑 2𝜌 𝐸 / 1 𝐸 8 𝜎 𝜌 𝑑 𝐸 / (3.2)
In this correlation, only valid for oblate spheroids, the terminal velocity V T depends on the bubble diameter d b , the fluid properties and the aspect ratio E less than 1. The aspect ratio is defined as the ratio of the polar lengths to equatorial lengths. The bubbles' aspect ratio was estimated in order to evaluate the terminal velocity for our experiments. The post-processing of the shadowgraph acquisitions revealed that the value of mean vertical velocity in the empty column is about 19 cm/s when the 1 mm nozzle is used. This value is close to 19.5 cm/s estimated by to the above empirical correlation. Switching from the 1 mm to the 0.25 mm nozzle, the bubbles mean axial velocity decreased to 17.3 cm/s, relatively close to 17.6 cm/s from the correlation of [START_REF] Tomiyama | Single bubbles in stagnant liquids and in linear shear flows[END_REF].

As aforementioned, the rising velocity of bubbles allowed the estimation of their mean residence time. The minimum distance travelled by a bubble was measured by assuming its passage on the shortest path possible, namely moving with a straight path along the axial direction. The bubbles' velocities and their rising path length allowed us to determine the mean residence time under various operating conditions. The findings suggest that the mixer enhances at least twice the mean residence time. The formation frequency of bubbles was also calculated by recording the nozzle area.

Conclusion

The main goal of the present work was to characterize the two-phase hydrodynamics in Sulzer SMX TM static mixers with different lengths. The experimental investigation was performed by bubbling nitrogen in stagnant liquid normal-heptane under various operating conditions: different superficial gas velocities, different mixer lengths and two nozzle sizes.

The bubbles' sizes, shapes, velocities and positions were quantified. An image postprocessing was implemented to estimate the mean Sauter diameter of the bubbles at inlet and outlet of the SMX mixers. The capability to predict the real sizes, the shapes and velocities of bubbles was verified by conducting several comparisons with empirical correlations and data reported in the literature. The liquid velocities were measured by the PIV technique for the first time owing to the transparent 3D printing.

The obtained results reveal that the SMX substantially increases the gas hold-up and the residence time of bubbles. An increase of coalescence and breakup phenomena was observed at high hold-up value under the highest gas superficial velocity. The second major finding was the existence of preferential paths inside the mixer. This could potentially affect the mass transfer throughout the device. Furthermore, this study suggests that the 15 elements SMX is long enough to ensure a dynamic equilibrium between the coalescence and break-up of bubbles flowing through the device. The static mixer exhibited a viable effectiveness in the redistribution of bubble sizes and positions passing across the mixer. Although the coalescence phenomena in the mixer can lead to large bubbles, a considerable percentage of small-scale bubbles (diameter smaller than 0.5 mm) was detected. In future investigations, it might be possible to use the experimental approaches presented in this work in order to collect further data, focusing on bubble breakup and coalescence phenomena.

Caption of figures

Caption of table

Fig. 1 .

 1 Fig. 1. Details of the 10 elements SMX static mixer. The length unit is mm.

Fig. 2 .

 2 Fig. 2. Gas hold-up values for the 0.25 mm (left) and 1 mm (right) nozzle injectors.

Fig. 2

 2 Fig. 2 illustrates the main findings. The comparison of the hold-up values with and without static mixer shows a substantial increase caused by the presence of the mixing device. It is interesting to note that in all of the eighteen cases with the SMX, the hold-up is increased with respect to the simple bubble column. Error bars show the standard deviations and depict the variability among the performed experiments. The results achieved for the empty column match those expected. The values of hold-up detected for the 0.25 mm nozzle suggest that this

Fig. 3 .

 3 Fig. 3. PIV results in the simple column: instantaneous vector field colored by velocity magnitude (l.h.s.) and averaged vector field in the same column section (r.h.s.). Results obtained with dn=1 mm and V s =1.35 mm/s.

Fig. 4 .

 4 Fig. 4. Raw PIV image and instantaneous flow field in the first SMX element (colored by axial component of velocity). dn=0.25 mm. V s =1.35 mm/s.

Fig. 5 .

 5 Fig. 5. Raw PIV acquisition in the first 2 elements of the 10 elements device (l.h.s.) and corresponding instantaneous vector field colored by velocity magnitude (r.h.s.). Results obtained with dn=1 mm, V s =1.35 mm/s.

Fig. 6 .

 6 Fig. 6. Liquid velocities distributions measured in the x-axis component (left) and y-axis component (right) in the column without SMX. dn = 0.25 mm. V s =3.37 mm/s.

Fig. 7 .

 7 Fig. 7. Liquid velocities distributions measured by the PIV in the x-axis component (left) and y-axis component (right) in the column with SMX. dn = 0.25 mm. V s =3.37 mm/s.

Fig. 8 .

 8 Fig. 8. Equivalent diameter distributions measured under different operating conditions: a) empty column, b) outlet of the 5 elements, c) outlet of the 10 elements, d) outlet of the 15 elements. V s =3.37 mm/s.

Fig. 9 .

 9 Fig. 9. Shadowgraph acquisitions and respective bubble occurrence probability detected in the 10 elements SMX fed by dn: 0.25 mm (left) and dn: 1 mm (right).

Fig. 10 .

 10 Fig. 10. Detailed views of the 1 st SMX element. dn: 1 mm. V s =1.35 mm/s. From left to right: a) Instantaneous bubble image, b) Bubble mean occurrence c) Mean PIV velocity field d) Mean vertical velocity profile (Vy).

Fig. 11 .

 11 Fig. 11. Vertical velocity components (Vy) distributions in the simple bubble column (left) and in the 10 elements SMX (right). dn=1 mm. V s =1.35 mm/s.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Details of the 10 elements SMX static mixer. The length unit is mm. ...................... 8

Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .

 4567891011 Fig. 4. Raw PIV image and instantaneous flow field in the first SMX element (colored by axial component of velocity). dn=0.25 mm. V s =1.35 mm/s. ................................................... 18 Fig. 5. Raw PIV acquisition in the first 2 elements of the 10 elements device (l.h.s.) and corresponding instantaneous vector field colored by velocity magnitude (r.h.s.). Results obtained with dn=1 mm, V s =1.35 mm/s. .................................................................................. 20 Fig. 6. Liquid velocities distributions detected by the measurement in the x-axis component (left) and y-axis component (right) in the column without SMX. dn=0.25 mm. V s =3.37 mm/s . ......................................................................................................................... 21 Fig. 7. Liquid velocities distributions detected by the PIV measurement in the x-axis component (left) and y-axis component (right) in the column with SMX. dn=0.25 mm. V s =3.37 mm/s. ......................................................................................................................... 22 Fig. 8. Equivalent diameter distributions measured in different operating conditions: a) empty column, b) outlet of the 5 elements, c) outlet of the 10 elements, d) outlet of the 15 elements. V s =3.37 mm/s. ......................................................................................................... 26 Fig. 9. Shadowgraph acquisitions and respective bubble occurrence probability detected in the 10 elements SMX fed by dn: 0.25 mm (left) and dn: 1 mm (right). .................................. 28

Table 1 :

 1 It should be noted that the presence of the static mixer inside the column does not affect the bubble formation frequency. The formation frequency of bubbles and the flow rate permits the estimation of the bubbles mean diameters. The diameters estimated by the bubbles' shadows are reported in the last column. The maximum deviation is less than 15%. Bubbles characteristics obtained by the post-treatment of the shadowgraph images.

	Nozzle	Superficial	Frequency	Calculated	Shadows
	diameter	gas velocity	formation	diameters	estimated
	[mm]	[mm/s]	[bubbles/s]	[mm]	diameters [mm]
	0.25	1.35	68	1.98	1.91
	0.25	3.37	89	2.45	2.17
	1	1.35	25	2.76	2.70
	1	3.37	45	3.09	3.05

The major results are gathered in Table

1

.

Table 1 .

 1 Bubbles characteristics obtained by the post-treatment of the shadowgraph images. ...................................................................................................................................... 32

Velocities were obtained by tracking the bubble displacement every 0.02 s. This short time interval was required in order to limit errors in the post-treatment process. The wide distribution may be due to both the oscillation of bubble shape and trajectory. In fact, the zigzag and spiral rising causes shape deformation and velocity instability. It is widely documented that the continuous changes of the bubble shape significantly affect the rising velocity [START_REF] Saffman | On the rise of small air bubbles in water[END_REF][START_REF] Mougin | Path Instability of a Rising Bubble[END_REF][START_REF] Tripathi | Dynamics of an initially spherical bubble rising in quiescent liquid[END_REF]. The bubbles' velocities evolved considerably when the SMX was employed. The histogram of the frequency distribution of vertical velocity components is significantly altered as outlined in Fig. 11 (r.h.s.).

The instantaneous bubbles' velocities inside the mixer are scattered over the range 0-24 cm/s. Bubble overlap phenomena in the SMX mixer introduced measurement errors especially for the estimation of the velocities under high gas superficial velocities. The mean axial velocity detected inside the SMX is about 8 cm/s (dn = 1 mm. Vs = 1.35 mm/s). A similar value was found for the horizontal component of the velocity in all of the elements facing the camera. The mean velocity in the first element (12 cm/s) is relatively higher than the others. Furthermore, no relevant changes of bubbles' mean velocity were observed inside the mixer after the third element.

A considerable amount of bubbles shows negligible velocity. These null values were mainly detected in proximity to the SMX crossbars. There are several possible explanations for this behavior. Firstly, the gap between the bars might be smaller than the bubble diameter, acting therefore as an obstacle. Furthermore, the space available decreases in some specific regions such as those at the connections between two consecutive elements. The energy required for the bubbles' deformation significantly affects the velocities.

A comparison between the measured velocity of the bubbles and those estimated by an empirical correlation was done. Various correlations for bubble rising velocity under different


Steven Coats

Adrien Barbaresi

Productivity of Anglicism Bases in Hyphenated German Compounds

Keywords: Anglicisms, German, Compounds, Corpus linguistics, Productivity, Entropy

This study investigates hyphenated German compounds that contain English constituents, a part of the German lexicon that exhibits great diversity. We determine the frequency of a set of English noun bases in different constituent positions in three corpora of online language, and quantify the productivity of bases in these compounds using a metric based on Shannon entropy, a measure of information content. Compound entropy values for English bases reflect their diversity of use, and are unequally distributed for left-hand, internal, and right-hand constituents. The semantics of the base types with the highest frequencies and entropy values reflect contemporary cultural and technological concerns. Differences in entropy according to constituent position may be an indication of word class conversion of anglicisms in German.

Introduction

English is the most important source language for new words in German at present, accounting for the majority of lexical borrowings [START_REF] Onysko | Anglicisms in German: Borrowing, Lexical Productivity, and Written Codeswitching[END_REF]. The prevalence of English in numerous public, job-related and international contexts in German society ensures a broad diffusion of language knowledge, so that a bottom-up diffusion of English-based neologisms and compounds is possible, in a sharp contrast to previous patterns of foreign lexical assimilations, for example of Latin or French words [START_REF] Krome | Anglizismen und andere fremdsprachige Neologismen als Indizien für Sprach-und Schreibwandel: Empirische Analysen zum Schreibusus auf der Basis von Textkorpora professioneller und informeller Schreiber[END_REF]. Anglicisms exhibit a great deal of variation in written German: They can be integrated with minimal modifications (e.g. Discounter), assimilated in morphology and orthography and adapted to German inflectional paradigms (e.g. geliked or gelikt, 'liked on social media') (Burmasova, 2010;Coats, 2018), or serve as the basis for calques (loan translations) and syntactic constructions. Recent research has cataloged their overall diversity [START_REF] Eisenberg | Das Fremdwort im Deutschen[END_REF](Eisenberg, , 2013)), investigated the extent to which they overlap in meaning with existing German lexemes [START_REF] Onysko | Necessary loans -luxury loans? Exploring the pragmatic dimension of borrowing[END_REF]Winter-Froemel, Onysko, & Calude 2011), or documented their assimilation to German orthography and inflectional morphology (Coats, 2018). English elements can also be joined to German constituents with hyphens to create compounds (e.g. Urlaubs-Feeling 'holiday feeling', Service-Zentrum 'service center'), a productive process which is the focus of the present research.

The processes by which composite words in German can be formed by combining indigenous and exogenous lexical material have been described in the literature [START_REF] Fleischer | Wortbildung der deutschen Gegenwartssprache[END_REF], and the importance of relative frequencies of bases for the recognition and processing of compounds has been shown in experiments (e.g. [START_REF] Lüdeling | German particle verbs and word-formation[END_REF][START_REF] Baayen | Lexical dynamics for low-frequency complex words: A regression task across tasks and modalities[END_REF], but the productivity of English bases in hyphenated compounds has not yet been a focus of German lexicography. Most research into productivity in German has focused on the productivity of affixes, rather than word bases [START_REF] Lüdeling | The emergence of productive non-medical -itis: Corpus evidence and qualitative analysis[END_REF][START_REF] Lüdeling | On measuring morphological productivity[END_REF]. Recent developments have highlighted the importance of corpus-based methods as well as the need to extract relevant information and adequately describe changes or findings based on the explanatory power of statistical indicators [START_REF] Hein | Morphological variation: the case of productivity in German compound formation[END_REF]. It is indeed still necessary to find a suitable methodology to study the dynamics of anglicisms in German, all the more since empirical frequency-based investigations have not always been the main research focus (Burmasova, 2010). In this study, we consider the productivity of English base constituents in hyphenated German compounds. By taking into account recent web and computer-mediated communication (CMC) corpora, we hope to capture phenomena unseen in standard written German, as these corpora consist of genres which are expected to differ from commonly accepted rules. Indeed, we do not stick to the concept of rules but rather try to derive norms from empirical data [START_REF] Habert | Régler les règles[END_REF]) by way of statistical indicators which are related to information theory and as such yield a particular view on language constituency and productivity.

Building upon quantitative approaches to the measure of morphological productivity developed by Baayen (1994aBaayen ( , 1994bBaayen ( , 2001) ) and others (Hay & Baayen, 2003;[START_REF] Del Prado Martín | Putting the bits together: an information theoretical perspective on morphological processing[END_REF], we utilize Shannon entropy [START_REF] Shannon | A mathematical theory of communication[END_REF] to measure the productivity of English constituents in different internal word positions in large corpora from the web and from Twitter. In light of findings from response latency experiments, this may be evidence that English constituents increasingly take part in productive word formation processes in German. In addition, the semantic values of the most productive English bases may shed light on broader developments in the German lexicon and in German-speaking society as a whole. The study addresses the following questions: 1) Which constituent base anglicism types are most frequent in hyphenated German compounds, and 2) What can morphological diversity measures such as Shannon entropy tell us about the dynamics of anglicisms borrowed into German compounds?

In the next section, a review of previous research in morphological productivity is provided, followed by a brief overview of German usage norms for hyphenated compounds. In Section 3, the data and methods used to calculate Shannon entropy from the corpora are presented and German compounds briefly reviewed. Section 4 presents the results, and Section 5 closes the paper with a summary and outlook for future research.

Previous work

2.1. Productivity measures [START_REF] Baayen | On frequency, transparency, and productivity[END_REF]Baayen ( , 1994aBaayen ( , 1994bBaayen ( , 2001) ) proposed several measures of morphological productivity, including the category-conditioned degree of productivity: the ratio of hapax legomena (words that occur once in a text or a corpus) for an affix to the size of its morphological category, which represents that the probability a new word encountered in a text or corpus will be a type that has not yet been encountered, given that it belongs to a particular morphological class. For example, for the German deadjectival nominal suffix -keit (e.g. Sparsamkeit 'thriftiness'), the categoryconditioned degree of productivity is the ratio of the sum of all hapax words ending in -keit to the sum of all words ending in -keit. Because -keit is more productive than suffixes such as -nis or -tum, it will have a higher value when using this measure.

For word bases in compounds, frequencies can be assessed by the morphological family size (the number of distinct types in which a base appears) and the cumulative family frequency (the sum of token frequencies for all types in which a base appears). Morphological family size is negatively correlated to reaction times in lexical recognition experiments [START_REF] Baayen | Lexical dynamics for low-frequency complex words: A regression task across tasks and modalities[END_REF]. For example, because a German base like Schrift 'writing' may occur in a large number of compound words (e.g. Schreibschrift 'handwriting', Schriftsteller, 'writer', Unterschrift 'signature', etc.) with relatively high frequencies, compounds containing the base are recognized more quickly than are compounds that contain constituents with lower frequencies or smaller family sizes, such as Schund 'rubbish', which is a constituent in a smaller number of words (e.g. Schundliteratur 'trashy writing').

Like morphological family size, cumulative family frequency has been shown to correlate negatively with reaction times in lexical recognition experiments (Baayen & Hay, 2002;[START_REF] Baayen | The morphological complexity of simplex nouns[END_REF]De Jong, Schreuder, & Baayen, 2000;[START_REF] Baayen | The morphological complexity of simplex nouns[END_REF]. [START_REF] Hay | Lexical frequency in morphology: Is everything relative?[END_REF] found that for English compounds, frequent words are processed more quickly, and thus likely to be stored in the mental lexicon as opaque single units of meaning, whereas infrequent compounds may be stored as decomposable items. For German verbs, [START_REF] Lüdeling | German particle verbs and word-formation[END_REF] found a negative relationship between morphological family size and response latencies in an experimental task.

Moscoso del Prado Martín, Kostić, and [START_REF] Del Prado Martín | Putting the bits together: an information theoretical perspective on morphological processing[END_REF] utilized a metric based on Shannon entropy to calculate an "information residual" for a word, or the difference between the logarithm of a word's frequency to the Shannon entropy for all inflected forms of the word. They found that in regression models of word response latencies, the word information residual provides a better fit than morphological family size or cumulative family frequency, meaning that from a statistical standpoint this additional indicator yields more fine-grained information and is thus suitable to draw conclusions on lexical use.

Hyphenation in German compounds

In standard German orthography, constituent elements in composite words are typically linked without a hyphen. Hyphens can be optionally used in composite words in order to emphasize particular constituents or to enhance the legibility of long composite words with multiple constituents (Duden, 2006, p. 39;Fleischer & Barz, 2012, p. 193). Hyphenation is recommended if a composite form contains a constituent that is an abbreviation or initialism (Fussball-WM 'football/soccer world cup'), and is preferred if the first constituent element of a compound is a proper noun, especially a personal name (Fleischer & Barz, 2012, p. 193; e.g. Merkel-Regierung 'Merkel government'). Hyphenation is also used in longer composite phrasal word forms (Pro-Kopf-Verbrauch 'per capita use') (Duden, 2006, p. 41;Fleischer & Barz, 2012, p. 175). Fleischer and Barz note that composite word formations in German can incorporate foreign constituents as first elements, internal elements, or final elements, "without restrictions" (2012, p. 111).

Data and methods

A list of potential English constituents was created by combining the 3,262 most common nouns in the British National Corpus (Kilgarriff, 1997) with the 10,000 most common nouns in the 9.6b-token ENCOW16ax corpus, a corpus of English texts from the web [START_REF] Schäfer | Processing and querying large web corpora with the COW14 architecture[END_REF][START_REF] Schäfer | Building large corpora from the web using a new efficient tool chain[END_REF], then converting to lower case and removing types containing punctuation or shorter than 4 characters. The list thus combines attested data from a stratified reference corpus and more current utterances from a large web sample. The frequencies of these 8,313 unique types as left-hand, central, or right-hand constituents in hyphenated German words were determined in three corpora of online German: A German Twitter corpus of 534m tokens (Coats, 2018), the DECOW16bx corpus, a German web corpus of 11b tokens [START_REF] Schäfer | Processing and querying large web corpora with the COW14 architecture[END_REF][START_REF] Schäfer | Building large corpora from the web using a new efficient tool chain[END_REF], and a corpus of German WordPress blogs with 2.1b tokens [START_REF] Barbaresi | Efficient construction of metadataenhanced web corpora[END_REF]. In order to account for non-standard capitalization (common on Twitter and in other informal online genres), all words were converted to lowercase. A regular expression was used to additionally target plural and genitive forms while taking potentially unknown forms into account.

For each of the 8,313 English potential base types, we used token counts for individual compounds and the cumulative family frequency for the base (i.e. the summed frequencies of all compound types containing the base) to calculate an entropy measure. The compound Shannon entropy of a base can be calculated according to the formula

H(B) = - n ∑ i=1 log 2 F (x i ) F (B) (1)
where B represents an anglicism base, F (x i ) the frequency of a particular compound type containing B, n the morphological family size for the base, and F (B) the cumulative family frequency for the base. The value can range from zero to log 2 n. As an example, the entropy for the English base payment can be calculated in a corpus of 8 tokens in which Payment-Taste 'payment button' occurs 5 times, Crypto-Payment-App 'crypto payment app' twice, and Online-Payment 'online payment' once. In this example, the English base 'payment' occurs as a left-hand constituent, as an internal constituent, and as a right-hand constituent. Entropy can be calculated by constituent position, or a total entropy score can be calculated that takes into account all possible configurations: In this example, the lefthand, internal, and right-hand compound entropies would be zero (because only one type occurs at each word-internal position), while the total entropy would be 1.

Results and discussion

The corpora feature a large number of hyphenated compounds containing anglicisms: the Twitter corpus 619,338 unique types, the most frequent of which are youtubevideo, live-tracking, and start-up; the DECOW16bx corpus 6,567,984 types (online-shop, html-code, and bb-code are the most frequent) and the WordPress corpus 808,648 distypes (us-dollar, online-shop, and after-sales-service are the most frequent).

Tables 1,2, and 3 show the base types with the highest cumulative family frequencies for the three corpora, their frequencies, left-hand, internal, right-hand and total entropy calculations for the types, and the three most frequent types containing the base elements.

Many of the most frequent bases in the three corpora denote entities related to technology or the internet (video, twitter, facebook, youtube, blog, internet, code, software). Left-hand, internal, right-hand, and total entropy values (indicated by H L , H I , H R , and H T in the tables) provide an overall indication of the diversity of the frequency distributions for compounds containing bases in that constituent position. Entropy values for the bases in different hyphenated word positions vary from low (dollar in right-hand position) to high (team, system in right-hand position). Lower entropy values can indicate that a base has been lexicalized in a hyphenated word (us-dollar), resulting in far higher frequencies of that type compared to other types in the morphological family. For the Twitter and DECOW16bx corpora, internal entropy values are the lowest, right-hand entropies intermediate, and left-hand entropies the highest. For the WordPress blogs corpus, right-hand entropy values are highest. 1 Because the base types considered in the study 1 Because the anglicism constituents are nouns and in German compound nouns are almost exclusively right-headed, it is conceivable that right-hand entropies may be lower. The reason for the reversal of this pattern in the WordPress blogs corpus is unknown at this stage. Although different text processing procedures may play a role, compounding creativity may explain this behavior.

are primarily English nouns, this value may also provide a preliminary indication of word class conversion of borrowings (Figure 1). This possibility, however, needs further exploration, for example by comparison with Englishlanguage compounds. 10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5

Left-right entropy difference Figure 2 shows the total compound morphological entropy versus the morphological family size for the Twitter corpus, the DECOW16bx corpus, and the WordPress blogs corpus. In the plots, each point represents an English base, the red line represents the maximum entropy, and the magenta line represents a nonparametric locally-weighted regression.

For many of the 8,313 English-language bases analyzed in the study, entropy values are close to the maximum possible entropy curves in the three corpora, which can be seen as an indication of the relative lack of syntactic or semantic constraints on hyphenated word formation in German. Comparing the regression curves (magenta lines in the figures) to the maximum entropy curves (red lines) shows overall higher entropy values for the WordPress blogs corpus and for the Twitter corpus, compared to the DECOW16bx corpus. This is likely due to the more informal nature of written language on Twitter and in blogs, genres that exhibit relatively high rates of creative textual features such as non-standard orthography, expressive lengthening, or emoticon and emoji use [START_REF] Argamon | Mining the blogosphere: Age, gender, and the varieties of self-expression[END_REF][START_REF] Coats | Grammatical feature frequencies of English on Twitter in Finland[END_REF], and that therefore may also exhibit a greater diversity of hyphenated compound types. In contrast, many of the genres that comprise the DECOW16bx corpus, such as news articles, consist of relatively formal, conventionalized writing in which non-standard usages are uncommon.

The bases with the highest total entropy values in the Twitter corpus are the forms team and chef, followed by media, twitter, and video. For the web corpus, the types with the highest total entropy are team and system, followed by forum, software, and service. For the blogs cor- 10 'orga-team', 659, 'dream-team', 239, 'blog-team', 224 system 26528 6.81 7.30 11.53 11.63 'erp-system', 481, 'herz-kreislauf-system', 318, 'crm-system', 256 video 23244 7.31 9.49 9.83 10.26 'youtube-video', 1478, 'youtube-videos', 1286, 'video-interview', 478 chef 21689 5.41 6.89 9.84 9.94 'spd-chef', 875, 'fdp-chef', 627, 'ex-chef', 520 version 20518 4.50 4.51 9.74 9.76 'beta-version', 1125, 'online-version', 564, 'pc-version', 564 service 19351 6.19 8.54 6.01 6.98 'after-sales-service', 7669, 'euro-finanz-service', 339, 'shuttle-service ', 300 film 19273 6.52 9.18 10.25 10.52 'film-reviews', 575, 'science-fiction-film', 433, 'bond-film', 328 dollar 17667 5.48 9.43 1.07 2.36 'us-dollar', 14271, 'us-dollars', 572, 'petro-dollar', 112 pus, the highest-entropy types are team and blog, then system, film, and video. Several of the most-attested types are words used in domains of interaction that have been particularly affected by the influx of English, and may represent examples of Bedürfnislehnwörter ('necessary borrowings', [START_REF] Carstensen | Englische Einflüsse auf die Deutsche Sprache nach[END_REF], or lexical elements whose denotation is not well-represented by existing German lexemes. This is the case for the brand names among the most frequent and highest-entropy bases (twitter, facebook, and youtube), and may also be true for workplace-related elements (team, chef, service, and marketing). Types with high total compound morphological entropy values represent those English-language elements that have been borrowed into the German lexicon and are the most flexible in terms of their potential productivity. Types with low values, on the other hand, are typically used only in one or a few set formulations.

It should be noted that many of the types in the base wordlist may not be anglicisms, but rather Greek-or Romance-language-derived words common to most Euro-pean languages (system, service, version, video, etc.), which may have undergone borrowing from the source language directly into German, or may also have been borrowed via English mediation. In addition, some types represent borrowings that have long been established in the German lexicon (e.g. film, chef ), and thus may no longer be perceived as anglicisms or borrowings.

Summary and future outlook

Compounding via hyphenization is a productive word formation process in German, and we found many hyphenated compound types including English elements across three different CMC and web corpora: a Twitter corpus, a corpus of diverse web texts, and a blog corpus. We measured the tendency of 8,313 English nouns to appear as elements in hyphenated German compounds and documented a tremendous diversity of types. Many of the most frequent types overall (e.g. online-shop, youtube-video) are hyphenated compounds that have been borrowed into German in order to denote new activities, technologies, or behaviors ("necessary borrowings"). The entropy analysis shows differences in entropy according to base constituent position within hyphenated compounds, and suggests that word formation via compound hyphenization of English bases is more productive on Twitter and on blogs, compared to other online genres. This can be interpreted as a consequence of the more spontaneous nature of text as used on blogs and on Twitter, which, as a paradigmatic form of CMC, has been suggested to have a status between speech and writing in terms of communicative typology and feature frequencies [START_REF] Barbaresi | For a fistful of blogs: Discovery and comparative benchmarking of republishable German content[END_REF][START_REF] Coats | Grammatical feature frequencies of English on Twitter in Finland[END_REF][START_REF] Tagliamonte | Linguistic ruin? Lol! Instant messaging and teen language[END_REF].

Future work with the data can be organized along three lines. First, a more thorough analysis of entropy according to constituent position within compounds and comparison with indigenous German lexical elements and English compound words may shed light on the dynamics of how borrowings are integrated into German morphological paradigms and whether conversion is taking place for some types. Second, many hyphenated compounds can also be written without hyphenation -a frequency analysis of the semantics of hyphenated and non-hyphenated compounds may be revealing. Finally, a frequency analysis of anglicism-containing hyphenated compounds of different structural types, according to the classification proposed by [START_REF] Fleischer | Wortbildung der deutschen Gegenwartssprache[END_REF], may give further insight into the productivity of this large, chaotic, and fascinating word class.

Figure 1 :

 1 Figure 1: Left-right entropy difference distribution, DE-COW16bx corpus

Figure 2 :

 2 Figure 2: Shannon entropy vs. morphological family size, Twitter corpus, DECOW16bx corpus, and WordPress blogs corpus

  30. In general, low entropy values indicate skewed frequency distributions, while high values indicate more uniform distributions.

Table 1 :

 1 Most frequent types, Twitter Corpus

	Base	Freq.	HL	HI	HR	HT	Most freq. types
	video	29412 8.72 7.98	6.91	8.67	'youtube-video', 7285, 'video-interview', 803, 'youtube-videos', 763
	twitter	27459 8.99 8.96	7.58	9.25	'twitter-account', 2602, 'twitter-zufallsstory', 1510, 'twitter-app', 772
	facebook	23901 8.40 8.14	5.98	8.56	'facebook-seite', 2740, 'facebook-gruppe', 751, 'facebook-fans', 606
	team	18113 8.63 6.90 10.68 11.02 'orga-team', 553, 'dfb-team', 335, 'social-media-team', 305
	chef	17818 7.81 4.90	9.63	9.88	'spd-chef', 573, 'fdp-chef', 452, 'ex-chef', 356
	news	17553 6.98 7.83	5.91	7.02	'heise-news', 1925, 'it-news', 1812, 'fake-news', 1189
	youtube	15435 4.71 6.44	5.61	4.87	'youtube-video', 7285, 'youtube-kanal', 1312, 'youtube-videos', 763
	blog	15396 5.78 3.85	8.88	8.70	'blog-eintrag', 1212, 'blog-beitrag', 838, 'blog-artikel', 668
	marketing 14121 8.64 8.42	4.80	8.02	'online-marketing', 2349, 'content-marketing', 1339, 'influencer-marketing', 414
	media	14097 8.34 8.95	2.45	9.38	'social-media', 1051, 'social-media-team', 305, 'social-media-marketing', 286

Table 2 :

 2 Most frequent types, DECOW16bx Corpus

	Base	Freq.	HL	HI	HR	HT	Most freq. types
	system	582231 9.91	9.68	11.97 12.22 'it-system', 16797, 'erp-system', 11115, 'content-management-system', 9506
	internet	507073 8.90 10.62	6.33	9.15	'internet-seite', 36068, 'internet-adresse', 19172, 'internet-auftritt', 16666
	forum	412839 8.96 10.27 10.24 10.63 'feuerwehr-forum', 17621, 'fan-forum', 10562, 'hifi-forum', 9812
	code	398698 8.46	9.61	3.57	4.17	'html-code', 151710, 'bb-code', 132344, 'qr-code'
	team	359205 9.31 10.36 12.64 12.85 'top-team', 5455, 'orga-team', 3963, 'support-team', 3307
	shop	344979 6.51	8.66	5.22	6.07	'online-shop', 171998, 'internet-shop', 9308, 'shop-system', 5905
	version	337625 7.07	7.67	9.85	9.89	'beta-version', 13907, 'pc-version', 10173, 'windows-version', 9784
	software 325250 8.07 10.93 10.55 10.47 'software-entwicklung', 9605, 'software-update', 7840, 'software-lösung', 7746
	service	321222 8.12	9.81	9.65	10.46 'full-service', 6824, 'it-service', 6728, 'service-center', 6591
	video	254431 9.32 10.80	8.53	10.27 'youtube-video', 15269, 'hd-video', 5563, 'video-kritik', 5517

Table 3 :

 3 Most frequent types, WordPress blogs corpus

	Base	Freq.	HL	HI	HR	HT	Most freq. types
	blog	47324 6.86 9.07 11.86 11.84 'blog-post', 743, 'satire-blog', 555, 'blog-event', 522
	shop	39271 6.29 8.02	4.91	5.18	'online-shop', 13952, 'online-shops', 9930, 'web-shops', 2969
	team	31366 7.16 7.97 12.00 12.