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An assessment of the dispersion of glycerol in dimethyl carbonate in a stirred tank Halina Murasiewicz, and Jesus Esteban Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b01061 • Publication Date (Web): 04 Apr 2019 Downloaded from http://pubs.acs.org on April 4, 2019

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Industrial & Engineering Chemistry Research

1

An assessment of the dispersion of glycerol in dimethyl carbonate in a stirred tank Halina Murasiewicz1,3, Jesús Esteban2,3* 1

Faculty of Chemical Technology and Engineering, West Pomeranian University of Technology, Aleja Piastow 17, 70-310 Szczecin, Poland 2 Molecular Catalysis Group. Max Planck Institute for Chemical Energy Conversion. Stiftstrae

34 - 36 Mülheim an der Ruhr, 45470, Germany 3

School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom *Corresponding author e-mail [email protected]

address:

[email protected]

/

Abstract Glycerol carbonate has gained attention as a value-added product from reacting glycerol and dimethyl carbonate. This work studies the dispersion in non-reacting conditions of the two compounds under conditions relevant to the production of glycerol carbonate. Images were acquired to obtain droplet size distributions and Sauter mean diameters (d3,2), which increased with dispersed phase volume fraction and viscosity, whereas the difference of interfacial tension with changing conditions could be neglected as its value remained very similar at all conditions. d3,2 was correlated with available theoretical models based on the Weber number and energy dissipation rate and two further correlations were proposed for high and moderate viscosities to describe the effect of viscosity, concentration of dispersed phase and hydrodynamic parameters. The predicted value of d3,2 correlated well with experimental data with the accuracy of both correlations reaching at least 93%. Keywords: glycerol, dimethyl carbonate, glycerol carbonate, image analysis, drop size distribution, Sauter mean diameter 1. Introduction Over the past decade there has been a large number of studies on the chemical valorization of the surplus of glycerol (Gly) generated by the biodiesel industry owing to the steep decrease of its retail princes 1. These studies include several processes conducted by microorganisms, enzymes or catalytic processes, which have been thoroughly covered in the literature 2-4. Some of these reactions to yield products of interest not only use Gly as feedstock, but also other reactants with which miscibility is very limited. For instance, the acetalisation of Gly to obtain ketals like glycerol formal or solketal requires reaction with cosubstrates formaldehyde 1

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2 5,

acetaldehyde 6 and acetone 7, respectively. Likewise, over the past decade there have been a

large number of studies to obtain glycerol carbonate (GC) as a value-added chemical from the valorization of glycerol (Gly) 8, 9. Its properties make it a valuable product in many applications as a green solvent for reactions and separation processes or in batteries, in the formulations of cosmetics and foods or as a building block for polymers and surfactants 8. GC production can be performed by transcarbonation with organic carbonates like dimethyl

10, 11,

diethyl

12

and

ethylene 10, 13 propylene and butylene carbonate 14. The mentioned systems have the common feature that they constitute dispersions at the start of the reactions and then, when the concentration of the products reach a certain value, they turn into single liquid phases, as depicted in the scheme in Figure 1 for the reaction between Gly and dimethyl carbonate (DMC) to yield GC and methanol 15. Additionally, this has been studied in detail for the systems of glycerol with acetone 16 and ethylene carbonate 17. For the synthesis of GC, some authors have approached this type of reactions adding solvents to help solubilize glycerol and the co-substrate to avoid mass transfer limitations

18-20.

These

reactions can be performed in the absence of any solvent, thus helping to save material and avoiding subsequent separation of the solvent 7, 11-13. Many processes in industry take place in liquid-liquid biphasic systems, including extractions or certain chemical reactions, for which the behaviour of the mixing of dispersions is decisive for adequate performance. In the case of chemical reactions, other different examples have been investigated. One case is the alkylation of olefins, where alkanes like isobutane and alkenes such as 1-propene, 1-butene or 1-pentene form the dispersed phase, which reacts with the aid of acid catalysts like H2SO4 21, present in the continuous phase. Another example would be the hydroformylation of olefins to yield linear or branched aldehydes, in which it is typical to use Pd or Rh-based catalysts to perform the reaction between the olefin and CO. In recent times, the approach has been to hold these expensive catalysts with the aid of ligands in a polar phase like water 22 or ethanol 23, so that they split from the final product phase, trying to avoid the use of additives. However, the overall rate of processes where different phases coexist does not depend solely on the intrinsic reaction rate, but also on the mass transfer among such phases, which is dependent on the specific interfacial area. In the examples mentioned above, it is vital to ensure that contact is good enough to reach a fast mass transfer rate between the phases, which is proportional to the interfacial area and obviously related to the size of the droplets in the 2


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dispersion for a liquid-liquid system. In turn, this area depends on the geometry both of the device used for mixing and the vessel, the physicochemical properties of the liquid phases involved (e.g., interfacial tension, density and viscosity) and the mixing intensity

24-27.

The

dispersion behavior is characterized by the droplet size distribution (DSD), which is controlled by the coalescence and breakage of liquid phases, with the main affecting factors being the flow patterns and energy dissipation distribution 28. Different techniques have been used to evaluate the behavior of liquid-liquid systems in stirred vessels. Maas et al.

26

compared different techniques to evaluate DSD, namely: forward

backward-ratio sensor, 2D-Optical Reflectance Measurement, focused beam reflectance measurement (FBRM) and imaged-based endoscopy outlining the advantages in disadvantages of each for liquid-liquid dispersions. The latter two seemed to offer greater advantages in terms of on-line measurements and measurement ranges and image-based analysis has actually become a standard to test the reliability of the measurements of other devices 29. FBRM was previously employed to monitor the disappearance of the biphasic liquid-liquid systems as the reaction between Gly and DMC 10, 11 as well as between Gly and EC took place 10, 13.

However, FBRM tends to significantly undersize the droplet size

26, 30,

which might be

due to the fact that this light back-scattering technique measures a chord length distribution (CLD) rather than a DSD, meaning that the light beam is not necessarily hitting the droplet at the longest chord possible (i.e., its diameter)

29, 31.

Building on this, some efforts have been

made to correlate CLD and DSD 32, 33. Pacek et al. developed a video microscopy technique to analyze the dynamics of dispersions during phase inversion in dispersions of non-polar chlorobenzene in polar phases formed by water and different proportions of glycerol 34, which they also employed to assess the influence of the impeller type on the DSD of different organic phases dispersed in water 35. More recently, an updated version of this technique has been used to assess the breakage and coalescing behaviour of dispersions based on perfluorocarbons for cell culture expansions, with subsequent analysis of the images by image processing software (ImageJ) supported with macro development 36. Also, video endoscopy using a SOPAT ® probe has been employed to analyze population balances and the coalescence and breakup behaviour of emulsions 37. Last, Qi et al. monitored the DSD and phase inversion of chloroaluminate ionic liquid–heptane dispersions in a stirred vessel combining video microscopy and FBRM, respectively 28.

3



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Thus, due to the interest of the mixing of DMC and Gly prior to chemical reaction to ensure adequate contact between the phases, in this work we aim to investigate the behavior of the dispersion formed by these chemicals in a stirred vessel fitted with a Rushton turbine. To undertake this study, the droplet size distribution will be obtained by analyzing the emulsification/dispersion. All of this is conducted employing holdup volumes and temperatures relevant to the eventual performance of the chemical reaction to yield GC upon addition of catalyst. 2. Experimental section 2.1. Materials The following chemicals were used for the experiments: extra pure glycerol (assay grade, purity = 99.88 %) from Fischer Chemical Co., Ltd. and dimethyl carbonate (anhydrous, purity  99%) supplied by Sigma Aldrich. Chemicals were used as received without any further treatment. 2.2. Determination of interfacial tension Interfacial tension measurements were made using a procedure and instruments similar to those described in previous work

38.

Samples were measured with a tensiometer (Krüss K100,

Germany) in a cylindrical sample vessel placed in a jacketed holder. The jacket is connected to a temperature controlled water bath (Tecam TE-7 Tempette, Italy), with which temperature could be controlled with an accuracy of ± 0.01 K. The measurements were made following the Wilhelmy plate method, using a platinum plate with geometry of 20 mm of length and a thickness of 0.18 mm. Three repetitions of each measurement were completed over a period of 600 s or less if the surface tension was determined constant (a variation of the standard deviation of less than 0.01 for ten consecutive measurements). Surface and interfacial tensions with the Wilhelmy plate method could be determined with a resolution of ±0.002 mN m-1. 2.3. Experimental setup and procedure The experiments were conducted in a flat-bottom 500 mL glass stirred tank of diameter DT=0.075 m with 4 equally spaced baffles of 10 mm of width. The level of the liquid was up to 0.075 m, hence having a level to reactor diameter of 1. The vessel is equipped with a Rushton turbine (power number=5 35) of diameter D=0.042 m, located at the middle of the height of the liquid, as depicted in the scheme of the experimental shown in Figure 2. This relative position was the one used in our previous references, where under catalytic reaction conditions, the 4


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kinetic regime of the reaction was attained, thus ensuring that the dispersion was proper 10, 11. The stirred vessel additionally includes a jacket for heat transfer connected with an external water bath to heat two-phase system and is covered with a lid to exclude air and prevent evaporation of the liquids inside, particularly DMC. Experimental sets consisted of measurements drop size at three different temperatures: 298.15, 333.15 and 343.15 K. At each temperature four molar ratios and five different impeller speeds were tested, the latter of which was controlled by the variable speed motor (IKA® Werke GmbH & Co. KG, Germany). The minimum speed of impeller was estimated from visual observation during the initial experiment when the complete dispersion of Gly was indicated in the whole volume. However, the maximum speed was chosen below the speed where air bubbles starts to occur in the vessel. The impeller speed was gradually increased from 300 to 500 rpm, every 50 rpm to finally receive minimum three measurement points for each graph. The experimental procedure was similar in all cases. Dispersions of viscous glycerol were prepared adding first the required amount of continuous phase (DMC) into the vessel at room temperature followed by loading of the appropriate amount of Gly (dispersed phase). Four different systems were formulated with the adequate molar ratio, described in Table 1, where the dispersed glycerol phases were estimated to be 30, 22, 15 and 8% by volume

11, 39, 40.

According to the general classification 41, the investigated dispersed phase can be categorized as a more concentrated system for 30% and 22% dispersion, moderately concentrated system for 15 and 8 % of dispersion. Gly settled on the bottom of the vessel due to its high viscosity after addition to the continuous DMC phase due to the density difference. The system was kept still until the temperature was adjusted and thereafter mixing was set to start. The temperature was constantly monitored during preparation and regular experiments. At each impeller speed, the system was agitated for 30 min to reach equilibrium drop size and drop size distribution was measured after that time at one position in the stirred vessel. 2.4. Image acquisition and processing Mean drop sizes and drop size distributions during breakage process were obtained from images captured by a video-microscope-computer system as seen in Figure 2 34, 35. Briefly, the strobe light (2) fed from a strobe flash (3) was placed in the vessel (1), which includes temperature control thanks to a water bath. The gap between the light and the vessel wall could be varied between 2 and 8 mm and was placed close to a deflector baffle to avoid undesired effects on 5



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the flow pattern. The cold light probe had dimensions of 12 cm of length and 0.6 cm of diameter and it was placed to flash through the system and directly into the microscope /camera lens. The influence of strobe flash on flow pattern was minimal. A stereo microscope (5) with variable magnification fitted with an extra lens to give a higher magnification was linked to the CCD camera (4) with its shutter frequency synchronised to the strobe. Both parameters could be adjusted depending on the agitator speed to produce sharp pictures of drops on the monitor (6). The use of stroboscopic illumination technique was pioneered by Pacek [32, 33], who has produced very high-quality sharp images, especially at high shears where image clarity is significantly affected by the fast motion of the sample. The time and space resolution of the camera are 15 fps and 1280x960 pixel, respectively. The capture scope was from 1.19·106 μm2 (or 1258.11x943.58 μm) to 13.14·106 μm2 (or 4187x3140.26 μm). The imaging position of the microscope was set at a centre of the level of liquid, at the position 0.037 m from the bottom of the vessel and in the halfway between wall and impeller because coalescence process might occur in the vicinity of the wall. For the current setting maximum achieved magnification was 1.3 μm pixel -1. Collected images were analyzed using the ImageJ program (1.52e release) supplemented with a plugin developed by us for the purpose of this work. Software converted the data from pixels to microns and the drop perimeter was calculated and then the value the diameter of droplets was estimated. For each case over 1000 drops were analyzed to determine diagrams of frequency and cumulative distributions considering previous experience showing that above this amount there is no significant impact on the Sauter mean diameters calculated from the distributions 34, 42. Droplets were analysed in semiautomatic way aided by the custom ImageJ plugin. Circular drops were appointed either by clicking on three points of the drops' perimeter or by sliding a set of two perpendicular lines to form a square with sides tangential to the circle. Elliptically deformed drops were drawn manually using again a set of two lines at a right angle and dragging a rectangle tangential to the drop. This technique made it possible to distinguish overlapping droplets as no image processing algorithms were utilized. 3. Results and discussion 3.1. Characterization of the system For calculations in subsequent sections it is indispensable to physicochemically characterize the liquid-liquid dispersion at hand. First, densities and viscosities are compiled in Table 2, whose values for DMC 43 and Gly 44 were obtained from literature at the temperatures used for the experimental work presented here. The only exceptions are the viscosity and density values of DMC at 343.15 K, which were extrapolated applying an Andrade and linear fitting to all 6


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available data, respectively (9 points ranging from 293.15 to 333.15 K)

43,

according to

equations 1 and 2. [1]

𝜌DMC = 1.46285 – 0.00134T 𝜂DMC = 0.03828 exp

(

593.01114 𝑇 ― 80.67033

)

[2]

where ρ is the density, η is the viscosity and T is the temperature in Kelvin and the numeric values are the parameters obtained after fitting the data. The residual means squared errors were 9.56 10-4 and 4.77 10-3 for the fittings in equations respectively. In addition, the interfacial tension (γ) between Gly and DMC was measured at 298.15, 333.15 and 343.15 K, which are those at which the experiments will be tested. The values obtained from the triplicate measurements are summarized in Table 2. The value of γ as well viscosities and densities of both liquids decreased with an increase of T, as was expected. Gly is highly viscous at room temperature and became remarkably less viscous at 333.15 and 343.15 K (almost 10 and 20 times at each temperature, respectively). From the molar ratios employed in literature for the reaction between Gly and DMC, dispersions as described in Table 1 will be formulated. Therein the molar and mass ratios can be seen together with the volume ratios at each of the temperatures. The values of disperse phase holdup ratios (ϕd) for identification of the different runs in subsequent sections are taken as average values of the ratios obtained from the data at 298.15, 333.15 and 343.15 K. Finally, it was found that Reynolds number was between 2100 and 3540 at 298.15 K for dispersions of ϕd=0.30 and ϕd=0.22 (at N=300 rpm). This means that the flow regime was here transition since increasing of volume fraction of dispersed phase, the viscosity of the dispersion increases and could change the flow from being turbulent to being transition/laminar. For the same temperature and lower volume fraction 22% (from N=350 rpm and higher), 15% and 8% and for dispersions at 333.15 and 343.15 K, the flow was turbulent with Reynolds number ranging from 5400 to 33700. 3.2. Influence of vertical cameral position on the measurement of the drop size distribution. For preliminary experiments, the DSD at different vertical positions from the bottom of the vessel (0.019 m, 0.037 m and 0.07 m from the bottom of the tank) was measured for the system at T= 298.15 K and two exemplary volume ratios of DMC:Gly equals 2.322 (ϕd=0.30), 5.805 7



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8

(ϕd=0.15) at the minimum impeller speed of 300 rpm. Figure 3 depicts the results obtained for ϕd=0.15, where the DSDs mostly overlap at the three positions and hence the uniformity of the generated dispersion is high. In addition, from the measurements, the maximum relative errors of the calculated d3,2 were of about 2% (ϕd=0.15) and at most of 12% (ϕd=0.30) in the worst case, but generally well within experimental error. The results of the initial experiment found clear support for the spatial uniformity of dispersion at different vertical positions as d3,2 and DSD appear to have low dependence on the position at which they were measured. Therefore, in subsequent experiments we decided to measure the DSD only at one position, i.e., at the middle of the liquid height. A similar conclusion was delivered by Pacek et. al 35, who studied the influence of impeller type on mean drop size and drop size distribution in chlorobenzene and sunflower oil in water systems and Pacek and Nienow

45,

where the system CLB-water was stirred by a 6DT impeller. According to

Coulaloglou and Tavlarides

46

a liquid‐liquid dispersion is nearly spatially homogeneous in a

turbulent agitated vessel. Following the obtained results, it was decided to conduct all experiments at one measurement position located at 0.037 m from the bottom of vessel. 3.3. Effect of impeller speed on drop size and drop size distribution The eﬀect of energy input (impeller speed), composition and temperature on drop size distribution and mean drop was studied during breakage mode (the impeller speed gradually increases). Examples of images at different impeller speeds and constant temperature (T=333.15 K) and volume fraction (ϕd=0.15) are presented in Figure 3. From these images, drop size distributions (DSD) and drop sizes (the Sauter mean diameter, d3,2) were obtained. The effect of impeller speed on DSD is presented in Figure 4, where stirring was varied employing different temperatures and ratios of DMC:Gly (i.e., different ϕd). In all cases, the drop size decreased as the impeller speed increased as expected, since an increase of energy input to a system leads to an augmentation of the shear and energy dissipation rate resulting in an increase of turbulent pressure fluctuation. The DSD curves showed a trend shifted towards to the smaller droplets size region. As a matter of fact, increasing the impeller speed leads to enlarge the volume of the breakage region, therefore the volume of the coalescence region is decreased. Graphs in Figure 5 (A) and (B) show a bimodal distribution with an asymmetrical shape with a broad distribution, shifted to the left (with impeller speed increased) with bias towards larger drops indicating a better susceptible coalescence. The curves presented in Figure 5 (C-F) are 8


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9

also shifted to lower drop size regions as impeller speed increased; however, the DSDs are more unimodal, narrower and more symmetrical. The width of the distribution curves mainly depends on the viscosity of the dispersed phase. The strong effect of impeller speed on drop size for all the viscosities and high concentration of dispersion is presented in Figure 6. As more energy is added to the system (i.e., as N increases), the rate of breakage increases causing a decrease of d3,2 because higher energy overcomes the cohesive forces that tend to keep droplets against breaking. This is also related with circulation time since the circulation time decreases as N progresses. Hence, the droplets need less time to travel to the impeller zone where the breakage process is controlled 47. This figure shows the large changes of d3,2 according to the viscosity of Gly over the range of N tested; in principle, the lower the viscosity the smaller the droplets owing to their easier breakup; on the other hand, it also facilitates coalescence. For the lower viscosity value, two different holdups are compared, where it can be seen that coalescence dominates leading to larger droplets. Also, at a low viscosity droplets become more stable and changes of d3,2 are smaller as N raises. Further to Figure 6, d3,2 declines as the impeller speed increases with a proportionality to Nb. The value of b varied from -1.03 to -0.98 for moderately dispersed phase viscosity and for most viscous it declined to -0.76, whilst for the lowest investigated dispersion and molar fraction of DMC to Gly of 10 b was -1.13. In the case of turbulent inertial breakage, Shinnar 48 suggested the value of b=-1 for drops size lower than the Kolmogorov length scale (ηk), and the theoretical exponent value b=-1.2 for drops large than ηk 49. When viscous stresses govern the breakage of droplets, the exponent b should be -1.5 for droplets of a size smaller than ηk. Calabrese and Leng 50 suggested for viscous dispersed phases, b should be −0.75 if viscous forces are essential to stabilize the droplet. In our case, the Kolmogorov length scale is of the order of 14 μm to 28 μm, with most droplets in this study being much larger than ηk. It may be suggested according to the Kolmogorov theory that turbulent inertial stresses more likely play the main role in droplets breakage for moderate viscosity drop but for the highest viscosity the transition of breakage mechanism is observed, and it depends on the viscous stresses. In addition, the exponent for moderately dispersed phase viscosity and concentration acquires a value close enough to -1.2. This slight discrepancy may be due to the fact that our investigation refers to a somewhat more concentrated system than others in the literature

48-51

and it may have also

impact on breakage of the droplets causing slight increases of exponent b. For highly viscous droplets, b acquired a value of -0.76, which is in good agreement with other work 49, 51, 52.

9



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10

3.4. Effect of temperature dependent variables on drop size distribution and Sauter mean diameter The values of viscosity and density of dispersed phase and interfacial tension decrease as temperature increases, leading to the ease of droplet breakup thereby reducing the energy required to form a small droplet. A fall of the viscosity of a bulk phase has a notable impact on the coalescence rate causing its increases 53. Since the differences of interfacial tension value in the studied systems were minimal, the main impact on droplet size distribution comes from the viscosity of dispersed phase, μd

54.

Its

reduction of viscosity changed the shape of DSDs from bimodal into unimodal as shown in Figure 5 (C-F). The distribution became narrower and close to normal and shifts to smaller droplets with increasing impeller speed. Comparison of DSDs reveals that they are mostly the same in shape since the difference of γ between moderate viscosities is rather small in such a way that the shape of drop size distributions are not much different from each other. Generally, the probability density function (PDF) by volume increased with decreasing together both viscosity of dispersed phase and size of the smallest droplets. Hence, high viscosity tends to produce dispersion with larger droplets. Comparison between the graphs in Figure 5 shows that the DSD curves shifted towards the large size of droplets as the dispersed phase viscosity increased. This is consistent with literature 47,

where oil dispersions in stirred vessels were investigated with DSD broadening as μd

increased, that is, the size of large droplets increased while the smallest also decreased. Wang and Calabrese

47

investigated oil emulsions in a stirred vessel and established that normal or

Gaussian or log-normal distributions for low and high μd were formed, respectively. DSDs were found to be strongly bimodal for each studied concentration at high viscosity of the dispersed phase, μd=945 mPa s. An asymmetrical shape of DSDs demonstrates the presence of the so-called daughter droplets as large and small daughter droplets as was also reported by De Hert and Rodgers 55. For high viscosities of the dispersed phase, Calabrese et al. 52 have found the DSDs are usually bimodal and as viscosity increases, they enlarge considerably because the small droplets become smaller and the large grow even more. De Hert and Rodgers reached a similar conclusion 55, observing that DSD was bimodal for silicon oils in the viscosity range from 328 to 29510 mPa s. The latter finding agrees with investigations conducted with crude oil of viscosity of 114 mPa·s at 313.15 K 47. Numerous studies investigated the effect of viscosity on DSDs and on droplet size/deformation in surfactant-free and surfactant-stabilized systems 42, 47, 49, 52, 56-59. Calabrese et al. 52 suggested 10


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that transformation of DSD from a unimodal to a bimodal is observed for silicon oils at μd≥1000 mPa s. However, in comparison with the result obtained in this study, it must be pointed out that for μd=945 mPa s it was found that the DSDs were already bimodal. Anyhow, this value is very close to that reported by Calabrese et. al. 52 and in good agreement with the work by De Hert and Rodgers 55, where the appearance of two types of droplets in the distribution (probably the beginning of bimodality) was observed at μd=327.9 mPa s, although bimodal distribution was clearly seen at μd=947.4 mPa s. For the similar range of viscosity 48-1000 mPas studied by El-Hamouz 60, surprisingly, the DSDs proved to be rather unimodal. According to our study and that by De Hert and Rodgers 55, it can be taken into consideration that the bimodality of DSD starts at around μd=945 mPa s, a slightly lower value than that proposed by Calabrese et. al. 52. The transition from unimodal to bimodal distribution is associated with the change of a breakage mechanism of parent droplets 52, 58. Viscous droplets, under the external forces, may stretch into threads prior to rupture and consequently generate a larger population of smaller droplets 49, 58, 59. The stretching increases with viscosity and therefore more and smaller droplets will be produced in systems with higher μd. In the case of non-viscous droplets, they break only into three segments 61. In Figure 5 (F) can be seen that for high viscosities the shape of DSDs are bimodal and broader whereas for low viscosities these are unimodal and narrower. The d3,2 at the same impeller speeds decreased simultaneously with μd, as observed from the values in Table S1. For the moderate viscosities (50.6 and 81.3 mPa s), these changes are not significant, but between moderate and at higher viscosity this change is more abrupt. At constant μd, the d3,2 increases as impeller speed decreased, as expected 47, 51, 59. Figure 7 presents the volume DSD for the three changing viscosity values of the dispersed phase at constant impeller speed, N=300 rpm, and ϕd=0.30, where the same trend discussed in Section 3.3 can be observed. The shape of DSD for moderate viscosities (81.3 mPa s and 50.6 mPa s) is similar due to the small difference in the value of μd and γ being both unimodal and narrower and different to that obtained at the highest viscosity, of bimodal shape. The droplets at high viscosity of the dispersed phase are stabilized by the inertial viscous force, which provides additional cohesive force, so more energy is needed to overcome it, leading to a decrease of the breakage of droplets. Droplets with higher viscosity also have lower drop breakage probability, where the breakage area in the stirred vessel become smaller 24, 41, 62. Conversely, for low μd, it seems that surface forces mostly govern droplet stabilization, and, in that case, the internal viscous force is neglected.

11



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The impact of temperature on drop size at constant impeller speed is presented in Figure 8, which shows that d3,2 decreases as temperature increased as was expected. The lines for the moderate dispersed phase are close to each other and their value is much lower than for high dispersed system. The reduction of d3,2 is much greater between temperature 298.15 and 333.15 K and smaller between 333.15 K and 343.15 K for all dispersions. That observation may be interpreted by a combination of different breakage mechanism assumed for high/moderate viscosity droplet and concentrated dispersions

26, 52, 53, 61.

The difference of μd between

temperature 298.15 and 333.15 K is approximately twelve times lower and almost twice between 333.15 and 343.15 K. The difference of drop size is not significant for moderate dispersion and viscosity. An increase of temperature leads to lowering of interfacial tension from 27.4 mN/s to 23 mN/s, respectively. However, there are small differences in the interfacial tension values at different μd. Therefore, the result again provides evidence of the influence on drop size mainly deriving from the viscosity of dispersed phase μd and less from interfacial tension, which is in resemblance with findings previously reported 54. 3.5. Effect of dispersed phase volume fraction on the Sauter mean diameter The events observed in dispersions, including coalescence, breakage and separation are affected by the concentration of the dispersed phase. An increase of ϕd leads to increase collision frequency of droplets so that breakage and coalescence occur more often 41. A highly dispersedphase concentration influences on small-scale turbulent eddies causing the reduction of their intensity; subsequently, they are less able to disperse droplets. This in turn means that the number of collisions between the droplets increases more than those caused by eddies (coalescence process is prevailing). When the dispersed phase is highly dispersed, the coalescence process is considered to present in the region away from impeller 35, 62. The drop dispersion in a non-stabilizing system is also dependent on the dispersed phase volume fraction. Figure S1 shows examples of images of investigated at the four different values of ϕd, while Figure 9 shows the mean Sauter diameter as a function of the same variable. At the same impeller speed and viscosity, large droplets are observed for the highest investigated volume fraction of dispersed phase as presumed. It seems that the size of droplets decreases as ϕd diminished at the same value of N and viscosity. Also, the results presented in Figure 9 show an increase of d3,2 with ϕd. This observation is more pronounced at low impeller speeds compared to high speeds. An explanation of this phenomenon relates to an expansion of the volume of the breakage zone as N increased and thus a reduction of the volume of the coalescence region 63. Much larger droplets were observed 12


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13

for the highest viscosity and values of d3,2 were separated from others. On the other hand, the value of d3,2 for lower viscosities are very similar, which is evidence of coalescence being dominated at higher ϕd due to the suppression of turbulent eddies, keeping their length larger than the diameter of droplets resulting in damping of further breakage of droplets

41, 60.

El-

Hamouz 60 observed no significant differences between d3,2 with time at highly viscous silicone oil system, which he studied in volume fractions ranging from 0.01 up to 0.5, in comparison with moderate and low viscosities system, where the impact of the dispersed phase volume fraction was more pronounced. d3,2 was smaller for lower ϕd in all studied systems. Calabrese et al.

47

have shown that droplet size was independent of dispersed volume fraction for oil

dispersion of ϕd between 0.08 to 0.24. This result is in disagreement with that of Khophar et al. 64,

who studied dispersed volume fraction from 10% to 50% of 60 mPa s oil and found droplets

size increase as ϕd raised and distribution became bimodal and broadened. The increase of droplets size with ϕd is directly in line with our work (recall Figure 5 and Table S1) as well as others for oil system in a turbulent stirred system

41, 51, 64-66.

However, most of the work has

been done for systems supplemented with surfactants, which help to prevent coalescence as the dispersed phase volume increases. In such systems, the impact of the dispersed phase volume fraction on the droplet size was found to be insignificant for ϕd up to 50%, whereas over this value, the droplet size started decreasing for highly viscous oils owing to the beginning of breakage of droplets where viscous stresses dominate viscosity rises 51. Figure 9 depicts the volume droplets size distribution for all investigated viscosities 945, 81.3 mPa s and 50.6 mPa s at constant impeller speed. The much stronger impact of ϕd on d3,2 is found at μd=945 mPa s, while for lower dispersed phase viscosity such impact is minimal. In all studied cases, the droplet size decreased with the reduction of dispersed phase volume, particularly for higher dispersed phase viscosity. Conversely, for moderate viscosity, this reduction is smaller. The results in this investigation indicate that at the same dispersed volume fraction but different viscosity DSD became wider and bimodal and narrow and unimodal. However, the bimodality does not develop as ϕd increases, as suggested by Khopar et al. 64, but comes from increases of μd, as established by Calabrese et al. 52 and found in this study. Comparison of d3,2 for high and low viscosities and all impeller speeds is presented in Table S1. At the same impeller speeds, smaller droplets were produced as both ϕd decreased from 0.30 to 0.08 and viscosity from 945 to 50.6 mPa s. Generally, smaller droplets generate a larger specific surface area than larger ones. For the specific case studied here, considering that Gly and DMC would react to generate the products GC and methanol in catalytic conditions, it is of great interest to generate larger specific interfacial areas so that the chemical reaction is as 13



Page 14 of 58

14

little hindered as possible by mass transfer. For this reason, following this logic, the most attractive reaction conditions would correspond to μd=50.6 mPa s and ϕd =0.08, i.e., a temperature of 343.15 K and a molar fraction of DMC to Gly of 10, which generate a specific surface area of approximately 2800 m-1. Nevertheless, for a value of ϕd =0.08, which corresponds to a molar excess of DMC to Gly of 10:1, it has been reported that upon production of GC, further products may generate from its reaction with excess DMC, which will in the end affect the yields to GC67. Therefore, careful consideration must be given for the selection of the proper molar excess of DMC to Gly despite it showing larger special interfacial areas. The data presented in Figure 5 revealed that the distribution became narrower for a dilute system. The peaks of the distribution of the small daughter drops are narrower with decreases of volume fraction but increases of impeller speed. It can also be seen that the reduction of volume fraction has an impact on size of the small and large daughter droplets. Thef for of published qualitative all data oil viscosities on increase modelof oils. under the droplet study issize consistent with increase with The data summarized data in Table S1 lead to a similar conclusion as the observations in Figures 7, 9 and 10 that droplets size increased with higher ϕd. As discussed before, the higher ϕd causes turbulent damping in continuous phase, however, it is important to recall again impact of the dispersed phase viscosity on d3,2. According to Table S1, the large droplets where observed for higher μd at the same impeller speed as was seen in DSDs presented in Figure 5. It may be explained by the fact that the dispersed phase viscosity acts on the breakage rate, and at a high viscosity of dispersed phase droplets are stabilized by both forces: surface and internal viscous. The presence of viscous forces required to use high turbulent intensities because of overcoming of additional cohesive force and thus reduce breakage of droplets 68. Therefore, in a system with viscous droplets, the breakage probability decreases due to a diminishing of events area compare to low viscosity 69. 3.6. Sauter mean diameter as a function of the Weber number In the past, authors developed correlations that relate droplet size (identified by d3,2) with the Weber number (We). Firstly, Hinze 70 proposed an equation, followed by modifications thereof by Chen and Middleman 24 and Calabrese et al. 52. We is defined by Eq. (3) 𝑑32 𝐷

= 𝐶1𝑊𝑒 ―0.6

[3]

This equation is relevant for non-viscous dispersed drops and diluted dispersions where the concentration of the dispersed phase is very low. The coefficient C1 depends on the type of impeller and for impeller applied in this work Leng and Calabrese 50 and Chen and Middleman 24

suggest C1=0.056. The literature review shows that the constant C1 reached higher range of 14


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15

0.081

51

to 0.11

36

at low dispersed-phase viscosity. Despite the fact, that there is a many

evidence of successfully applications of Eq. 4 36, 41, 54, 71, it was found that the exponent at Weber number should be altered at different operating criterions when the formula for Weber number, 𝑑3,2 ∝ 𝑊𝑒 ―0.6, is applied for high phase ratio dispersed phase fraction

41, 71, 72.

The

investigations have been demonstrated that the exponent at Weber number was lower than theoretical value of -0.6 for high dispersed fraction 41 and higher when dispersed phase of high density was studied 36. The reduction of the value of the exponent at We is caused by the fact the Eq. 3 was developed for dilute and low viscosity system, much differ than these investigated in this work. In such case, the rate of coalescence is negligible and the concentration of the dispersed phase is not considered. The extension of Eq.3 for higher concentrations is stated in Equation 4, where coalescence process becomes more notable in the region away from impeller together with a possibility of reduction of the turbulence in the continuous phase in the presence of the dispersed phase 62, 71 in a system: 𝑑32 𝐷

= 𝐶2(1 + 𝜙𝐶3)𝑊𝑒 ―0.6

[4]

The constant 𝐶2 depends on the impeller type (and is relevant to C1 and C4 in Equation 5) while 𝐶3 defines the tendency of a system to coalesce. Several values of 𝐶3 have been reported in the literature ranging from about 3

35, 41

up to 20 71. The higher value of 𝐶3 means that a system

coalesce easily, lower value of constant indicates slow coalescence. However, Pacek et. al. 71 suggested that an equation should be used where the exponent of the Weber number is to be inferred experimentally. The effect of viscous forces is neglected in Equation 4, which is applicable for an inviscid liquid. Since viscous force has an important impact on the cohesive stress at high viscosities, this factor should be included in the expression. This effect of viscosity can be implemented by incorporating a dimensionless viscosity number Vi 47 1

𝑑32 𝐷

= 𝐶4𝑊𝑒

where 𝑉𝑖 is viscosity number defined by 𝑉𝑖 =

𝑑32

0.6

( ))

―0.6

(1 + 𝐶5𝑉𝑖

3

𝐷

[5]

𝜇𝑑𝑁𝐷 𝜌𝑐 0.5 𝜎

(𝜌𝑑) . This expression considers the viscous

energy dissipation in the dispersed phase during the breakage process; both stabilization forces surface and viscous are included. Records of successful application of Equation 5 for experimental data collected in stirred vessels have been found in the literature 47, 52, 72.

15



Page 16 of 58

16

Figure 11 presents a dimensionless size ratio (d3,2/D) as a function of We for a progressive viscosity of dispersed phase and dispersed volume fraction. The data were firstly fitted with Equation 3 and then with Equation 4, which is applicable for more concentrated systems. Pacek et al.

35

proposed to use two ways for correlation by using Equation 4 where, firstly, the

constants C2 and C3 were established by correlating experimental data with linear regression when exponent at We equals -0.6 and second, three unknown coefficients were determined in Equation 4: both constant and exponent at We. It seems that Equation 3 fits well to the data for both cases; however, the exponent of We has not exactly met the theoretical value of -0.6, although it is close enough. This discrepancy occurs owing to the fact that Equation 3 was developed for a dilute system where breakup processes were dominant, with a volume fraction of dispersed phase smaller than 5%. In the current investigation, high and moderate volume fractions of dispersion was studied. Our results for every viscosity of the dispersed phase are shown in Figure 11 (A) and slightly differ with the findings of Abidin et al. 54, where the exponent of We was close to the theoretical value estimated for a turbulent flow and dilute non-coalescing system of −0.6 and its value decreased with μd. This difference in value and trend of the exponent of We comes from the investigation of the varied volume fraction of dispersed phase: ϕd=0.01 (dilute system) studied by Abidin et al.

54

and ϕd=0.3-0.08 in the present work. When comparing the changes of constant C1, the

same trend is observed, and value of constant increased with μd but decreased with ϕd (see also Figure 11 (B)). The values of C1 retrieved from correlation varied from 0.08 to 0.128 as μd increased, being greater than available results with the same impeller

24, 59.

This appears that

the physical properties which are contained in We possibly affect the constant C1/C2 in Eq.3-4. However, the increasing volume fraction of dispersed phase is also known to cause increases of C1 in both coalescent and non-coalescent systems as the dispersed phase is considered to suppress the turbulence 24. This contrasts with our results, where C1 decreases as ϕd grows. It may be a result of the impact both parameters μd and ϕ on d3,2 and eventual simplification of Equation 3, which is applicable for non-viscous dispersed drops and dilute dispersion. Plotting normalized d3,2/D (Fig. 11 (B)) as a function of We for different ϕd showed no significant differences between data at moderate viscosities, as can also be seen in Table S1; however, for high viscosity, the difference is quite remarkable, particularly, for ϕd=0.30. This deviation can be explained by the fact that the experiments, in this case, were performed in a transient flow, Re=2100-3540. Generally, the exponent at We escalates as ϕd increases, which agrees with the conclusion reached by Kraume et al. 41. At small volume fractions of dispersed phase, the breakage process prevails over coalescence, so the exponent of We is close to 16


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17

theoretical value. The probability of a higher coalescence rate increases with ϕd and μd, so it seems that coalescence process dominates in the system due to decrease of breakage rate. At the highest viscosity and ϕd, d3,2/D is proportional to We-0.38 and quite close to the theoretical description derived for a system dominated by coalescence 48. Our results suggest that at the highest viscosity and volume fractions the coalescence process of droplets prevails due to a much higher contribution of viscous force in the stabilization of droplets against breakage than for moderate viscosity. The results discussed above clearly indicate both viscosity of the dispersed phase and the volume fraction affect the degree of coalescence and thus the constant C1/ C2 and exponents at We. Since Equation 3 does not consider the effect of volume fraction, Equation. 4 was adopted and the constants and We exponents were evaluated and summarized in Table S2 by applying the modification proposed by Pacek et al. 35, where all constants and indices at We were estimated. A similar trend of changes of exponent at We was found with respect to those obtained from Equation 3. The value of exponent increased with the viscosity of dispersed phase, from -0.59 to close to -0.38 with regression coefficient, R2, >0.9657 and decreased with volume fraction ϕd at constant μd. The values of -0.59 for moderate viscosity and dispersed fraction is in very close agreement with the theoretical value. However, the equivalent correlation for others is much further from the theoretical value of the exponent. The value of constant C2 seen in Table S2 is not in all cases exactly in the range 0.05-0.11 reported for this impeller since these values were predicted for low dispersion and viscosity system. Although, values of C2 showed the increment as ϕd decreased. As discussed above, the physical properties included in We, viscosity and volume fraction of dispersed phase may affect constant C2. The constant C3 was between 3.3 to 10.9, which indicates Gly in DMC is coalescing system 62, 73 (after agitation stopped, the system separated promptly in all cases), and much faster coalescence process occurs for 8% of the concentration of dispersion. The data above indicates that there is a strong effect of viscosity on d3,2 over μd, but this aspect is neglected in Equation 4. Therefore, the use of viscosity number may be more suitable as it represents the ratio of viscous to surface forces

47.

Applying the value of liquid properties

summarized in Table 2 together with used impeller speed gives the value of Vi number from 0.42 to 11. However, the value of Vi number decreases with an increase of viscosity of dispersed phase and for moderate viscosity, its value is

An assessment of the dispersion of glycerol in ... - ACS Publications

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