Influence of impeller geometry on hydromechanical stress in stirred

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Thermodynamics, Transport, and Fluid Mechanics

Influence of impeller geometry on hydromechanical stress in stirred liquid/liquid dispersions Chrysoula Bliatsiou, Alexander Malik, Lutz Böhm, and Matthias Kraume Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03654 • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 19, 2018

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Industrial & Engineering Chemistry Research

Influence of impeller geometry on hydromechanical stress in stirred liquid/liquid dispersions Chrysoula Bliatsiou*, Alexander Malik, Lutz Böhm, Matthias Kraume Chair of Chemical and Process Engineering, Technische Universität Berlin, FH6-1, Straße des 17. Juni 135, 10623 Berlin, Germany KEYWORDS. stirred tank, impeller, particle stress, multiphase flow, drop size distribution, liquid/liquid dispersion ABSTRACT. Hydromechanical stress is a crucial parameter for a broad range of multiphase processes in the field of (bio-)chemical engineering. The effect of impeller type and geometry on hydromechanical stress in stirred tanks is important. The present study aims at characterizing conventional and new impeller types in terms of particle stress. A two-phase liquid/liquid noncoalescing dispersion system is employed, and the drop breakage is monitored in-line in a stirred tank. The published effects of agitation on drop deformation were confirmed and expanded significantly for five modified new impeller types. Radial impellers are advantageous for applications where low shear conditions are desired. A modified propeller with a peripheral ring and the developed wave-ribbon impellers present remarkable results by producing significantly low and high hydromechanical stress respectively. The results obtained were correlated in terms of mean and maximum energy dissipation rate, as well as circulation frequency in the impeller swept volume.

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INTRODUCTION

In industrial application, stirred tank reactors are broadly used in chemical and biochemical processes. Stirring is a crucial process parameter, which must fulfill several and often conflicting goals, i.e., bulk fluid mixing, multiphase dispersion, heat and mass transfer, homogeneity of the processed material, shear stress on suspended particles. For systems with suspended particles (e.g., crystals, flocs, drops), or growing organisms (e.g., biological cells, microorganisms) the stirring conditions define the mechanical stress on the suspended material. The particle stress can often be desired to produce an increased interfacial area between two phases in emulsification, polymerization, dispersion, and aeration processes.1–6 On the other hand, processes such as crystallization,

precipitation,

or

biotechnological

applications,

where

shear-sensitive

microorganisms or cell structures are present, can be detrimentally affected by particle stress. 7–11 Whether beneficial or not, the hydromechanical stress is of crucial significance for the design and operation of chemical and biochemical processes. Particle stress is mainly the result of the relative velocity between particles and the surrounding fluid. Most frequently, dispersion processes in stirred tanks are performed under turbulent flow conditions.12,13 The stress acting on particles is determined by the local turbulent velocity 2 fluctuations over time √u' . Additionally, if there is a significant density difference between the

two phases, i.e., bulk fluid and particles, the mean velocities of the particles and the fluid also differ, which leads to impact stress.12,14 The latter is defined as the stress caused either by the contact between particles, between a particle and the impeller element, or between a particle and the tank wall. However, when the density differences or the particle concentrations are low, the impact stress is considered negligible.12,14


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In a stirred tank the turbulence of flow can be described by the theory of energy cascade.15 Under turbulent flow conditions eddies of different sizes are formed. The turbulent kinetic energy is transferred successively from large energy-rich eddies to smaller ones with a decreased energy content. This process is limited by the viscosity of the fluid, which causes the kinetic energy to be ultimately dissipated as thermal energy in eddies of minimal size present in the fluid.12,15 Under isotropic turbulence conditions, these terminal eddies have a characteristic ¼

 3 length  known as the Kolmogorov microscale  = ( fl ⁄loc ) , where fl is the kinematic viscosity of the fluid and loc the local specific energy dissipation rate.16 In stirred reactors, although the main flow is not isotropic, local isotropy can be assumed.15 The maximum local energy dissipation rate max occurs in the impeller region and defines the minimum size of eddies that are formed in the stirred tank. For the hydromechanical particle stress, the size ratio between particles and flow eddies is of crucial significance. Particle disintegration is mainly caused by eddies with a size comparable to that of the particles.12,15 When the eddies are significantly larger than the suspended particles, the particles follow them in a convective movement. Eddies much smaller than the particles have an energy content which is too low to induce breakage. In the velocity field of the determining eddies, the dynamic stress acting on particles is defined ̅̅̅̅2 . Considering the distance r = dP between according to the Reynolds stress t = ∙u´ neighboring points in the flow field, the stress is given by: 12,15 2

Inertial range: r > 25∙ , t ∝∙(loc ∙Δr)3 Dissipation range: r < 6∙, t ∝∙Δr2 ∙

loc fl

(1) (2)

When r < 3∙ , the shear stress becomes independent of r, with

1

 t ∝∙( loc )2 .17 fl


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In stirred systems, the particle stress has been correlated with different process parameters, such as the mass specific average energy dissipation rate ̅ =

P ∙V

, the impeller tip speed utip , the

maximum local energy dissipation rate max , the circulation time tc , and the energy dissipation circulation function (EDCF). The mean specific energy dissipation rate and the impeller tip speed have been insufficient to interpret the stress phenomena in stirred systems, where local characteristics of turbulence play a significant role, and thus they have been proven to be impractical criteria for scale-up.7,18,19 On the other hand, direct measurements of the local energy dissipation are experimentally difficult.20 According to published studies up to 60% or even 80% of the energy dissipation occurs in the impeller region.21–23 In this region the most severe breakage of suspended particles is expected to happen and as a result the ratio of maximum local to mass-averaged energy dissipation rate

max 

is

significant for the hydromechanical stress caused by a given impeller and reactor geometry. Table 1 presents correlations available in literature to estimate

max 

as a function of the impeller

and reactor geometrical characteristics. These correlations often lead to contradictory results for the hydromechanical stress caused by different impeller types (axial, radial). Works based on fluid dynamic measurements (e.g. Particle Image Velocimetry-PIV, Laser Doppler AnemometryLDA), such as the one published by Geisler24, report that axial impellers with low power numbers are characterized by low

max 

ratios. For this reason, axial stirrers were considered to be

“low-shear” agitators in the past.25 Indirect methods to estimate the particle stress caused by different stirrers were applied by other researchers. Henzler and Biedermann14 and Pacek et al.26 used two-phase particulate systems for their investigations (floc suspensions and drop dispersions respectively) and they recorded the particle breakage that occurred during stirring. These studies together with the work of Jüsten et al.18, who worked on the fragmentation of


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filamentous bioagglomerates, were the first to conclude that axial stirrers cause higher hydromechanical stress leading to an increased particle breakage. These results could indicate higher

max 

ratios for the case of the axial impellers in comparison to the radial ones. The

contradictions among the various approaches to estimate

max 

are represented by the mathematical

models summarized in Table 1. McManamey estimated the maximum dissipation rate by accepting that the main energy dissipation occurs in the impeller region.27 Instead of the total tank volume, he used the impeller swept volume VI to evaluate the order-of-magnitude of the maximum energy dissipation. This approach has been adopted widely in the literature to correlate particle sizes with

max 

in mixing systems.26,28,29 Henzler and Biedermann proposed that

for the definition of the impeller volume VD , where the largest part of the energy dissipates, the geometrical features of the impeller have to be considered.14 They introduced a geometrical function F, which allows the approximation of

max 

. To interpret the particle stress in a universal

way by using only the maximum to average energy dissipation rate is challenging.13,24 To overcome this challenge, it has often been stated that apart from the maximum energy dissipation, the local distribution of energy dissipation and the local residence time of particles in the respective energy dissipation zones should be taken into consideration to assess the particle stress in stirred systems.19, 24,30 In 1996 Jüsten et al.18 introduced a concept known as energy dissipation circulation function (EDCF). This function combines the effect of both the maximum energy dissipation in the impeller region and the frequency with which the suspended material passes through this region (circulation time, tc ). Jüsten et al. examined systematically the influence of stirrer geometry on the morphology and fragmentation of Penicillium chrysogenum in unaerated vessels and proved


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d

that, at the same specific power input, radial paddle impellers and Rushton turbines with large D ratios caused less hyphae fragmentation in comparison to axial impellers with small

d D

ratios and

with low power numbers. In an attempt to find a proper scale-up parameter, it was reported that P

P

1

I

c

both the V and the utip approach failed. The energy dissipation circulation function, V ∙ t , which is a modified concept of an earlier trial of Smith et al.8, seemed to be the correlation approach with the best results.18 In the biotechnological field, further studies used the EDCF successfully to interpret the effect of agitation on the growth, fragmentation and morphology of microorganisms.9,10,31–33 In the field of liquid/liquid dispersions Zhou and Kresta19 were also the first to consider the drop break-up as the result of the interaction between the local max and the circulation time of the mean flow tc . Table 1. Correlations for the estimation of the ratio of maximum to mean energy dissipation rate in stirred tanks. Reference

1 H max D 3 3 = 0.14∙C∙Ne ∙ ( ) ∙ ( )  D d

Geisler24

max cD D 3 V = π3 ∙ ∙ ( ) ∙ ( 3)  Ne d D

Liepe34 McManamey27 Henzler and 12,14 Biedermann

Research method Laser Doppler Anemometry

Correlation

max 

∙V

P

.F = P ∙ D



= (∙V ) ∙ ( P ) = V with VI = 4 ∙hI ∙d2 I

max 

P

V

Liquid/liquidmodel system Liquid/liquidsystem

VD V

𝑑 2

= (𝐷)

c

I

= F with 2

2

2 h 3 H -3 ∙ ( dI) ∙NB 0.6 ∙(sin)1.15 ∙NI 3 ∙ (D)

Solid/liquidmodel system

Investigations with real systems, such as chemical reactive emulsions or growing microorganisms or, remain complex, time- and cost-intensive and affected by multiple (bio-


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)chemical parameters. For this reason, the use of model particle systems has been proposed and reported widely in literature, to facilitate investigations towards a more cost-effective optimization of the stirring parameters in the reactors of interest.12 The most frequently reported model

particle

systems

include

enzymes

immobilized

on

carriers12,

oil

(or

solvent)/water/surfactant emulsions13,26,28,35–40 and a clay/polymer flocculation system14,29,41–43. These systems have been used to investigate mechanical stress phenomena in stirred tanks29,44, shake flasks40, model viscometers14, pumps38 and airlift reactors17,45 in a more cost- and timeeffective way. The objective of this work is to investigate the influence of various impeller geometries on the particle stress in a stirred tank. To quantify the hydromechanical stress, a liquid/liquid model system is developed, and the drop breakage induced by different impeller types is monitored inline during the stirring process with an endoscope measuring technique. Apart from the conventional impeller shapes, which are widely used in technical applications, modifications of the impeller geometries are tested in this study. The goal is to identify geometrical modifications, which could be used to develop “low shear” agitators, in terms of reduced particle breakage. Five newly developed impellers are investigated in this work. The design of these impeller configurations is mainly based on the cooperation with EvoLogics GmbH. The various stirrers are primarily compared in terms of mean specific energy dissipation rate per mass . In an attempt to interpret the basic hydrodynamic mechanism, which defines the particle stress, literature approaches to estimate the maximum energy dissipation and the circulation frequency in the impeller swept volume are applied for the correlation of the experimental results. In this study the reported results are obtained in the frame of a project with biotechnological inititiave. They concern a break-up controlled liquid/liquid dispersion, but can also find application in any


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multiphase process where the deformation of (solid or fluid) particles and the control of the particle size is of importance.


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MATERIALS AND METHODS

In the present study, the developed model system consisted of two liquid phases. A Newtonian fluid silicon oil M100 (Carl Roth) with density D = 965.4 kg/m3 and dynamic viscosity  = 96.2 mPa∙s at 22.5 °C was chosen as the dispersed phase. Ultrapure water (  0.055 µS/cm, PURELAB flex 2 system, ELGA Labwater) with density D = 997.6 kg/m3 and dynamic viscosity   0.95 mPa∙s at 22.5 °C was used as the continuous phase. The volume phase fraction of the dispersed phase was D = 1.5% v/v. To avoid coalescence of the droplets the nonionic surfactant Triton X-100 (Merck, purity 99.8%) was added at a concentration of 0.232 mmol/L (  0.15% w/w with respect to water), which corresponded to a concentration ten times higher than the critical micelle concentration of the surfactant/water system (CMC = 0.0232 mmol/L). The interfacial tension between the phases was measured to be   5.08 mN/m. The dynamic viscosities of the single phases were determined using a cone-plate rheometer (MCR 302, Anton Paar) with temperature control mechanism. The density measurements were conducted using the oscillating U-tube principle (DSA 5000 M, Anton Paar). The measurements of the interfacial tension between the phases were carried out according to the Pendant drop method (OCA 20, Data Physics). Experiments were performed in a cylindrical glass tank with a dished bottom (Figure 1), an inner diameter of D = 160 mm and the filling height

H D

= 1. Fourteen impellers with various

dimensions and geometries were investigated (Table 2, Figure 2). These included common impeller types such as Rushton turbines, pitched blade turbines and propellers and five newly developed impellers; a propeller with an incorporated circumferential ring and four patent pending impellers of EvoLogics GmbH (bionic-loop impeller and wave-ribbon impellers). The blade length and the disc diameter of the employed Rushton turbines were not designed


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according to the standard dimensions usually reported in literature, but based on the dimensions of Rushton turbines employed in a prototype lab-fermenter. The off-bottom clearance hc , defined as the distance between the centerline of the impeller blades and the bottom of the tank impeller, was kept constant at hc = 0.33∙D. The vessel was fitted with four equally spaced stainless-steel baffles connected at their bottom with a ring. The baffles had a width BB = 12 mm, thickness TB = 2 mm, immersed length HB = 114 mm and a baffle ring of BRB = 10 mm width. The distance of the baffles from the tank walls was AB ≈ 5 mm. The absence of baffling below the impeller plane was a characteristic feature of the employed set-up, with the goal of geometrically simulating a prototype lab-fermenter. The temperature in the system was controlled at 22.5 °C using an external thermostat.

Figure 1. Experimental set-up and dimensions of the stirred tank and basic impeller dimensions.


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Table 2. Geometric dimensions and power number (turbulent flow regime) for the investigated impellers. Impeller Rushton turbines pitched blade turbines propellers propellerring impeller

d D

h d

[-]

NB [-]

 [°]

RT-d/D=0.6 RT-d/D=0.4

0.6 0.4

6 6

90 90

0.2 0.2

RT-d/D=0.33

0.33

6

90

PBT-6×90° PBT-6×45° PBT-6×45°-h/d=0.2 PBT-6×22.5° PROP-h/d=0.28 PROP-h/d=0.33

0.33 0.33 0.33 0.33 0.33 0.325

6 6 6 6 3 3

PROPRing-h/d=0.33

0.338

3

Abbreviated symbol

hI d

t d

Additional dimension For RT impellers: b d = 0.3, dd = 0.54 d

[-]

Νe [-]

0.2 0.2

0.02 0.02

4.2 4.06

0.2

0.2

0.02

3.52

90 45 45 22.5 25 25

0.24 0.24 0.2 0.24 0.28 0.33

0.24 0.17 0.14 0.09 0.12 0.14

0.02 0.02 0.02 0.02 0.02 0.02

4.07 1.53 1.47 0.51 0.3 0.34

25

0.33

0.15

0.02

0.36

= 0.02 Ring dimensions: hR = 0.15, d

0.7

= 0.04 Ring dimensions: hR = 0.05, d

[-]

[-]

td d

tR d

bionic-loop impeller

BiLOOP WRI-d/D=0.33-51.2° WRI-d/D=0.4-41.4° WRI-d/D=0.4-28.8°

wave-ribbon impellers

0.33 0.33 0.4 0.4

7 -

55

0.24

51.2 41.4 28.8

-

0.19 0.49 0.35 0.25

0.02 0.01 0.01 0.01

0.52 0.33 0.23

tR d

= 0.02 -

An endoscope measurement technique (SOPAT GmbH) was used for the in-line detection of the transient and steady state drop size distributions. Two endoscope probes were used in order to cover a wide range of drop sizes. The endoscope tip was positioned at the stirrer level, hend H

≈ 0.3 in the middle of the two baffles at a distance of approximately 2 cm from the tank wall.

Measurements at different regions of the tank

hend H

≈ 0.8 and 0.65 with respect to the bottom of

the tank and close to the shaft were also conducted. The deviation of the mean Sauter diameter d32 measured at the different tank regions was up to 5%, which is well within the experimental error, showing spatial homogeneity of the dispersive system in terms of drop sizes inside the tank.


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Figure 2. Impellers under investigation.


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For the enhancement of the image quality a mirror was attached to the endoscope tip with a gap size of 5 mm. The spherical shape of the produced drops allowed a simple determination of their size through an automated image analysis software (SOPAT GmbH). For each measurement point at least 2500 drops were analyzed. The minimal detectable drop size was ~10 m. The reproducibility of the experiments was exemplarily tested for ten operating conditions, revealing deviations in d32 from 0.4-7.2%. The experiments had a duration of 1.5-6 h depending on the time needed to reach a steady state 1 i

d32,i -5 ∑j=i-5 d32,j d32 ) = t steady state ti -ti-5

condition, which was defined as (

≤ 0.06

m . min

The minimal stirrer

speed was chosen to ensure fully developed dispersion (by means of visual observation) and the maximal stirrer speed was limited to prevent air entrainment from the surface. The absence of drop coalescence was confirmed experimentally by lowering the agitation speed drastically after a long time of stirring. The drop sizes remained unaffected, even 2 h after stirring at low rotational frequency, proving that drops do not coalesce in the system within this timescale. All experiments were carried out in the turbulent regime, where the power number Ne of an impeller is constant. The measurements of the power numbers were conducted with ultrapure water in the same vessel. For these measurements, the stirrers were attached to a viscosimeter (HAAKE Viscotester VT 550, Thermo Fischer Scientific GmbH) to measure torque and rotational speed. The agitation power and the power number Ne were calculated as following: Ne =

2∙∙N ∙Μ ∙Ν3 ∙d5

=

P ∙Ν3 ∙d5

(3)


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RESULTS AND DISCUSSION The following sections focus at first on the transient and steady-state drop size distributions of the examined liquid/liquid-system. A suitable characteristic drop diameter is chosen as reference parameter to quantitively describe the influence of the impeller type on the dispersion process and the drop breakage. Then, the detailed investigation of the effect of the impeller geometry on drop breakage is presented, by using the mean power input per unit mass as a base for the comparison among the impellers. Finally, the literature approaches correlating the particle breakage with the maximum energy dissipation and the impeller circulation frequency are applied to the obtained results in order to interpret the main hydrodynamic mechanism for the drop breakage. Drop Size Distributions The first goal of this study was to determine the appropriate characteristic drop size, which is used to describe breakage kinetics and allow the comparison of the drop deformation caused by different impeller types. According to Hinze46, in a break-up controlled dispersive system the maximum stable drop diameter dmax solely depends on the maximum local energy dissipation rate max and can be used to indirectly assess the hydromechanical stress in turbulent systems.40,47 By accepting that the equilibrium Sauter mean diameter d32 is proportional to dmax , most of the stirred tank reactor studies address d32 as the characteristic size of dispersion processes.28,38,48–50 In this study, the evolution of the drop size distributions is analyzed in order to fully comprehend the working dispersive system and the break-up mechanisms and to objectively choose an appropriate drop diameter as criterion for the comparison of the various impeller types. Figure 3 shows the development of the characteristic drop diameters over time for experiments with the Rushton turbine RT-d/D=0.33. The break-up process is clearly depicted by


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the maximum drop diameter dmax , as well as by the various volume based drop diameter percentiles (dv10 , dv50 , dv90 ) and the Sauter mean diameter d32 . The number based drop sizes (dn10 , dn50 , dn90 ) and the arithmetic mean diameter d10 do not evolve significantly over time.

Figure 3. Evolution of drop diameters during the experiment (RT-d/D=0.33, =0.24 W/kg). To interpret this physical behavior, the cumulative number distributions need to be examined. Figure 4(a) and Figure 5(a) depict exemplary number based cumulative distributions at different points in time of the experiment and under the variation of . Figure 4(a) shows that since the earliest experimentation stages more than 60% of the droplets have a diameter of dP ≤ 50 m, while up to 90% of the counted droplets have a diameter of dP ≤ 100 m. Over time, as a result of the breakage process and the lack of coalescence, the absolute number of the droplets dP ≤ 100 m increases significantly, but their percentage changes only slightly. Therefore, the changes in the number based percentiles (dn10 , dn50 , dn90 , d10) during the experiment are insignificant. Figure 5(a) presents the steady state Q0 distributions as a function of  for the Rushton turbine RT-d/D=0.33. It is remarkable again that the increase of  makes the Q0 rise less


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steeply at first (dP ≤ 50 m) and thus surprisingly the percentage of small droplets is smaller for higher ̅. By observing the slope of the distribution curves, it can be seen that the steepness of the Q0 increases with increasing  for dP > 50 m, but it is only at dP ~100 m that the curves intersect. These findings indicate a mechanism where the breakage of large drops produces a greater number of secondary droplets in the range of 50 m ≤ dP ≤ 150 m, while small droplets of dP ≤ 50 m are steadily produced and are stable due to the presence of surfactant. Similar development of the Q0 functions were reported by Wille et al.28 in a study with a coalescence inhibited liquid/liquid system. Moreover, these findings verify the conclusion of Zhou and Kresta37, who reported that the arithmetic mean diameter d10 was inappropriate as characteristic size to relate the droplet size with the turbulent flow created by different impeller types. At the same time, the small/medium size droplets (dP ≤ 100 m) dominating the Q0 distributions, are almost negligible for the volume based Q3 distributions. The latter are strongly affected by the presence of large drops, since the volume is proportional to ~ dP 3 . Over time (Figure 4(b)) and by increasing  (Figure 5(b)), the Q3 distributions move to smaller droplets, recording the break-up of the big drops present in the dispersion system. These large drops as shown in Figure 4(a) and Figure 5(a) correspond only to 10% of the total particle number and the change of their number could not be depicted clearly in the number distributions. Thus, only volume based drop diameter percentiles can be used to describe the influence of the power input and impeller type on the drop breakage.


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Figure 4. Transient cumulative distribution of (a) number and (b) volume for the RT–d/D=0.33 at =0.24 W/kg.

Figure 5. Cumulative distribution of (a) number and (b) volume at steady state for different mean specific energy dissipation rates  for RT-d/D=0.33.


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Self-similarity of drop size distributions The shape of the drop size distribution provides significant insight into the nature of microprocesses involved in forming the distributions. The self-similarity of drop size distributions means that distributions follow an invariant pattern and have similar shapes with respect to dispersion time, agitation speed or any other variable of interest. This invariance can be revealed by a normalization of the distributions, often based on d32 and dmax.40,47,50–52 To compare the self-similarity of the drop size distributions in the present work various criteria are used as displayed in Figure 6. The diagrams show the related standard deviation ratios and

3 d32

0 0 , dn50 d32

for the steady state drop size distributions of all impellers. For each impeller the whole

operating range of mean specific energy dissipation  is taken into consideration and presented as an average single point with the respective deviation bars representing the deviations of selfsimilarity for different stirring frequencies. In Figure 6(a) the strong deviations of

0 dn50

make

apparent that the number based distributions are not self-similar. Large deviations are observed for each impeller separately at the different operating conditions, as well as among the impellers. Therefore, no correlation can be established between the number based drop sizes for the various impellers. Nevertheless, when the volume based size d32 is used, the ratio of the standard deviation of the number distributions and the Sauter diameter of the various impellers is constant 

with an average value of d 0 = 0.36 ± 10%. At the same time, Figure 6(b) clearly proves the self32

similarity of the volume based distribution with an average value of

3 d32

= 0.35 ± 10%. The

aforementioned average values derive only from the first eleven impellers in the order presented in Figure 6. The wave-ribbon impellers are excluded from the calculation of the average values. Their distributions show systematically larger deviations from all other impeller types, indicating


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that the dispersion mechanism and the microprocesses in the reactor induced by these impellers probably differ. By examining the widths of the number and volume based distributions, similar conclusions were reached. Lack of self-similarity was also observed when the span0: the number based distributions was considered, while the span3:

dv90 -dv10 dv50

dn90 -dn10 dn50

of

indicated that the volume

based distributions are equally wide for the various impellers (excluding again the wave-ribbon stirrers).







Figure 6. Related standard deviation (a) d 0 , d 0 and (b) d 3 of all steady state drop size n50

32

32

distributions in the whole operating range of mean specific energy dissipation rates  for the investigated impellers. Finally, Figure 7 shows a constant average value of

d32 dmax

= 0.54 ± 10% for the different

operating conditions and impellers apart from the wave-ribbon impellers, which is well in agreement with literature data in the range of 0.56-0.61 for break-up controlled dispersion systems.2,47,48 It is concluded that in the investigated coalescence inhibited dispersion system, the


19


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hydromechanical stress caused by various impellers can be quantified only by examining volume based drop size distributions. The Sauter mean diameter d32 , as a volume based averaged size, emphasizes the changes of the large droplets with the time, the power input and the impeller type. For all further correlations the Sauter mean diameter d32 is used as reference size.

d

Figure 7. Ratio d 32 of all steady state drop size distributions in the whole operating range of max

mean specific energy dissipation rates  for the investigated impellers. Comparative study of impeller type and geometry In this section, the steady state Sauter mean diameter d32 is plotted over the mean specific energy dissipation rate  for the various impeller types. The correlation function between these two -b

physical sizes has the form: d32 ∝  . Based on the model of Shinnar and Church15, Henzler12 and Wollny36 transformed the correlation as following: d32 ∝  dissipation range and d32 ∝ 

-2/5

-1/3

for the particle stress in

for the particle stress in inertial range. The models are valid if

the flow field is fully turbulent. For fully developed turbulence, the following condition must be 

satisfied:  150...250, with  being the macroscale of turbulence.12,34 


20

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To characterize the predominant forces (inertial, viscous) of the particle stress in the system under investigation, the determined drop sizes are compared with the size of Kolmogorov microeddy  under the various operating conditions in the stirred tank. The calculation of  prerequisites the estimation of max for every impeller. To estimate this, the equation of Liepe34 as displayed in Table 1 is used. Values for the factor cD of the formula are extracted from literature.34,36 However, data are not available for all impeller types employed here and thus  is estimated only for some of the impellers. The calculated turbulence parameters are given in Table S1. In the majority of cases the condition of

d32 

< 6 is satisfied, indicating particle stress

in the dissipation range of microturbulence and dominant viscous stresses. For this reason, the experimental data in the following diagrams are plotted using the correlation d32 ∝ 

-1/3

to which

they fit at a remarkable degree. In Figure 8(a) the effect of the impeller diameter ratio

d D

on the droplet size is presented. The

Sauter mean diameter d32 is plotted versus the mean specific energy dissipation rate  for three d

Rushton turbines with varying diameter. At equal  the impellers with larger D ratios produce less breakage of the dispersed droplets, which confirms the results reported in relevant research works.12,14,18,36 At equal  a larger impeller operates at a significantly lower rotational frequency and thus at a lower tip speed, which apparently plays an important role in the drop break-up. Zhou and Kresta53 conducted LDA measurements, showing that the impeller diameter has a great effect on the maximum turbulent energy dissipation rate max . The authors reported a change of the turbulent flow field with increasing impeller diameter and a decrease of strong interactions between the impeller and the tank walls.53 The lower

max 

max 

, attributed to

values for larger

impellers are assumed to be the reason for the reduced particle stress.


21


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d

Figure 8. Influence of (a) the impeller diameter ratio D and (b) the stirrer blade angle on the steady state drop size d32 in correlation with the mean energy dissipation rate . Figure 8(b) shows the effect of the impeller blade angle  on the drop size for pitched blade turbines. The only varying parameter for the stirrers was the blade angle, while the ratios of the d h t

other dimensions D, d,

d

were kept constant. The decrease of the blade angle corresponds to a

significant decrease in power number (Table 2), which further results in increased droplet breakage when equal power input per unit mass is applied. The results agree with the work of Henzler and Biedermann12,14, who considered that the increase in the angle of the impeller blades reduces the particle stress. The PBT-6×22.5° and PBT-6×45° are axial flow impellers, while the impeller PBT-6×90°, which is in fact a flat paddle impeller with small

h d

ratio, causes an

important change in the flow direction, which is expected to become radial in this case. Apparently, the radial induced flow is beneficial for reduced particle stress. Ranade and Joshi54 investigated the effect of impeller blade pitch (=30°, 45° and 60°) on the flow pattern by means of LDA. They established that the blade angle significantly affects the flow characteristics, since


22

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an increased  (up to 60°) results in an enlarged average liquid velocity, increased total flow circulation, and higher turbulence intensity. However, these findings cannot be directly correlated with the results of the present study to which they seem contradictory. In Figure 9 various propeller types are compared in terms of drop break-up. A comparison of the two conventional 3-blade propellers (PROP-h/d=0.28 and PROP-h/d=0.33) with different blade height

h d

shows that an increase in the impeller height leads to an increase in the power

number of the agitator and thus to reduced drop breakage at equal . Newly developed propeller types were also investigated in this study. The bionic loop impeller BiLOOP, as well as the wave-ribbon configurations WRI-d/D=0.33-51.2°, WRI-d/D=0.4-41.4°, WRI-d/D=0.4-28.8° are compared with the conventional 3-blade propellers. The BiLOOP, which is here operated in an up-pumping mode, forms relatively larger drops than the PROP-h/d=0.33 and PROP-h/d=0.28 at equal . The wave-ribbon impellers produce the greatest drop breakage and thus the largest interfacial area per volume. Therefore, they appear to be particularly suited for dispersion processes, where a large droplet surface is required. Nevertheless, they could not accommodate the requirements of a “low shear” demanding process, where the particle breakage is undesired. Additionally, the wave ribbon impeller WRI-d/D=0.33-51.2° causes less drop d

break-up than the wave ribbon impellers with larger diameter ratios D, leading to the conclusion that the angle of the band is more crucial than the impeller diameter. Finally, the conventional 3-blade propeller PROP-h/d=0.33 was modified by adding a ring to connect the blades. The addition of the circumferential ring has a small impact on the power number of the impeller (Ne=0.34 for PROP-h/d=0.33 and Ne=0.36 for PROPRing-h/d=0.33 respectively). Nevertheless, stirring with the propeller PROPRing-h/d=0.33 results in droplet size distributions with significantly larger droplet diameters. This propeller type seems to cause the


23


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lowest particle stress of all examined propeller shapes. It is assumed that due to the addition of the ring the supplied energy dissipates in a more equally distributed way in the impeller region, decreasing the shear strength of the agitator. These results show that a modification of conventional propellers with the usage of circumferential rings could probably change the flow field in a significant way and consequently the hydromechanical stress acting on particulate material. It is estimated that modifications in this direction could lead to an impeller geometry suited for applications where “low shear” stirring conditions are desired.

Figure 9. Influence of the propeller type on the steady state drop size d32 in correlation with the mean energy dissipation rate . The comparison of the various impeller geometries investigated in the present work is depicted in Figure 10. The radial impeller types, i.e., Rushton turbines and the PBT–6×90° (which is practically a type of flat paddle impeller with small

h d

ratio), cause less drop breakage at equal

specific power input in comparison to the axial propellers (pitched blade turbines, propellers) and the modified bionic-loop and wave-ribbon impellers. Simultaneously, the drop breakage caused


24

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by the axial 6×45°-pitched blade impellers and the modified propeller with the peripheral ring PROPRing-h/d=0.33 is low and comparable with the one produced by the radial impellers.

Figure 10. Influence of the impeller type on the steady state drop size d32 in correlation with the mean energy dissipation rate . The power input range of operation for the different impellers varies significantly. The radial impeller types can ensure a complete oil dispersion at lower power inputs. An increase in the impeller diameter d for the Rushton turbines, as well as in the blade angle  for the pitched blade turbines result in a fully developed droplet dispersion at lower . All four modified stirrers (PROPRing-h/d=0.33 and WRIs) are especially characterized by a limited operational area of , providing a full dispersion only at high power inputs and causing surface aeration shortly after that point. In the past, the axial flow impellers had been considered as “low shear” agitators due to their low power numbers.25 However, the studies in particulate systems reveal that the particle stress caused by these impellers is higher.13,14,26,28,36 This statement is in general agreement with the


25


Page 26 of 47

results of the present study with the exceptions of PBT-6×45° and PROPRing-h/d=0.33. The interpretation of the increased hydromechanical stress caused by axial impellers was proven to be challenging. Due to their low power numbers, the axial stirrers need to rotate at higher speed in order to operate at equal specific power input with the radial ones. Nevertheless, at the same time fluid dynamic investigations correlate the axial impellers with lower

max 

ratios. Which fluid

dynamic effect is responsible for the high hydromechanical stress of the conventional axial impellers is not yet clear. Wollny36 tried to enlighten this research topic by means of Computational Fluid Dynamics (CFD). He compared the flow profiles produced by a radial Rushton turbine and an axial 3×24°-pitched blade turbine. According to the conducted simulations, the significant region for the particle stress corresponds to a volume smaller than 1% of the total reactor volume and is limited in the impeller zone and. The volume of the impeller zone as estimated by Wollny was in fact of similar magnitude with the impeller swept volume as defined by McManamey27 (Table 1). This volume, which is affected by high velocity gradients, was found to be smaller for the axial impeller. At equal mean specific power input, the shear gradients in the impeller zone were significantly bigger for the axial pitched blade agitator. The amount of elongation gradients barely differed for the two impeller types. It was concluded that the axial flow impellers are characterized by a smaller volume where the particle deformation can occur, but also by higher shear gradients in this region, which leads to an increased particle stress in comparison to the radial impellers. Wille et al. 28 also concluded that axial flow impellers with low power numbers cause higher particle stress than radial stirrers. However, Wille et al.13 and Langer et al.42 considered as the predominant cause of the particle deformation and breakage the elongation gradients attributed to the axial induced agitators, and not the shear gradients as Wollny described. Langer et al.42 showed experimentally that in the


26

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macroscopic flow field the elongation flow can cause stronger particle breakage than the shear flow. Wille et al.13 carried out PIV measurements for a radial Rushton turbine and an axial 3×24°-pitched blade turbine. At equal specific power input, the axial flow impeller produced a considerably high elongation flow. At the same time, for the axial impeller, elongation and shear gradients extended over the whole volume between the impeller and the bottom of the tank. In the case of the radial stirrer, the respective gradients were present only to the vicinity of the impeller. It was concluded that the axial impellers build a larger area with high velocity gradients. This results in longer residence times of the particles in the corresponding region, increasing the probability of particle breakage. Despite the contradictory approaches

concerning the responsible forces

for the

hydromechanical stress (shear, normal stresses) in stirred tanks, the published studies agree on the fact that low power number axial impellers cause greater break-up on suspended particles. However, in the present study, the two 6×45°-pitched blade impellers produce drop size distributions very similar to the radial Rushton turbine RT-d/D=0.33 despite the important difference in the power number among these stirrer types (Table 2). Similar results had been reported by Wille et al.28, where a Rushton turbine and a 6×45°-pitched blade turbine produced similar equilibrium drop sizes, despite the higher circumferential velocity reached by the pitched blade impeller in order to operate at equal specific power input. On the other hand, the modified propeller PROPRing-h/d=0.33 with the peripheral ring appears to form significantly large droplets despite the very low power number. It is estimated that the addition of the ring allows a more homogeneous distribution of the energy dissipation in the impeller region, which reduces the drop breakage. Preliminary investigations of the flow field with PIV indicated a significant change in the flow direction by the addition of the


27


Page 28 of 47

peripheral ring. Although the conventional propellers induce an axial flow, the flow field formed by PROPRing-h/d=0.33 shows radial components as well. With respect to the other newly developed impellers, the abovementioned preliminary PIV investigations indicated an axial induced flow for WRI-d/D=0.33-51.2° and BiLOOP, an axial flow with radial components for WRI-d/D=0.4-41.4° and a radial flow with axial components for WRI-d/D=0.4-28.8°. The drop breakage caused by BiLOOP and WRI-d/D=0.33-51.2° is moderate and equivalent to conventional axial stirrers. On the other hand, the decrease in the angle of the wave-ribbon configurations triggers strong breakage leading to very small drop sizes. It is worth mentioning that the drop size distributions recorded for the wave-ribbon impellers do not fulfill the criterion of self-similarity described in Figure 6 and Figure 7. This is probably caused by different fluid dynamics, long residence time of drops in regions with high shear/elongation stresses, or even by impact stress between the drops and the impeller. Further comparison with literature-Correlation approaches The results in the previous paragraphs confirmed the published effects of agitation on hydromechanical stress in stirred tanks but also expand them by considering modified and newly developed impeller types. It is apparent that in stirred tanks by considering the average specific power input the drop breakage depends strongly on the impeller geometry. Apart from the mean mass or volume specific power input, other parameters have often been used in the literature to correlate the experimental results. Most frequently the efforts focus on using power input based parameters that can indirectly correlate the particle size with the maximum energy dissipation max in the stirred reactor. The most significant of these correlations are applied here in order to put the present work into the general framework of the currently available literature that concerns the selection of impeller type in stirring processes. The Sauter


28

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mean diameters at the steady state are used for all further correlations presented in the following paragraphs. In the attempt to comprehend the effect of max on drop breakage, one must take into consideration that the drops are subject to stress mainly in the impeller swept volume VI where the maximum energy dissipation max occurs. McManamey27 defined the impeller swept volume 

by VI = 4 ∙hI ∙d2 , estimating the maximum energy dissipated in the swept volume of the impeller as

max 

=

V 4 V = ∙ VI  d2 ∙hI

(Table 1). The calculated values of VI for the impellers under investigation

are presented in Table S2. Figure 11 presents the modified data based on VI . It becomes clear that approaching max by

P ∙VI

can achieve a general clustering of the experimental data for the

conventional impeller types. With respect to the modified impeller types, the BiLOOP impeller correlates well with the other data, while the PROPRing-h/d=0.33 deviates up to 30%. The data of the modified wave-ribbon impellers are not in agreemement with the rest of the experimental results. The estimation of the critical impeller volume as proposed by McManamey has limitations when it comes to non-conventional stirrer types. Limitations of the approach have been mentioned in literature by other authors as well.14,19, 26


29


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Figure 11. Influence of the impeller type on the steady state drop size d32 in correlation with the P

mean energy dissipation rate per impeller swept volume ∙V . I

Henzler and Biedermann14 suggested a modification of the calculation of the impeller volume so that other geometrical parameters of the impeller, e.g., number of blades and blade angle, are also taken into account. Therefore, they introduced a geometrical factor F (Table 1) to approximate the maximum energy dissipation rate as

max c = F. 

For the impellers employed in this

study, the F factors were calculated (Table S2), with the exception of the wave-ribbon impellers due to the lack of actual blades in these configurations. In Figure 12 the steady state Sauter mean 1

̅ . This function correlates the experimental data of the diameter is plotted as a function of F ∙

conventional impeller types to a good degree but again it fails to predict the results of BiLOOP and PROPRing-h/d=0.33, which appear to deviate up to 30% and 50% respectively. These deviations can be justified by the fact that the F function does not include any term that can describe the influence of the circumferential ring. In general, the F function approaches in a satisfactory way the critical volume around the impeller, where the drop breakage takes place,


30

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for conventional stirrer types, but it must be expanded to facilitate the geometrical description of new, more complex impeller types.

1

Figure 12. Correlation of the steady state drop size d32 with the F ∙ ̅ for all impellers. Jüsten et al.18 proposed the use of the energy dissipation circulation function (EDCF), defined P

1

I

c

as V ∙ t , to correlate and predict the breakage of the various impellers. This function considers not only the maximum energy dissipation in the impeller zone but also the frequency at which the particles are present in this zone. Even though the EDCF approach originates and finds application mainly in biotechnological systems, similar approaches have been followed also for liquid/liquid dispersions. Zhou and Kresta19 stated the need to consider simulateneously the local max and the circulation frequency

1 tc

in order to correlate the data for their employed silicon

oil/water dispersion. In this work, the EDCF approach as defined by Jüsten et al.18 is applied. To calculate the circulation frequency i.e.,

1 tc

=

Fl∙N∙d3 , V

1 tc

the approach of Smith et al.8 and Jüsten at al.18 was used,

where Fl is the impeller flow number. To accommodate the range of impellers


31


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employed, the flow numbers Fl for the standard impellers were calculated based on the power numbers, by using formulas available in literature as they have been reviewed by Jüsten et al.18. The calculated flow numbers for every impeller are displayed in Table S2. No prediction could be made for the modified impeller types. Figure 13 presents the clustering of the experimental data as a function of

P 1 ∙ VI tc

for the

conventional impellers. By this approach, the correlation of the measured drop sizes for the various impellers is again satisfactory. The deviations among the stirrers are considered insignificant (constantly less than 20%), taking into account that the flow numbers derive from general formulas and not from experimental measurements in the specific stirred system. The good correlation achieved by using the EDCF indicates the importance of the frequency at which the drops are subjected to high stresses near the impeller and the need to consider the circulation time as key-element for the interpretation of the particle stress in stirred systems.

Figure 13. Steady state drop size d32 as a function of energy dissipation rate per impeller swept P

1

I

c

volume and circulation frequency V ∙ t .


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CONCLUSIONS This work investigated the effect of the impeller geometry on particle stress in stirred tanks. The most widely used conventional agitators and five new impellers were examined in terms of particle stress. To quantify the hydromechanical stress in stirred tanks, a non-coalescing liquid/liquid dispersion system was used. The drop breakage was recorded in-line by means of an endoscope measuring technique. To describe the influence of the power input and impeller type in breakage only the volume based distributions could be used as reference parameters. Therefore, the Sauter mean diameter d32 was used as reference size under a broad range of operating conditions. The comparison of the impellers was based on the mean specific energy dissipation rate ̅ . The diameter d of the impeller, the impeller blade angle  and the impeller blade height h were proven to be important geometrical features of the agitator. An increase of the aforementioned geometrical dimensions resulted in reduced particle stress and thus larger drop sizes. The impeller type was also decisive for the drop breakage and the particle stress in stirred tanks. The high power-number, radial impellers caused reduced drop breakage compared to the low powernumber, axial agitators. Exceptions were the results of the 6×45°-pitched blade turbines and the modified propeller type PROPRing-h/d=0.33. These axial impeller types, despite their low power number, resulted in drop sizes comparable to the ones formed by the radial stirrers. The addition of a peripheral ring in the modified propeller must be further examined as a possible alternative for the development of a “low shear” impeller, for application where the particle breakage is undesired. The modified impellers, designed by EvoLogics GmbH, followed the general trend of the conventional propellers employed in this work. Especially, the wave-ribbon configurations resulted in the smallest drop sizes and could be of high interest in multiphase


33


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dispersion applications where the formation of a large interfacial area is desired. In these configurations, the angle of the band seemed to be a more crucial dimension than the impeller diameter and must be considered for further design optimization. All modified impellers were additionally characterized by a narrow operational area of power input being limited by the conditions of fully developed dispersion and surface aeration. To interpret the influence of the impeller type on the particle stress, multiple fluid dynamic effects need to be considered. The indirect correlation of the drop sizes with the maximum local energy dissipation rate max was made. For this purpose, the approaches of McManamey27 and Henzler and Biedermann14 to estimate the critical impeller swept volume (VI and VD ), where the maximum energy dissipation occurs, were followed. Both approaches clustered well the results for the conventional impeller types, but they do not match the data for the modified impeller geometries. The concept of EDCF was applied here, showing that the frequency by which the drops are passing through the impeller region must be quantified and used for further clarification of the particle stress induced by the impeller in a stirred system. Nevertheless, further systematic fluid dynamic investigations are needed to fully characterize the size of the area where the high velocity gradients occur and the circulation time of the mean flow for the conventional as well as the new stirrer types. Indisputably, as next research step, the exact flow fields formed by each stirrer, as well as the mechanisms (shear, elongation forces) responsible for the particle stress, need to be described by means of further experimental (PIV) and numerical investigations (CFD) in order to allow a more complete interpretation of the results obtained in the present study. Further fluid dynamic analysis of the new impeller types should be carried out. Finally, the reported results are valid for the specific employed set-up, which is characterized by absence of baffling below the impeller


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plane. Whether and how the baffle position could affect the particle stress induced by the examined stirrers should also be a topic of further research.


35


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NOMENCLATURE Symbols used AB BB BRB b C, c cD D d dd dp d10 d32 dn10 , dn50 , dn90 dv10 , dv50 , dv90 dmin , dmax F Fl H HB h hc hend hI (= h ∙ sin ) hR M N NB Ne NI P PD Q0 , Q3 TB t t tc td tR utip u' V

[mm] [mm] [mm] [mm] [-] [-] [mm] [mm] [mm] m] m] m] m] m] m] [-] [-] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [N∙m] [rpm], [rps] [-] [-] [-] [W] [W] [-] [mm] [mm] [min], [h] [s] [mm] [mm] [m/s] [m/s] [m3]

Distance of baffles from the tank wall Width of baffles Width of baffle ring Blade length for Rushton turbines Constant factors  Impeller factor for estimation of max (Liepe34)  Stirred tank diameter Impeller diameter Disk diameter for Rushton turbines Particle size Arithmetic mean diameter Sauter mean diameter Number based percentiles Volume based percentiles Minimum and maximum diameter Geometrical factor (Henzler and Biedermann12,14) Flow number of impeller Filling height of stirred tank Immersed length of baffles Height of impeller blades Off-bottom clearance Position level of endoscope tip Vertical impeller height Height of impeller ring Torque Rotational frequency Number of impeller blades Impeller power (Newton) number Number of impellers Power input Power input in a defined volume VD Cumulative drop size distribution of number and volume Thickness of baffles Thickness of impeller blades Time Impeller circulation time Disk thickness for Rushton turbines Thickness of impeller ring Impeller tip speed Velocity of turbulent fluctuation Volume of fluid in stirred tank


36

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VD VI Greek symbols   r ̅ loc , max  h  (≈ ) 2   fl , D 

[m3] [m3], [cm3]

Defined volume around the impeller Impeller swept volume

[°] [% w/w] [m] [W/kg] [W/kg] [S/cm]

Angle of impeller blades Mass fraction of surfactant with respect to water mass Distance between two neighboring points in the flow field Mean specific energy dissipation rate Local and maximum energy dissipation rate Electrical conductivity

[mm]

Macroscale of turbulence

[mm], [m] [mPa∙s] [m2/s] [kg/m3] [mN/m]

Kolmogorov microscale Dynamic viscosity Kinematic viscosity of fluid Density of fluid and disperse phase Interfacial tension Standard deviation of drop size distribution of number and volume Turbulent stress Volume fraction of dispersed phase with respect to total fluid volume

0 , 3

m]

t

[N/m2]

D

[% v/v]


37


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ASSOCIATED CONTENT Supporting Information. (Table S1) Estimated ranges of turbulence parameters; (Table S2) Impeller swept volume VI, geometrical factor F and flow number Fl for the investigated impellers AUTHOR INFORMATION Corresponding Author *Chrysoula Bliatsiou, Chair of Chemical and Process Engineering, Technische Universität Berlin, Tel: +49 30 314 25538, E-mail: [email protected] ORCID Chrysoula Bliatsiou: 0000-0001-9394-0031 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources The research was financially supported by the Deutsche Forschungsgemeinschaft (DFG SPP1934). Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENT This work is part of the Priority Program “Dispersity-, structural, and phase- changes of proteins and biological agglomerated in biotechnological processes”. Financial support by the Deutsche Forschungsgemeinschaft (DFG SPP1934) is gratefully acknowledged. The authors wish to thank EvoLogics GmbH for the cooperation and Ms. Lena Hohl for constructive criticism of the manuscript. ABBREVIATIONS CFD, Computational Fluid Dynamics; LDA, Laser Doppler Anemometry; PIV, Particle Image Velocimetry.


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Influence of impeller geometry on hydromechanical stress in stirred

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