RESEARCH Open Access [616207]

RESEARCH Open Access
Characterization of hydromechanical stress in
aerated stirred tanks up to 40 m3scale by
measurement of maximum stable drop size
Andreas Daub1, Marina Böhm1, Stefanie Delueg1, Markus Mühlmann1, Gerhard Schneider2and Jochen Büchs1*
Abstract
Background: Turbulence intensity, or hydromechanical stress, is a parameter that influences a broad range of
processes in the fields of chemical engineering and biotechnology. Fermentation processes are often characterized
by high agitation and aeration intensity resulting in high gas void fractions of up to 20% in large scale reactors.
Very little experimental data on hydromechanical stress for such operating conditions exists because of the
problems associated with measuring hydromechanical stress under aeration and intense agitation.
Results: An indirect method to quantify hydromechanical stress for aerated operating conditions by the
measurement of maximum stable drop size in a break-up controlled dispersion was applied to characterize
hydromechanical stress in reactor scales of 50 L, 3 m3and 40 m3volume with a broad range of operating
conditions and impeller geometries (Rushton turbines). Results for impellers within each scale for the ratio of
maximum to specific energy dissipation rate ϕbased on measured values of maximum stable drop size for aerated
operating conditions are qualitatively in agreement with results from literature correlations for unaerated operating
conditions. Comparison of data in the different scales shows that there is a scale effect that results in higher values
forϕin larger reactors. This behavior is not covered by the classic theory of turbulent drop dispersion but is in
good agreement with the theory of turbulence intermittency. The data for all impeller configurations and all
aeration rates for the three scales can be correlated within ±20% when calculated values for ϕbased on the
measured values for d maxare used to calculate the maximum local energy dissipation rate. A correlation of the
data for all scales and all impeller configurations in the form ϕ= 2.3 ∙(ϕunaerated )0.34∙(DR)0.543is suggested that
successfully models the influence of scale and impeller geometry on ϕfor aerated operating conditions.
Conclusions: The results show that besides the impeller geometry, also aeration and scale strongly influence
hydromechanical stress. Incorporating these effects is beneficial for a successful scale up or scale down of this
parameter. This can be done by applying the suggested correlation or by measuring hydromechanical stress with
the experimental method used in this study.
Keywords: Drop size, Turbulence, Hydromechanical stress, Energy dissipation, Aeration, Multiphase reactors
Background
Turbulence intensity, or hydromechanical stress, is a
parameter with an important impact on many different
processes in the fields of chemical engineering and bio-
technology. Since it governs the break-up of bubbles and
drops in a turbulent flow field [1] it is very important in
processes where interfacial area for mass transfer canbecome rate limiting [2]. Furthermore, turbulence inten-
sity has been discussed for a long time to have a large
influence on biotechnological processes by a direct ac-
tion on the biological phase [3]. E.g. cell viability in
microcarrier based cell culture processes can be corre-
lated with turbulence intensity [4]. In submerged fungal
fermentations turbulence intensity may interact with
morphological behaviour of the fungus [5]. It was shown
that volumetric power input in shake flasks is compar-
able to volumetric power input in stirred fermenters
[6,7] for typical operating conditions. Nevertheless, even* Correspondence: jochen.buechs@avt.rwth-aachen.de
1AVT.Biochemical Engineering, RWTH Aach en University, Worringerweg 1, Aachen
52074, Germany
Full list of author information is available at the end of the article
© 2014 Daub et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain
Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article,
unless otherwise stated.Daub et al. Journal of Biological Engineering 2014, 8:17
http://www.jbioleng.org/content/8/1/17

at comparable levels of volumetric power input pellets
grow much larger in shake flask culture compared to
cultures in stirred tank reactors because turbulence in-tensity is much lower than in stirred reactors [8-10].
There is a close interaction between morphology, broth
rheology and agitation intensity in submerged fungal fer-mentations in stirred tank reactors that can impact
process performance [11]. Production scale for fermen-
tation processes can be as large as several hundred m
3.
The development of these large scale processes is con-
ducted in lab or pilot scale fermenters. This poses the
question how to scale down the conditions prevalent inlarge production scale to the development scale and vice
versa. Typical parameters of interest may be mass trans-
fer coefficient k
La, volumetric power input P/V L, impel-
ler tip speed u tip, turbulence intensity in the form of
maximum local energy dissipation rate εmax, circulation
frequency t c, or a combination of these parameters like
the energy dissipation to circulation function EDCF (first
introduced by [12]) that is basically the ratio of εmax/tc.
Based on an estimation of the values of these parametersin large scale, small scale operating conditions (agitation
and aeration rates) can be estimated that resemble the
respective values of these different parameters in largescale. Testing these operating conditions in small scale
may reveal which of these parameters (if at all) is a suit-
able proxy for scaling up or scaling down a particularprocess. The work of Jüsten [11-13], e.g., showed that
scale up of mycelial flocs can be correlated with hydro-
mechanical stress and circulation frequency in the formof the energy dissipation to circulation function EDCF.
The morphology of the fungus in this case depends on
the break up in the impeller region that is governed byhydromechanical stress and the aggregation of mycelial
flocs in regions where turbulence intensity is low. Circu-
lation frequency is decisive for the time for aggregationand for the frequency the mycelial flocs pass the high in-
tensity region close to the impeller where they break up.
The whole procedure of testing different parameter can-
didates strongly depends on the validity of the correlations
used to calculate these parameters. Although turbulence
intensity is often discussed to influence biological pro-
cesses only few data exists on the influence of geometry,
scale and aeration on this parameter. There are two cir-cumstances that strongly complicate the intention of es-
tablishing comparable levels of turbulence intensity in
large and small scale: first, in industrial practice, geomet-rical similarity throughout the scales is hardly found
[14,15]. Therefore, the influence of geometry on turbu-
lence intensity must be known for a successful scale up orscale-down of this parameter. Second, in aerobic fermen-
tations the working medium is a multiphase gas-liquid
dispersion which is characterized by a volumetric gashold-up of up to 20% in production scale reactors [15]. Ofcourse, this is accompanied by much higher gas hold-ups
in the vicinity of the turbulence inducing agitators. Very
little is known on the influence of such high gas hold-upson turbulence characteristics in stirred tanks because it is
very hard to measure this parameter under these condi-
tions. Particle image velocimetry (PIV) and laser Doppleranemometry (LDA) are often used to measure maximum
local energy dissipation rates in small scale, single-phase
reactors [16-23]. However, these methods cannot be ap-plied in high gas hold-up conditions. Most available data
was measured in lab scale with low agitation intensity. A
review on existing data for maximum local energy dissipa-tion was presented in [24].
It would be desirable to have a simple and practical
method at hand to experimentally investigate turbulenceintensity in large-scale multiphase reactors. This would
enable a more rational approach to the scale-up and
scale-down of this parameter for existing process equip-ment and it would help to throw light onto this range of
operating conditions that are important for many pro-
cesses yet extremely hard to access experimentally.
Therefore, a method was established to measure
hydromechanical stress that can be applied in large scale
equipment at intense agitation and aeration. Details onthe development of the measurement method are speci-
fied in Daub et al. [25]. The method is based on the the-
ory of turbulent drop dispersion and uses the wellestablished correlation of the maximum stable drop size
d
maxwith maximum local energy dissipation rate εmax
for break-up controlled dispersions:
In an agitated tank, kinetic energy is introduced to the
liquid by the action of the impeller. This energy dissipates
in the reactor volume inhomogeneously. A maximumlocal value of energy dissipation, ε
max,e x i s t si nt h ei m p e l –
ler region that defines the most severe action of the flow
field on dispersed drops, bubbles or microorganisms. Theratio of maximum local energy dissipation rate to volume-
averaged energy dissipation rate is given by:
ϕ¼εmax
εð1Ț
Ø
where εØis the average energy dissipation rate in the reactor
volume per unit mass. εØis related to the volumetric power
input via the density of the liquid phase εØ=P / (ρVL).ϕis
constant for a given impeller, i.e. independent of agitationrate in single-phase op eration [23]. It, therefore, character-
izes a given reactor configuration in terms of the hydro-
mechanical stress. ε
maxcan be related to the maximum
stable drop size in a break-up controlled dispersion by [26]
dmax¼K1⋅σ
ρc/C18/C193=5
⋅ε−2=5
max ⋅1țK2⋅ηd
σεmax⋅dmax ðȚ1=3/C16/C173=5
⋅
ð2ȚDaub et al. Journal of Biological Engineering 2014, 8:17 Page 2 of 14
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with K 1= 0.23 [ 27] and K 2= 2.5 [ 26]. If d maxandεØare
known, ϕcan be calculated iteratively from Eqs. 1and2.
Since this equation models an effect of microturbulence,the constants should be independent of geometry and
scale [ 26].
This theory is valid if the flow field is fully turbulent and
the drop size is much smaller than the macroscale of tur-
bulence Λ=0 . 4h( Λ/d
max> 10) and much larger than the
microscale of turbulence λ=(ν3/ε)1/4(dmax/λ>1 0 ) . T h e
flow field is fully turbulent when the Reynolds number is
Re > 5 ∙103andΛ/λ> 150 [26].
There are different correlations available in literature
that allow an estimation of ϕfor single-phase operation
without aeration as a function of the impeller geometry for
Rushton type impellers. These are listed in Table 1. Prob-ably the most commonly used approach is McManamey ’s
equation [28] that estimates maximum energy dissipation
by relating the total impeller power to the volume sweptby the impeller. Jüsten et al. used this apprach to calculate
the energy dissipation to circulation function EDCF
[11-13]. Davies, 1985 [29] and [30] used the principle tocorrelate drop sizes for stirred tanks with different other
mixing devices, [31] used this approach to correlate par-
ticle stress in stirred tanks. Kresta and Brodkey [32] rec-ommend this approach “as the best practice estimate ”to
calculate maximum energy dissipation.
The experimental method based on the measurement
of maximum stable drop sizes was successfully applied
in a 3 m
3pilot scale reactor with 1.2 m inner diameter
to investigate the influence of aeration on the maximumlocal energy dissipation rate. The results were reported
in Daub et al. [24]. It was shown for impeller configura-
tions B-1 and B-3 (for geometrical details see Table 2)that energy dissipation in the impeller region is much
less intense for aerated operating conditions than for
unaerated operating conditions when compared at equalvolumetric power input. The ratio of maximum to
volume-averaged energy dissipation rate was reduced by
64% for impeller setup B-1 and by 52% for impellersetup B-3, respectively. Thorough control experiments
were presented concluding, that the interpretation of the
data on the basis of the theory of break-up controlled
drop dispersion is valid. Particularly the presence of co-
alescence as an explanation for increased drop sizesunder aerated operating conditions was ruled out byexperiments with and without aeration where dispersed
phase concentration was varied up to factor 20 between
lowest and highest concentration.
The same method will be applied in the current report
with 8 different reactor configurations with Rushton type
impellers in reactors of scales 50 L, 3 m
3and 40 m3in a
wide range of operating conditions (geometrical details
are given in Table 2). It is the goal of this study to pro-
vide a broad data basis to demonstrate the applicabilityof this method to real life equipment of different scales,
to characterize different reactor configurations with re-
spect to hydromechanical stress as a basis for successfulscale-up or scale-down of this parameter under aerated
operating conditions and to test whether established lit-
erature correlations for the estimation of hydromechan-ical stress for different impellers can be applied with
acceptable accuracy.
Results and discussion
Turbulence parameters
Parameter values for the turbulence parameters for the
range of operating conditions used in the present study
are presented in Table 2. The microscale of turbulence
was calculated with maximum local energy dissipationrates based on Eq. 1 with values for ϕalso given in
Table 2. All parameters are within the validity ranges for
the application of the theory of turbulent drop disper-sion (Re > 5 ∙10
3
,Λ/dmax> 10, d max/λ> 10 and Λ/λ> 150).
Drop size distributions in different scales
The shape of a drop size distribution reveals important
insight into the nature of the processes that formed the
distribution. It was argued that a similarity of drop sizedistributions for different operating conditions or differ-
ent equipment is a strong indication that the micropro-
cesses involved in forming the drop size distribution arecomparable. Brown and Pitt [34], Chen and Middleman
[35], Konno et al. [36], and Peter et al. [9], e.g., showed
that a plot of a normalized drop diameter versus the cu-mulative volume distribution reveals invariant drop size
distributions with respect to agitation rate and disper-
sion time. Normalization was done either by the Sautermean diameter d
32or the maximum stable drop size
dmax. Invariance of normalized drop size distributions is
referred to as self-similarity. Pacek et al. [37] point outthat the observation of self-similarity might partly be
due to a smoothing of fine differences by the cumulative
distribution that is typically used for these plots. Theyargue that differences in drop size distributions might be
clearer recognized in volume density distributions.
Therefore, these will be used in this work.
Volume density distributions for all three reactor sizes
used in this study are compared with each other in
Figure 1. Configuration A-2 is shown for the 50 LTable 1 Literature correlations
McManamey [ 28] ϕ¼4
π⋅VL
d2⋅h(3)
Okamoto et al. [ 33] ϕ¼0:85⋅h
DR/C16/C17−1:38
⋅e−2:46⋅d=DR (4)
Liepe et al. [ 26] ϕ¼0:1⋅π3
Po⋅VL
d2⋅h(5)
Liepe et al. [ 26] ϕ¼0:11⋅π3⋅VL
d3 (6)
Literature correlations for the estimation of the ratio of maximum to volume-
averaged energy dissipation rate ϕfor Rushton impellers for single-phase,
unaerated operating conditions.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 3 of 14
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Table 2 Geometrical details of the reactors used, geometrical details of impeller configurations and ranges of turbulence parameters
Geometrical details of reactors Geometrical details of impellers Turbulence parameters
Reactor
configurationNominal
reactor sizeDR VL HNumber of
impellersC ΔC d h w d/D Rh/d w/d Po n Re λλ /Λ dmax/λΛ /dmax
m m m m – – – – 1/s – μm- –
A-1
50 L 0.293 0.035 0.52 3 0.095 0.190.104 0.023 0.029 0.35 0.22 0.28 5.5 4.0 –11.7 4.3 –12 ∙10416–32 286 –571 14 –28 11 –39
A-2 0.15 0.05 0.05 0.51 0.33 0.33 8 3.6 –8.0 8.1 –18 ∙10413–23 400 –688 17 –21 19 –40
A-3 0.17 0.05 0.05 0.58 0.29 0.29 7.1 3.3 –7.2 9.6 –21 ∙10414–23 402 –674 17 –21 19 –39
A-4 0.19 0.05 0.05 0.65 0.26 0.26 6.4 2.8 –6.1 1.0 –2.2 ∙10513–23 396 –695 17 –21 19 –42
B-1
3m31.2 2.4a2.2 3 0.51 0.690.41 0.09 0.12 0.34 0.22 0.28 4.9 2.1 – 5.8 2.5 –9.7 ∙10511–23 1.5 –3.2 ∙10314–23 71 –211
B-2 0.45 0.09 0.12 0.38 0.2 0.26 5 1.9 –5.1 3.7 –10 ∙10511–23 1.5 –3.2 ∙10315–26 64 –185
B-3 0.51 0.12 0.18 0.43 0.24 0.34 5.9 1.3 –4.2 2.6 –11 ∙10511–25 1.9 –4.4 ∙10315–24 82 –261
C-1 40 m32.8 30 5 3 0.92 1.8 1.19 0.22 0.29 0.42 0.19 0.24 4.7 0.8 –2.3 1.1 –3.3 ∙10611–22 3.9 –8.3 ∙10313–24 163 –652
All impellers were 6-bladed Rushton type impellers installed in a three impeller configuration. Power numbers were estimated with Eq. 10, except for setup B-1 and B-3 for which Power numbers could be measured.
afor 0.1 vvm aeration rate: 2.6 m3, see Daub et al. [ 24].Daub et al. Journal of Biological Engineering 2014, 8:17 Page 4 of 14
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reactor, B-3 for the 3 m3reactor and C-1 for the 40 m3
reactor. It must be emphasized that the reactor configu-
rations are not geometrically similar. The drop size dis-
tributions shown were chosen to represent comparable
maximum stable drop sizes in all three scales. Agitation
rates and volumetric power inputs differed strongly for
the experiments shown (values are given in the caption
of Figure 1). The three drop size distributions with the
smallest drop sizes, e.g., did occur at 11 kW/m3in the
50 L reactor (A-2), at 6.2 kW/m3in the 3 m3reactor
(B-3) and at 2.0 kW/m3in the 40 m3reactor (C-1). The
drop size distributions are governed by a strong main
peak that can be fit very well by a normal distribution
(solid lines in the graph). There is a slightly increased
tendency to bimodal distributions with increasing scale.
This results in a reduced maximum value of the main
peak of the volume density distributions because the
integral of the volume density distribution is unity bydefinition. A second peak in the small diameter range,
therefore, reduces the area of the main peak. Very small
drops in the range < 50 μm are also present that might
be daughter drops that developed during break up of lar-
ger drops and did not coalesce to larger droplets any
more. These small droplets are not relevant for the sub-
ject of this work as described in [9] and [25]. Table 3
compares characteristic values for the main peaks of the
distributions that were calculated from the fitted normal
distributions. The ratio of d 32/dmaxfalls within a narrow
range of 0.56 to 0.61 for all the distributions from the
three scales. This shows that the drop size distributions
for the different operating conditions and scales are self-
similar. The values found for d 32/dmaxare well in agree-
ment with data from other groups found in break-up
controlled single-phase experiments without aeration.
Calabrese et al. [38], e.g., found values of 0.6 for moder-
ately viscous dispersed phases.
Maximum stable drop sizes calculated from these dis-
tributions are indicators for hydromechanical stress. To
perform a scale-up or scale-down of hydromechanical
stress it is necessary to correlate the maximum stable
drop size with operating conditions. This is the focus of
the following paragraphs.
Correlation of maximum stable drop size with impeller tip
speed u t
Maximum stable drop sizes for the different scales and
different impellers are compared in Figure 2 at an aeration
rate of 0.7 vvm (volume gas/volume liquid/minute). The
data for the different impellers within the 50 L and the 3
m3scale are in good agreement with each other. This
shows that a correlation of hydromechanical stress with
impeller tip speed u t=π∙n∙d gives reasonable results as
long as the scale is not changed. However, a comparison
of the results for the different scales shows that a scale-up
Figure 1 Measured drop size distributions with similar
maximum stable drop sizes in three different scales with
different reactor configurations. Dispersion of paraffin oil in 1 mM
PO4-buffer at pH 7.3. A:A-2 (50 L reactor), B:B-3 (3 m3reactor),
C:C-1 (40 m3reactor). See Table 2 for details on geometry. Aeration
rates in all measurements 0.7 vvm. Symbols: measured values for
agitation rates: A: ( ●) 8.0 1/s (11 kW/m3), (♦) 5.2 1/s (4.4 kW/m3), (ș)
3.6 1/s (1.3 kW/m3); B: (●) 3.7 1/s (6.2 kW/m3), (♦) 2.3 1/s (1.7 kW/m3),
(ș) 1.3 1/s (0.6 kW/m3); C: (●)1 . 81 / s( 2 . 0k W / m3), (♦) 1.3 1/s (0.9 kW/m3),
(ș) 0.8 1/s (0.2 kW/m3). Solid lines: fitted normal distributions.
Table 3 Comparison of maximum stable drop sizes d max
and Sauter mean diameters d 32for all three scales
Reactor
configurationAgitation
rateMaximum stable
drop size d maxSauter mean
diameter d 32d32/dmax
1/s μm μm-
A-28.0 207 125 0.60
5.2 305 183 0.60
3.6 500 296 0.59
B-33.7 226 129 0.57
2.3 350 196 0.56
1.3 501 293 0.59
C-11.8 238 146 0.61
1.3 355 215 0.61
0.8 539 312 0.58
Operating conditions were chosen to result in similar maximum stable drop
sizes for the different scales.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 5 of 14
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with constant impeller tip speed will not result in compar-
able values of d max. Therefore, the levels of hydromechan-
ical stress in the different scales will be different if u tis
kept constant. This is in accordance with the results of
Jüsten et al. [13] who showed that the fragmentation of
Penicillium chrysogenum mycelium can be correlated
well with impeller tip speed for different impeller geom-
etries within one scale but not for different scales.
Figure 3 shows the maximum stable drop sizes versus
impeller tip speed for reactor configuration B-3 operated
with different aeration rates from 0.1 vvm to 0.7 vvm to-
gether with a power function correlation of the data.
Most data for the highest aeration rate of 0.7 vvm lies ator above the fitted line while most data for the lowest
aeration rate of 0.1 vvm lies below the fitted line. Gener-
ally, at the same impeller tip speed, higher aeration rates
yield larger maximum stable drop sizes. This shows that
there is an influence of aeration on maximum stable
drop size that cannot be incorporated using u t.
Especially in industrial practice impeller tip speed is
frequently applied as a correlator for hydromechanical
stress. Margaritis and Zajic [39] estimate that 20% of the
fermentation processes in industry are scaled up based
on this rule. The results shown here, in accordance with
earlier analyses on the value of impeller tip speed for
scale-up of processes [13,15,40,41], clearly show that im-
peller tip speed is not well suited to correlate hydro-
mechanical stress in fully turbulent aerated stirred tanks.
Correlation of maximum stable drop size with volumetric
power input
The theory on drop break-up (as described in the back-
ground section) suggests a correlation of maximum
stable drop size for a given impeller with power per unit
mass εØor equivalently volumetric power input P/V L.I t
was already reported in Daub et al. [24] for configura-
tions B-1 and B-3 that if results are compared on the
basis of aerated volumetric power input the aeration rate
has no relevant influence on the maximum stable drop
size in the investigated range. Hence, with aerated volu-
metric power input as the correlating parameter, the in-
fluence of aeration on energy dissipation is directly
reflected. This means turbulence intensity scales directly
with volumetric power input also in the aerated case.
This is demonstrated in Figure 4 with the same data as
in Figure 3. The solid line shows that the data is well in
accordance with the theoretical prediction from Eqs. 1
and 2 ( ϕ= 6.9).
For cell culture processes, not only the effect of max-
imum energy dissipation induced by the flow field is rele-
vant for cell damage [42,43]. More importantly, bubble
formation at the sparger and bubble rupture at the liquid
surface are known to be the major cause for cell death by
hydrodynamic forces in these processes [44-46]. Attach-
ment of cells to bubbles plays an important role in the le-
thal effects of bursting bubbles in cell culture processes
[47,48]. There is no evidence that these effects may have
a ni n f l u e n c eo nt h em a x i m u ms t a b l ed r o ps i z e .M e a –
surements were conducted with aeration rates varied
from 0.1 vvm to 1 vvm. If bubble rupture had a consid-
erable influence on the maximum stable drop size a cor-
relation of maximum stable drop size with aeration
intensity migh be expected. Additionally, when unaer-
ated and aerated data were compared in a previous pub-
lication [24], maximum stable drop size was smaller
without aeration than with aeration (with the same
volumetric power input). Hence, it can be concluded
Figure 2 Maximum stable drop size as a function of impeller
tip speed u tfor all impellers as indicated in the legend
(impeller geometries according to Table 2). Lines indicate power
law fit for different scales: solid: 50 L scale, dashed: 3 m3scale, small
dashed: 40 m3scale. Dispersion of paraffin oil in 1 mM PO 4-buffer at
pH 7.3. Maximum stable drop size measured after 3 h agitation.
Aeration rates in all measurements 0.7 vvm.
Figure 3 Correlation of maximum stable drop size with
impeller tip speed for reactor configuration B-3 (3 m3scale)
for different aeration rates. Dispersion of paraffin oil in 1 mM
PO4-buffer at pH 7.3. Maximum stable drop size measured after 3 h
agitation. Solid line indicates fitted power law curve.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 6 of 14
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that the experimental resul t ss h o w ni nt h i ss t u d ya r e
not influenced by the effects of bursting bubbles.
Figure 5 shows the correlation of maximum stable
drop sizes for all three reactor scales with volumetric
power input. The results for configurations A-1 and A-4
in the 50 L reactor and for B-2 in the 3 m3reactor again
demonstrate that the influence of aeration for each im-
peller type is well reflected by correlating the data with
aerated volumetric power input. Therefore, the data
for the reactor configurations where aeration rate was
not varied can be regarded as representative for these
reactor configurations. The data for all scales and all
impeller geometries follow generally the prediction of
the theory for turbulent drop break-up. This is indi-
cated by the lines in Figure 5. These were calculated
on the basis of Eqs. 1 and 2 by fitting the value of ϕ
to the whole data set of each impeller by means of the
least squares method.
The measurements clearly discriminate between the
different impeller configurations in the 50 L reactor. The
larger the impeller, the larger the maximum stable drop
size at a given volumetric power input. This is equivalent
with a decrease in the ratio of maximum to specific en-
ergy dissipation rate with increasing impeller size and
consistent with existing literature data for unaerated op-
erating conditions [28].
The characteristics of the impellers used in the 3 m3
reactor are relatively similar in relation to the measure-
ment accuracy for the maximum stable drop size and
the impellers can hardly be distinguished. Nevertheless,
a sequence of the three impeller configurations is appar-
ent that is in accordance with the results for the 50 L re-
actor. The smallest impeller B-1 produces the smallestmaximum stable drop sizes at a given volumetric power
input. The larger impeller B-2 with the same impeller
blades as B-1 produces larger drops and the largest
impeller with larger impeller blades B-3 results in the
largest maximum stable drop sizes at a given volumetric
power input.
For the 40 m3reactor, the data suggests a higher slope
than predicted by the classic theory of drop dispersion
that is represented by Eqs. 1 and 2. However, the data is
relatively scarce because the reactor was only available
for a short period of time. The quality of the fit of the
data by the correlation is compared for all reactor con-
figurations in Table 4. The quality of the fit is measured
by the standard deviation of the relative difference be-
tween measured value and calculated value for d max. For
all reactor configurations, including the 40 m3reactor,
the values are below the standard deviation of d maxfor
independent experiments which was determined to
approx. 10% [25]. That means the deviation between
measurement and model has a similar magnitude as the
Figure 4 Correlation of maximum stable drop size with
volumetric power input for reactor configuration B-3 (3 m3
scale) for different aeration rates. Dispersion of paraffin oil in 1
mM PO 4-buffer at pH 7.3. Maximum stable drop size measured after
3 h agitation. Solid line represents theoretical prediction based on
Eqs. 1 and 2 with ϕ= 6.9.
Figure 5 Maximum stable drop sizes measured in three
different scales: A: 50 L, B: 3 m3,C :4 0m3.Dispersion of paraffin
oil in 1 mM PO 4-buffer at pH 7.3. Maximum stable drop size
measured after 3 h agitation. Symbols for different reactor
configurations as indicated in legend of Figure 2 (geometries
according to Table 2). Code for different aeration rates: +-center: 0.1
vvm, full symbol: 0.4 vvm, open symbol: 0.7 vvm, x-center: 1.0 vvm.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 7 of 14
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deviation between independent experiments. It is, there-
fore, not possible to clearly distinguish between a sys-tematic deviation of the results from the classic theory
of drop dispersion and measurement inaccuracy for a
relatively small set of data as for the 40 m
3reactor.
Turbulence intermittency might explain an increased
slope for d max. This extension of the classic theory of
drop dispersion takes into account the intermittent char-acter of fine-scale turbulence as laid out by Baldyga and
Podgorska [27] and Baldyga et al. [49]. In this concept,
ε
maxis not taken as a constant but as a stochastic vari-
able that fluctuates about its mean value. The theory
predicts that rare but strong bursts of high energy
become more and more important for the evolution ofthe maximum stable drop size with increasing dispersion
time. This results in a long-term drift of maximum
stable drop sizes towards smaller drops. As a conse-quence, the exponent on maximum energy dissipation
rate becomes time-dependent with values up to -0.62 for
very long dispersion times [49]. Additionally, intermit-tency is stronger for higher Reynolds numbers [50] and,
therefore, the effect becomes increasingly important with
increasing scale.
All data presented in this study were measured be-
tween 100 and 180 min of dispersion time. The max-
imum stable drop sizes measured were essentiallyconstant during this time span in all reactors. Examples
for this were shown in Daub et al. [25]. Extending the
experimental time to up to 9 h yielded a further decreaseof the maximum stable drop size in the range of 10%
compared to the value at 3 h dispersion time in the 3 m
3
reactor. This is qualitatively in agreement with the pre-
diction of the effect of intermittent turbulence, but the
extend of the effect is relatively small and comparable to
the reproducibility of the measured values in independ-
ent experiments. The data for the 3 m3reactor follows
equally well the classic theory of drop dispersion as thedata for the 50 L reactor. It must be assumed that the
scale-effect on the slope cannot be resolved with the ap-
plied measurement method because it is below thereproducibilty of the experimental method. If the meas-
urement accuracy in the 40 m
3reactor is similar to that
in the other scales and taking into account that the ef-fect of turbulence intermittency on the slope was not
strong enough to be detected for the other reactor con-
figurations it seems justified to assume that the differ-ences between measurement and model for the 40 m
3reactor rather reflect measurement inaccuracy than the
effect of intermittency on the slope. We, therefore, sim-
plify the analysis and restrict the value of the slope tothat of the classic theory of drop dispersion.
The data for the largest impeller in the 50 L reactor
(A-4) exhibits a higher slope than expected for all aer-ation rates. This impeller has an extreme geometry with
very large d/D
R-ratio of 0.65 and large impeller blades.
The distance between the impeller tip and the baffles isonly 0.02 m. This probably gives rise to a nonstandard
flow-field which may result in a modification of the
turbulence characteristics. Additionally, the calculatedvalues for power input based on Eq. 8 might possess a
larger error than for the other impellers that are closer
to standard geometry. The impellers for A-2, A-3 andA-4 have the same impeller blades but different impeller
diameters. A-3 generates larger maximum stable drop
sizes at the same power per unit volume than A-2. If thistrend is extrapolated to A-4 than larger maximum stable
drop sizes may be expected for A-4 than for A-3 at the
same volumetric power input. The values for the lowerrange of power inputs for A-4 up to 4 kW/m
3are in
agreement with this expectation but the data for the
higher power inputs tend towards smaller maximumstable drop sizes than expected. By interpreting the data
on the basis of Eqs. 1 and 2 the value of ϕfor this im-
peller might be overestimated in comparison to theother impellers.
Estimation of maximum local energy dissipation rate εmax
and the ratio of maximum to specific energy dissipation
rateϕ
The literature correlations for the ratio of maximum to
specific energy dissipation rate ϕgiven in Table 1 can be
used to calculate the maximum local energy dissipation
rateεmaxfor different operating conditions and reactor
geometries. It must be emphasized that these correla-
tions were derived for single-phase, unaerated operating
conditions and not for aerated operating conditions.However, up to now the only practical way to estimate ϕ
for different reactor configurations for aerated operating
conditions was to assume that these correlations can beapplied also in the presence of aeration. This was first
supported by the data of Bourne [51] that is based on a
chemical method to measure micromixing efficiency.Bourne [51] came to the conclusion that ϕis not influ-
enced by aeration. Fort et al. [52] report on a roughly
20% reduction of turbulence intensity in the presence ofaeration. However, their data is based on the measure-
ment of pressure fluctuations at constant agitation rate.
There is no clear conclusion with regard to the influenceof aeration on ϕ. The data presented in Daub et al. [24]
clearly shows that ϕis reduced by aeration based on the
same measurement technique that is used in this study.Table 4 Quality of the fit for all 8 reactor configurations
Reactor configuration A-1 A-2 A-3 A-4 B-1 B-2 B-3 C-1
Standard deviation [%] 6.1 2.0 1.7 9.0 3.9 5.1 4.0 6.7
Standard deviations of the relative difference between measured values for
dmaxand calculated values based on Eqs. 1and 2(values for ϕsee Table 5)
were used as a measure for the quality of the fit.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 8 of 14
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The relation of these results to the findings of Bourne
[51] and newer literature data incorporating similar
methods are discussed in Daub et al. [24]. As an ex-
ample for the value of the correlations from Table 1 for
aerated operating conditions, Figure 6 compares all data
obtained in this work with εmaxcalculated with the cor-
relation of McManamey [28]. This equation was used
because it might be the most common correlation to es-
timate εmax[24]. Given the simplicity of this type of cor-
relation, the broad spectrum of impeller geometries used
in the experiments and the broad range of scales applied,
the results are in reasonable agreement. The prediction
from this simple correlation is probably accurate enough
for crude estimations in industrial practice.
Figure 7 shows the data for all impeller configurations
and all operating conditions for the three scales with
the maximum local energy dissipation rate calculated
with the values for ϕbased on the experimental data
and Eqs. 1 and 2. Most of the data lies within ±20%
around the prediction as indicated by the solid and
dashed lines in Figure 7. A very accurate correlation of
t h ed a t ai sa c h i e v e d .T h i se m p h a s i z e st h ei m p o r t a n c eo f
the experimental method applied for scale-up and
scale-down studies of hydromechanical stress in aerated
stirred tanks.
Table 5 allows an analysis of the main factors that in-
fluence the value of ϕ. The table shows the values for ϕ
that were derived from the aerated experiments and the
values calculated with the different literature correlations
from Table 1. The absolute values for ϕfor each impel-
ler differ strongly for the different correlations and incomparison to the values that are based on the measure-
ments. This was expected and already discussed in Daub
et al. [24]. Despite the differences in the absolute values,
the relative order of the impeller configurations within
the 50 L and the 3 m3scales is the same for the mea-
surements as for all the different correlations. That
means the influence of geometry within one scale is
qualitatively well predicted by the correlations.
The absolute values for ϕthat were derived from the
measurements are small compared to the values from
literature correlations. It was shown in Daub et al. [24]
that a comparison of maximum stable drop sizes under
aerated and unaerated operating conditions for reactor
configurations B-1 and B-3 reveals a strong attenuation
of turbulence intensity by the presence of air. ϕwas re-
duced by aeration by 64% for B-1 and by 52% for B-3
when compared with unaerated operating conditions on
the basis of equal volumetric power input. The low
values for ϕfound for the data presented in this study fit
well into this pattern and support this finding.
If different scales are compared with each other the
measured values for ϕsuggest a scale-effect with higher
values for ϕin larger scales. A-1 and B-1 for example
are close to geometric similarity and the literature corre-
lations predict similar values for ϕfor the two impeller
configurations. McManamey ’s [28] correlation, e.g., pre-
dicts that the ratio of the values of ϕfor B-1 compared
to A-1 should be 1.1. However, the ratio of the values
ofϕderived from the measurements is 1.7. That means
that hydromechanical stress at equal volumetric power
Figure 6 Maximum stable drop size as a function of maximum
local energy dissipation rate εmax.εmaxcalculated from εØ
withϕ=εmax/εØbased on the equation of McManamey [28] for
non-aerated conditions. Dispersion of paraffin oil in 1 mM PO 4-buffer
at pH 7.3. Maximum stable drop size measured after 3 h agitation.
Geometries for different reactor configurations according to Table 2.
Code for different aeration rates: +-center: 0.1 vvm, full symbol: 0.4
vvm, open symbol: 0.7 vvm, x-center: 1.0 vvm.
Figure 7 Maximum stable drop size as a function of maximum
local energy dissipation rate εmax.εmaxcalculated on the basis
ofϕ=εmax/εØbased on the measurements. Dispersion of paraffin oil
in 1 mM PO 4-buffer at pH 7.3. Maximum stable drop size measured
after 3 h agitation. Geometries for different reactor configurations
according to Table 2. Code for different aeration rates: +-center: 0.1
vvm, full symbol: 0.4 vvm, open symbol: 0.7 vvm, x-center: 1.0 vvm.
Solid line: Theoretical prediction based on Eqs. 1 and 2, values for ϕ
from Table 5. Dashed lines: plus/minus 20% deviation from
theoretical prediction.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 9 of 14
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input is higher in the 3 m3reactor than in the 50 L re-
actor although the impeller geometries are close to geo-
metric similarity. A comparison of the data for the 40m
3reactor with the 3 m3reactor also shows this scale-
effect. C-1 has a larger diameter impeller than B-1 with
similar sized impeller blades in relation to the reactordiameter. Within one scale this combination results in a
lower value for ϕfor the larger impeller (e.g. A-2 in
comparison with A-1). This is also predicted by the cor-relation of McManamey [28] that predicts a ratio of the
values of ϕfor C-1 compared to B-1 of 0.6. The experi-
mental data however gives a ratio of 1.7 for C-1 com-pared to B-1, i.e. hydromechanical stress is higher at the
same volumetric power input in C-1 than in B-1. The
classic theory of drop dispersion as expressed in Eqs. 1and 2 does not predict a scale-dependence of maximum
stable drop size for geometrically similar reactor config-
urations for aerated operating conditions. However,Baldyga et al. [49] show for inviscid drops in unaerated
dispersions that turbulence intermittency can explain a
scale-dependence of d
maxthat leads to smaller drops in
larger scales. The extent of the scale-dependence is re-
lated to dispersion time through the “multifractal scaling
exponent ”. A parameter that is not readily available for
practical applications. For long dispersion times the the-
ory predicts a dependence in the form d max~D R-0.543
[49]. If this is the case and the data is still interpreted on
the basis of the classic theory of drop dispersion this
will result in an apparently higher value of ϕfor large
reactors. If the case of inviscid drops is considered with
dmax~εmax-0.4then ϕ~D R0.543would result following
t h et h e o r yo fB a l d y g a .T h ep r o p o r t i o n a l i t y ϕ~D R0.543
can be used to calculate the theoretical ratios of ϕfor
the different reactor scales used in this study assuming
geometric similarity: the ratio of ϕfor the 3 m3reactor
compared to the 50 L reactor is 2.2. The calculated ratioofϕfor the 40 m3reactor compared to the 50 L reactor is
3.4 and the ratio of ϕfor the 40 m3reactor compared to
the 3 m3reactor is 1.6. These differences are in reasonable
agreement with the differences seen in the experimental
results for ϕ. Although the effect of intermittency on the
exponent on energy dissipation rate could not be resolvedwith the measurement method applied in the experi-
ments, the effect of intermittency on ϕis strong and must
be incorporated in the analysis.
For practical applications it is desirable to estimate ϕ
based on a simple engineering correlation instead of
conducting time consuming and costly experiments(particularly in large scale). It is possible to get a first ap-
proximation by applying one of the correlations from
Table 1. However, these only model the effect of geom-etry on ϕfor unaerated operating conditions. It would
be favourible to generalize these correlations by add-
itionally incorporating the effects of aeration and scale.It is clear that a correlation based on the limited set of
data presented in this study can only be preliminary and
approximate. Nevertheless, it might be helpful for practi-tioners and will hopefully inspire further work to elabor-
ate the results presented in this work. The impeller
geometry can be incorporated using, e.g. the equation of
McManamey [28] for single-phase, unaerated operating
conditions (Eq. 3, Table 1). The results presented inDaub et al. [24] indicated already that the effect of aer-
ation on ϕis geometry-dependent, i.e. turbulence at-
tenuation by aeration is stronger for impellers thatexhibit larger values of ϕunder unaerated conditions.
The data in this study strongly support the presence of
this phenomenon. The results can only be correlated sat-isfactorily when the geometry-dependence of the effect
of aeration on ϕis considered. This can be done in the
form ϕ~(ϕ
unaerated )awhere “a”is a constant. The effect
of scale can be estimated by ϕ~D0.543based on theTable 5 Comparison of experimental values for ϕand values from literature correlations
Reactor
configurationResults from experiments
with aerationCorrelations for single-phase, unaerated operation
McManamey (1979) Okamoto (1981) Liepe (1988) Liepe (1988)
Eq. ( 3) Eq. ( 4) Eq. ( 5) Eq. ( 6)
ϕ[−] ϕ[−] ϕ[−] ϕ[−] ϕ[−]
A-1 5.7 60 12 26 35
A-2 2.8 13 2.8 4.0 12A-3 2.0 10 2.4 3.5 8.1A-4 1.9 8.2 2.0 3.1 5.8B-1 9.9 67 13 33 40B-2 8.1 56 12 27 30B-3 6.9 33 7.2 17 21C-1 17 41 10 21 20
Values for ϕcalculated for all 8 reactor configurations from the experimental data for maximum stable drop size from aerated experiments in comparison with
results from literature correlations (Table 1) for single-phase, unaerated operation.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 10 of 14
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work of Baldyga et al. [49]. This results in the following
correlation:
ϕ¼2:3⋅ϕ0:34
unaerated ⋅D0:543
R ð7Ț
The proportionality constant and the exponent
onϕunaerated were found by means of least squares
fitting to the values of ϕbased on the measurements of
maximum stable drop size (Table 5). ϕunaerated was calcu-
lated based on the impeller swept volume (Eq. 3). Figure 8
shows the excellent agreement of the results calculated
with Eq. 7 with the values based on the measured data for
maximum stable drop size for all impeller geometries and
scales from 50 L to 40 m3.
Conclusions
For the first time, results from drop dispersion experi-
ments in aerated stirred tanks were presented that cover
a broad range of operating conditions, impeller geom-
etries (Rushton impellers) and reactor scales of 50 L, 3
m3and 40 m3volume. A comparison of the volume
density distributions in the three different scales show
that the drop size distributions are self-similar and that
d32/dmaxfor the aerated dispersions are in the same
range as reported by other groups for single-phase, una-
erated dispersions e.g. [38]. It was shown that the influ-
ence of aeration and scale on hydromechanical stress is
not considered correctly when using impeller tip speed
as the correlator. The influence of aeration for each im-
peller type is well reflected by correlating the data with
aerated volumetric power input. This is in accordancewith the classic theory of break-up controlled drop dis-
persion if the ratio of maximum to volume averaged en-
ergy dissipation rate ϕis independent of the operating
conditions. Absolute values for ϕthat were calculated
for each impeller based on literature correlations for
unaerated operating conditions differ strongly for the
different correlations and in comparison to the values
derived from the measurements with aerated operating
conditions. The relative order of the impellers within
each scale is the same for all correlations for unaerated
operating conditions as for the values that are based on
the drop size measurements for aerated operating condi-
tions. Hence, the behavior of the impellers relative to
each other within each scale is qualitatively well pre-
dicted by the correlations even though they are strictly
valid only for unaerated operating conditions. The low
values for ϕfound for the data presented in this study
support the finding reported in Daub et al. [24] that
hydromechanical stress is strongly reduced ( ϕis reduced
by approx. 60%) for aerated operating conditions com-
pared to unaerated operating conditions at the same
volumetric power input. Comparison of data in the dif-
ferent scales shows that there is a scale effect that results
in higher values for ϕin larger reactors. This behavior is
not covered by the classic theory of turbulent drop dis-
persion but is in good agreement with the theory of tur-
bulence intermittency that predicts an up to 3.4 times
larger value for ϕin the 40 m3reactor than in the 50 L
reactor. The data for all impeller configurations and all
aeration rates for the three scales correlate very well
when calculated values for ϕbased on the measured
values for d maxare used to calculate the maximum local
energy dissipation rate. Most of the data lies within 20%
around the theoretical prediction from the classic theory
of drop dispersion when these values for ϕare used. A
correlation of the data for all scales and all impeller con-
figurations in the form ϕ= 2.3 ∙(ϕunaerated )0.34∙(DR)0.543is
suggested that successfully models the influence of im-
peller geometry, aeration and scale on ϕfor aerated op-
erating conditions. Incorporating the effects of aeration
and scale on hydromechanical stress is beneficial for a
successful scale up or scale down of this parameter. This
can be done by applying the suggested correlation or by
measuring hydromechanical stress with the experimental
method used in this study.
Materials and methods
Reactor and impeller configurations
Experiments were conducted in stainless steel vessels. A
schematic drawing of the reactors is depicted in Figure 9.
Geometrical details of the tanks are given in Table 2.
The 50 L and 3 m3reactors were equipped with 4 baffles
of width D R/10. The 40 m3reactor had cooling pipes in-
stalled that act as baffles. Due to the size of the cooling
Figure 8 Parity plot of measured and calculated values of ϕfor
all impeller configurations and scales. Measured values as given
in Table 5, calculated values based on Eq. 7 with ϕunaerated
calculated with Eq. 3. Dotted lines indicate +/- 30%-lines.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 11 of 14
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pipes it can be assumed that the influence of the pipes
on the flow field is comparable to conventional baffles
[26,53]. The filling volume was chosen to result in
equivalent ratios of unaerated liquid height to tank
diameter of approx. 1.8 in all three scales. The sampling
ports were at different positions in all three reactors. It
was not possible to align the sampling ports in the three
reactors because additional ports could not be installed.
Since the dispersion is break-up controlled it can be
assumed that the reactor is homogeneous with respect
to the drop size distribution. The sampling positions
should, therefore, not be relevant. This was tested in the3m3tank where a second sampling point was available
on the bottom of the reactor and direct sampling
through the manway opening at the top was also pos-
sible. Comparison of samples from these alternative
sampling positions with the results from the standard
sampling point showed no influence of the sampling
position on the measured drop size distribution (data
not shown). In the 50 L reactor the sampling port was
located at 0.24 m from the tank bottom between the
middle and the upper impeller. In the 3 m3reactor, the
sampling port was at 2.1 m from the bottom close to the
unaerated liquid surface above the upper impeller and in
the 40 m3reactor it was at 3.5 m from the tank bottom
above the second impeller. All sampling ports were half
way between two baffles or cooling pipe installations,
respectively. Rushton type 6-bladed impellers with differ-
ent geometries were used in the experiments. The geo-
metrical details are given in Table 2. All impellers were
installed in a three impeller configuration which is typ-
ical for high aspect ratio reactors used, e.g., in the fer-
mentation industries.
Measurement of drop size distributions and maximum
stable drop size
The development of the experimental procedure to
measure drop size distributions and maximum stable
drop size including the rationale for the dispersed and
continuous phases used for the dispersion experiments
were reported in Daub et al. [25]. Details on the prepar-
ation of the 50 L reactor were also given there. Experi-
mental details specific for the 3 m3reactor were
presented in Daub et al. [24]. The experiments in the 40
m3reactor were conducted in the same way as explained
for the 3 m3reactor in Daub et al. [24]. All experiments
were conducted with the same production batch of par-
affin oil (Weissöl Ph Eur., Brenntag, Germany).
Power input and power number Po
Power input was determined in different ways for the
three reactors due to different technical limitations in the
different scales. The 50L reactor was not equipped with
power measurement. The power input was estimated
using the equation from Middleton and Smith [54]:
P¼0:18⋅Fl−0:2⋅Fr−0:25⋅P0 ð8Ț
with power input under aeration P, the impeller flow
number Fl, impeller Froude number Fr and the unaer-
ated power input P 0that can be calculated from
P0¼Po⋅ρc⋅n3⋅d5ð9Ț
where Po is the power number, ρcthe continuous phase
density, n the agitation rate and d the impeller diameter.
Figure 9 Schematic drawing of the reactors used for
the experiments.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 12 of 14
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Power numbers were estimated using the equation of
Liepe et al. [ 26]:
Po¼5:9⋅n0:8
bl⋅h
d/C18/C190:9
ð10Ț
where n blis the number of impeller blades and h is the
impeller blade height, except for impeller configurations
B-1 and B-3 where the power number was measuredbased on experiments without aeration. The reliability of
this correlation can be tested by comparing the mea-
sured values for B-1 and B-3 with the calculated powernumbers for these impeller configurations. The calcu-
lated power number for configuration B-1 is 5.5 vs.
the measured value of 4.9 (+12%) and for configur-ation B-3 5.8 vs. the measured value of 5.9 (-2%). Both
values are in reasonable agreement with the measured
values. This correlation for power number can be con-sidered very helpful and reliable within engineering ac-
curacy and within the accuracy needed for the power
data for the analyses conducted in this work. It resem-bles correctly the relative influence of blade height and
impeller diameter.
Power input in the 3 m
3and in the 40 m3reactors
were measured through the electrical power draw of the
engine corrected for friction and other losses. For the
3m3reactor the power input to the liquid was calcula-
ted from the raw value by a linear correction function as
described in detail in Daub et al. [24]. Power losses were
evaluated by an instationary temperature method that iscompletely independent of the electrical power meas-
urement. The correlation for power losses was tested
against electrical power measurement in the empty re-actor and both measurements of power loss were in
good agreement. Reproducibility of the electrical power
measurement was very good with a standard deviationof 5%. For the 40 m
3reactor a linear correlation of the
power data with n3showed a good correlation of the
data with an R2of 0.99 when an offset of 25.2 kW was
used. The two lowest agitation rates had very low power
inputs (0.13 kW/m3f o rn=0 . 7 81 / sa n d0 . 3 6k W / m3for
n = 1.0 1/s). It was decided to use calculated values forpower input for these operating conditions instead of
the measured values to avoid large measurement errors
in this low range of operating conditions.
Notation
a: Constant [-]
C: Bottom clearance of first impeller [m]
ΔC: Impeller spacing [m]
d: Impeller diameter [m]d
max: Maximum stable drop size [ μm]
DR: Reactor diameter [m]
d32: Sauter mean diameterFl: Impeller flow number [-]
Fr: Impeller Froude number [-]
h: Impeller blade height [m]H: Unaerated liquid height [m]
K
1: Constant in Eq. 2 [-]
K2: Constant in Eq. 2 [-]
n: Agitation rate [1/s]
nbl: Number of impeller blades [-]
P: (Aerated) power input [W]P
0: Unaerated power input [W]
Po: Power number [-]
ut: Impeller tip speed [m/s]
VL: Total liquid volume [m3]
w: Impeller blade width [m]
Greek letters
εØ: Volume averaged energy dissipation rate [W/kg]
εmax: Maximum local energy dissipation rate [W/kg]
ρc: Continuous phase density [kg/m3]
ϕ:εmax/εØ[-]
σ: Interfacial tension between dispersed and continuous
phase [N/m]
ηD: Dynamic viscosity of dispersed phase [Pa ∙s]
Competing interests
The authors declare that they have no competing interests.
Authors ’contributions
AD developed the method, performed experiments and prepared the
manucript. SD, MB and MM performed experiments and contributed to
experimental planning and analysis of data. GS and JB initiated the project.GS gave important guidance for the experimental work. JB contributed tomethod development, data analysis and manuscript preparation. All authors
approved the final manuscript.
Acknowledgements
The authors would like to acknowledge financial support for the projectfrom Sandoz GmbH, Kundl, Austria.
Author details
1AVT.Biochemical Engineering, RWTH Aachen University, Worringerweg 1, Aachen
52074, Germany.2Sandoz GmbH, Anti-Infectives Operations Development,
Biochemiestraße 10, Kundl A-6250, Austria.
Received: 8 January 2014 Accepted: 30 May 2014
Published: 7 July 2014
References
1. Hinze JO: Fundamentals of the hydrodynamic mechanism of splitting in
dispersion processes. AIChE J 1955, 1(3):289 –295.
2. Fujasova M, Linek V, Moucha T: Mass transfer correlations for multiple-impeller
gas-liquid contactors. Analysis of the effect of axial dispersion in gas
and liquid phases on “local ”k(L)a values measured by the dynamic
pressure method in individual stages of the vessel. Chem Eng Sci 2007,
62(6):1650 –1669.
3. Henzler H-J: Particle stress in bioreactors. Adv Biochem Eng Biotechnol
2000, 67:35–82.
4. Gregoriades N, Clay J, Ma N, Koelling K, Chalmers JJ: Cell damage of
microcarrier cultures as a function of local energy dissipation created bya rapid extensional flow. Biotechnol Bioeng 2000, 69(2):171 –182.
5. Kelly S, Grimm LH, Hengstler J, Schultheis E, Krull R, Hempel DC: Agitation
effects on submerged growth and product formation of Aspergillus niger .
Bioprocess Biosyst Eng 2004, 26(5):315 –323.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 13 of 14
http://www.jbioleng.org/content/8/1/17

6. Büchs J, Maier U, Milbradt C, Zoels B: Power consumption in shaking
flasks on rotary shaking machines: I. Power consumption measurement
in unbaffled flasks at low liquid viscosity. Biotechnol Bioeng 2000,
68(6):589 –593.
7. Büchs J, Maier U, Milbradt C, Zoels B: Power consumption in shaking flasks
on rotary shaking machines: II. Nondimensional description of specific
power consumption and flow regimes in unbaffled flasks at elevated
liquid viscosity. Biotechnol Bioeng 2000, 68(6):594 –601.
8. Fujita M, Iwahori K, Tatsuta S, Yamakawa K: Analysis of pellet formation of
Aspergillus niger based on shear-stress. JF e r m e n tB i o e n g 1994, 78(5):368 –373.
9. Peter CP, Suzuki Y, Büchs J: Hydromechanical stress in shake flasks:
correlation for the maximum local energy dissipation rate. Biotechnol
Bioeng 2006, 93(6):1164 –1176.
10. Büchs J, Zoels B: Evaluation of maximum to specific power consumption
ratio in shaking bioreactors. J Chem Eng Jpn 2001, 34(5):647 –653.
11. Jüsten P, Paul GC, Nienow AW, Thomas CR: Dependence of Penicillium
chrysogenum growth, morphology, vacuolation, and productivity in
fed-batch fermentations on impeller type and agitation intensity.
Biotechnol Bioeng 1998, 59(6):762 –775.
12. Jüsten P, Paul GC, Nienow AW, Thomas CR: Dependence of mycelial
morphology on impeller type and agitation intensity. Biotechnol Bioeng
1996, 52(6):672 –684.
13. Jüsten P, Paul GC, Nienow AW, Thomas CR: A mathematical model for
agitation-induced fragmentation of Penicillium chrysogenum .Bioprocess
Eng1998, 18(1):7–16.
14. Einsele A: Scaling-up bioreactors. Process Biochem 1978, 7:13–14.
15. Junker BH: Scale-up methodologies for Escherichia coli and yeast
fermentation processes. J Biosci Bioeng 2004, 97(6):347 –364.
16. Baldi S, Yianneskis M: On the quantification of energy dissipation in the
impeller stream of a stirred vessel from fluctuating velocity gradient
measurements. Chem Eng Sci 2004, 59:2659–2671.
17. Costes J, Couderc JP: Study by laser Doppler anemometry of the
turbulent flow induced by a Rushton turbine in a stirred tank: Influence
of the size of the units: spectral analysis and scales of turbulence.
Chem Eng Sci 1988, 43(10):2765 –2772.
18. Ducci A, Yianneskis M: Direct determination of energy dissipation in
stirred vessels with two-point LDA. AIChE J 2005, 51:2133–2149.
19. Escudié R, Liné A: Experimental analysis of hydrodynamics in a radially
agitated tank. AIChE J 2003, 49(3):585 –603.
20. Micheletti M, Baldi S, Yeoh SL, Ducci A, Papadakis G, Lee KC, Yianneskis M:
On spatial and temporal variations and estimates of energy dissipation
in stirred reactors. Chem Eng Res Des 2004, 82(A9):1188 –1198.
21. Sharp KV, Adrian RJ: PIV study of small-scale flow structure around a
Rushton turbine. AIChE J 2001, 47(4):766 –778.
22. Wu H, Patterson GK: Laser-Doppler measurements of turbulent-flow
parameters in a stirred mixer. Chem Eng Sci 1989, 44(10):2207 –2221.
23. Zhou GW, Kresta SM: Impact of tank geometry on the maximum
turbulence energy dissipation rate for impellers. AIChE J 1996,
42(9):2476 –2490.
24. Daub A, Böhm M, Delueg S, Mühlmann M, Schneider G, Büchs J: Maximum
stable drop size measurements indicate turbulence attenuation by
aeration in a 3 m3 aerated stirred tank. Biochem Eng J 2014, 86:24–32.
25. Daub A, Böhm M, Delueg S, Büchs J: Measurement of maximum stable
drop size in aerated dilute liquid-liquid dispersions in stirred tanks.
Chem Eng Sci 2013, 104:147–155.
26. Liepe F, Meusel W, Möckel HO, Platzer B, Weißgärber H: Stoffvereinigung in
fluiden Phasen. InVerfahrenstechnische Berechnungsmethoden, vol. 4. Edited
by Weiß S, Berghoff W, Grahn E, Gruhn G, Güsewell G, Plötner W, Robel H,
Schubert M. Weinheim: VCH Verlagsgesellschaft; 1988.
27. Baldyga J, Podgórska W: Drop break-up in intermittent turbulence:
maximum stable and transient sizes of drops. Can J Chem Eng 1998,
76(3):456 –470.
28. McManamey WJ: Sauter mean and maximum drop diameters of
liquid-liquid dispersions in turbulent agitated vessels at low dispersed
phase hold-up. Chem Eng Sci 1979, 34:432–434.
29. Davies JT: Drop sizes of emulsions related to turbulent energy dissipation
rates. Chem Eng Sci 1985, 40(5):839 –842.
30. Bauer R: Untersuchungen zur Dispergierung in flüssig-flüssig Systemen. PhD
Thesis , PhD Thesis. Köthen, Germany: Engineering School of Köthen; 1985.
31. Henzler H-J, Biedermann A: Modelluntersuchungen zur Partikelbeanspruchung
in Reaktoren. Chemie Ingenieur Technik 1996, 68(12):1546 –1561.32. Kresta SM, Brodkey RS: Turbulence in Mixing Applications. InHandbook of
Industrial Mixing: Science and Practice. Edited by Paul EL, Atiemo-Obeng VA,
Kresta SM. Hoboken, New Jersey, USA: John Wiley & Sons, Inc.; 2004.
33. Okamoto Y, Nishikawa M, Hashimoto K: Energy dissipation rate
distribution in mixing vessels and its effects on liquid-liquid dispersion
and solid-liquid mass transfer. Int Chem Eng 1981, 21(1):7.
34. Brown DE, Pitt K: Drop size distribution of stirred non-coalescing liquid-liquid
system. Chem Eng Sci 1972, 27(3):577 –583.
35. Chen HT, Middleman S: Drop size distribution in agitated liquid-liquid
systems. AIChE J 1967, 13(5):989 –995.
36. Konno M, Kosaka N, Saito S: Correlation of transient drop sizes in breakup
process in liquid-liquid agitation. J Chem Eng Jpn 1993, 26(1):37 –40.
37. Pacek AW, Man CC, Nienow AW: On the Sauter mean diameter and size
distributions in turbulent liquid/liquid dispersions in a stirred vessels.
Chem Eng Sci 1998, 53(11):2005 –2011.
38. Calabrese RV, Chang TPK, Dang PT: Drop breakup in turbulent stirred-tank
contactors. 1. Effect of dispersed-phase viscosity. AIChE J 1986, 32(4):657 –666.
39. Margaritis A, Zajic JE: Mixing, mass transfer, and scale up of polysaccaride
fermentations. Biotechn Bioeng 1978, 20(7):939 –1001.
40. Humphrey A: Shake flask to fermentor: what have we learned? Biotechnol
Prog 1998, 14(1):3–7.
41. Märkl H, Bronnenmeier R, Wittek B: Hydrodynamische Belastbarkeit von
Mikroorganismen. Chemie Ingenieur Technik 1987, 59(12):907 –917.
42. Bluestein M, Mockros LF: Hemolytic effects of energy dissipation in
flowing blood. Med Biol Eng 1969, 7(1):1–16.
43. Li F, Hashimura Y, Pendleton R, Harms J, Collins E, Lee B: A systematic
approach for scale down model development and characterization of
commercial cell culture processes. Biotechnol Prog 2006, 22(3):696 –703.
44. Liu Y, Li F, Hu W, Wiltberger K, Ryll T: Effects of bubble –liquid two-phase
turbulent hydrodynamics on cell damage in sparged bioreactor.
Biotechnol Prog 2014, 30(1):48 –58.
45. Hu W, Berdugo C, Chalmers JJ: The potential of hydrodynamic damage to
animal cells of industrial relevance: current understanding.
Cytotechnology 2011, 63(5):445 –460.
46. Oh SKW, Nienow AW, Al-Rubeai M, Emery AN: The effects of agitation
intensity with and without continuous sparging on the growth and
antibody production of hybridoma cells. J Biotechnol 1989, 12(1):45 –61.
47. Meier SJ, Hatton TA, Wang DIC: Cell death from bursting bubbles: role of
cell attachment to rising bubbles in sparged reactors. Biotechnol Bioeng
2001, 74(6):544 –546.
48. Dey D, Emery AN: Problems in predicting cell damage from bubble
bursting. Biotechnol Bioeng 1999, 65(2):240 –245.
49. Baldyga J, Bourne JR, Pacek AW, Amanullah A, Nienow AW: Effects of
agitation and scale-up on drop size in turbulent dispersions: allowance
for intermittency. Chem Eng Sci 2001, 56(11):3377 –3385.
50. Baldyga J, Bourne JR: Interpretation of turbulent mixing using fractals and
multifractals. Chem Eng Sci 1995, 50(3):381 –400.
51. Bourne JR: Distribution of energy-dissipation rate in an agitated gas-liquid
system. Chem Eng Tech 1994, 17(5):323 –324.
52. Fort I, Machon V, Kadlec P: Distribution of energy dissipation rate in an
agitated gas-liquid system. Chem Eng Tech 1993, 16:389–394.
53. Hemrajani RR, Tatterson GB: Mechanically Stirred Vessels. InHandbook of
Industrial Mixing: Science and Practice. Edited by Paul EL, Atiemo-Obeng VA,
Kresta SM. Hoboken, New Jersey, USA: John Wiley & Sons, Inc.; 2004.
54. Middleton JC, Smith JM: Gas-liquid Mixing in Turbulent Systems. In
Handbook of Industrial Mixing: Science and Practice. Edited by Paul EL,
Atiemo-Obeng VA, Kresta SM. Hoboken, New Jersey, USA: John Wiley &
Sons, Inc.; 2004.
doi:10.1186/1754-1611-8-17
Cite this article as: Daub et al. :Characterization of hydromechanical
stress in aerated stirred tanks up to 40 m3scale by measurement of
maximum stable drop size. Journal of Biological Engineering 2014 8:17.Daub et al. Journal of Biological Engineering 2014, 8:17 Page 14 of 14
http://www.jbioleng.org/content/8/1/17