Stirring: Theory and Practice
Marko Zlokarnik
Murk0
Zlokurnik
Stirring
Theory
and
Practice
@WILEY-VCH
Weinheim
-
New York
-
Chichester
-
Brisbane
-
Singapore
-
Toronto
Prof:
Dr.
Marko
Zlokarnik
GrillparzerstraBe
58
8010
Graz
Austria
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Printed in the Federal Republic
of
Germany.
Printed on acid-free paper.
Typesetting
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Printing
Strauss Offsetdruck GmbH,

1.4.1
1.4.2
1.4.2.1
1.4.2.2
1.4.3
1.4.3.1
1.4.3.2
1.4.3.3
1.4.4
1.4.5
1.4.5.1
1.4.5.2
1.4.6
1.4.6.1
1.4.6.2
1.4.6.3
Stirring,
general
1
Stirring operations
1
Mixing equipment
2
Mixing tanks and their fittings
Stirrer types and their operating characteristics
Nozzles and spargers
11
Sealing of stirrer shafts
12
Mechanical stress

G/L
material systems
34
Heterogeneous
L/L
material systems
34
Pumping capacity
of
stirrers
34
Surface motion
36
Vortex formation. Definition of geometric parameters
Gas entrainment via vortex
39
Micro-mixing and reactions
40
Introduction
40
Theoretical prediction
of
micro-mixing
43
Chemical reactions for determining micro-mixing
2
G
16
3G
45

1.6.6
1.6.6.1
1.6.6.2
2
2.1
2.1.1
2.1.2
2.2
2.2.1
2.2.2
2.3
Experimental determination of micro-mixing 48
Short introduction to rheology
50
Newtonian liquids
50
Non-Newtonian liquids
51
Dimensionless representation of material functions
Short introduction to dimensional analysis and scale-up
Introduction 60
Dimensional analysis
62
Fundamentals
62
Dimensions and physical quantities
62
Primary and secondary quantities; dimensional constants
Dimensional systems
63

Advantages of use
of
dimensional analysis
Range of applicability of dimensional analysis
57
60
62
66
67
68
69
70
72
72
73
74
Stirrer power
76
Stirrer power in a homogeneous liquid
Newtonian liquids 76
Non-Newtonian liquids 82
Stirrer power in
G/L
systems
Newtonian liquids 83
Non-Newtonian liquids 90
Flooding point
94
;
83

4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.3
4.3.1
4.3.1.1
4.3.1.2
4.3.1.3
4.3.2
4.3.2.1
4.3.2.2
4.3.2.3
4.3.2.4
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.4.5
4.4.6
4.5
4.5.1
4.5.2
4.5.2.1
4.5.2.2
4.5.3
Chemical measurement methods

126
Temperature dependence of
kLa
129
Saturation concentration
c,
of the gas in the liquid
Definition of the characteristic concentration difference
Ac
Consideration of the absorption process from
a
physical and industrial
viewpoint
132
Determination of
k~a
132
Unsteady-state measurement methods
132
Measurement with oxygen electrodes
133
Pressure gauge method
133
Dynamic response methods
134
Steady-state methods
134
Sulfite methods
134
Hydrazine methods

126
130
130
138
139
141
143
145
149
151
4.6
Gas fraction (gas hold-up) in gassed liquids 153
4.6.1
Definition
of
E
154
4.6.2
Determination of
E
154
4.6.3
Process relationships for
c
155
4.7
Gas bubble diameter
db
and its effect upon
k~

4.12.1.3
Comparison of hollow stirrer and turbine stirrer
4.12.1.4
Sorption characteristics
190
4.12.2
Surface aerators 190
4.12.2.1
Centrifugal surface aerators
190
4.12.2.2
Power characteristic
191
4.12.2.3
Sorption characteristic
192
4.12.2.4
Plunging water jet aerators
4.12.2.5
Horizontal blade-wheel reactor 197
4.12.3
Gas spargers
199
4.12.3.1
Sintered glass or ceramics plates, perforated metal plates and static
4.12.3.2
Injectors
(G/L
nozzles)
201

206
Homogeneous suspension
207
Distribution of solids upon suspension
Suspension characteristics
21
1
Relevance lists and pi spaces
Specification according to the nature of the target quantity
n,
Specification according to particle property
d,
and/or
w,,
21
1
Suspension characteristics with
d,
as the characteristic particle
dimension
21
2
Relevance list and pi space
212
The process relationship
213
Power requirements upon suspension
206
206
208

6.2.5
6.2.6
6.2.7
6.2.8
6.3
6.3.1
6.3.2
6.3.3
6.3.4
6.4
6.5
6.6
6.7
Power requirement for the critical stirrer speed
n,
Scaling up in suspension according to the criterion
n,
Suspension characteristic with
w,,
as the characteristic particle
property 217
Determination of the particle sinking velocity in the swarm
w,,
The relevance list and the pi space
The process relationship
220
Final discussion from the viewpoint of the dimensional analysis
Establishing of scale-up criteria 230
Suspension characteristic with the energy dissipation number
E*

236
237
241
Dispersion in
L/L
Systems
244
Lowest stirrer speed for dispersion
Dispersion characteristics
246
The target quantity
d32
246
Coalescence in the
L/L
system 247
Determination method for
djz
247
Dimensional-analytical description 248
The process characteristics
249
Effect of coalescence and of
pv
on
d3z
Effect of viscosity 251
Effect of stirring duration 252
Droplet size distribution 253
Fundamentals 253

273
x
I
Contents
7.2
7.2.1
7.2.2
7.3
7.4
7.4.1
7.5
7.6
7.6.1
7.7
7.7.1
7.7.2
7.7.3
7.8
7.8.1
7.8.2
7.9
8
8.1
8.1.1
8.1.2
8.1.2.1
8.1.2.2
8.1.3
8.2
8.2.1

stirrers for a maximum removal of reaction heat
Heat transfer for G/L material systems
Dimensionally analytical description
291
Heat transfer in S/L systems
Direct heat exchange ice cubes/water
293
Indirect heat exchange for
Ap
>
0
Indirect heat exchange at
Ap
0
295
Heat transfer in
L/
L
material systems
Direct heat exchange 298
Indirect heat exchange 298
Heat transfer in G/L/S material systems
275
278
286
288
291
293
294
298

system 314
Dispersion in pipe flow 314
Dispersion in pipe with static mixer
Micro-mixing and chemical reaction
Pipe reactor 317
Pipe reactor with a jet mixer
Pipe reactor with static mixer
Modeling of mixing processes in pipes
Pipe flow 322
308
309
310
311
315
31
6
319
320
322
Contents
I
xi
8.6.2
Pipe with Tee mixer
323
8.6.3
Pipe with static mixer
323
8.7
Stirring in pipes and mixing columns

Only someone who has studied this topic intensively since the
1950’s
can fully
appreciate the immense advances made feasible by new physical measuring methods
and computers.
Forty
years ago determination of the stirrer speed still required
a
stop-watch or a stroboscope!
Today, the whole field of classical stirring technology can be regarded as largely
accessible to scientific method,
so
that a standard design for stirrers for any stirring
operation on an industrial scale is ensured. Research is shifting increasingly to
mathematical simulation of stirring processes. In the future, interesting sugges-
tions for industrial practice can be expected from this work.
I
wish to express my sincere thanks to my friend Dr. Dr Ing. e.h. Juri Pawlowski
for his many helpful suggestions, to my long-standing colleague and co-worker,
Dr Ing Helmut Judat from Bayer-Leverkusen for putting at my disposal the exten-
sive, partly jointly collected, scientific literature from the
1950’s
to the
1970’s,
and
to Dr Ing. H J. Henzler from Bayer-Elberfeld and to Dr Ing. habil. Peter Zehner
from BASF-Ludwigshafen for the critical reading of
a
chapter of the manuscript.
Classification

Table
0.1
is recommended.
Tab.
0.1
aggregation
of
the major component
Classification
of
mixing operations according to the state
of
State ofoggregotion Unit operotion
Stondord
mixing equipment
gaseous mixing, spraying
mixing chamber, nozzle
liquid stirring
stirrer, static mixing elements
paste-like kneading kneader, screw extruder
solid (particulate) mixing, blending mixer
To
avoid misunderstandings, it should be pointed out that the above-used mixing
terms do not enable
a
clear distinction to be made between the unit operation as
action and as aim. Thus the term mixing includes both the unit operation of blend-
ing or intermingling and the result
of
this unit operation namely the preparation

cannot be ignored.
It
should therefore be borne in mind that the available terms such as mixing,
blendmg, stirring, kneading denote the unit operations
of
unifylng processes, but
tell
us
little or nothing about the result of the operation. (In this they differ from
other unit operations such as grinding, filtration, distillation, etc. Here, the expected
result is fully described by the term used.)
This book has been exclusively devoted to stirring for
a
number of reasons: in-
tensive research in this field has been carried out in the last
10-15
years, largely
driven by the development
of
biotechnology, meriting a separate book and several
books devoted to the other unifying operations (mixing of solids, mixing in ex-
truders) have been published’) in the German language literature, making consid-
eration
of
these topics unnecessary.
It is neither the task nor in the ambit of the author, to mention all the significant
scientific contributions over the last
50
years within the field covered by this book,
much less,

3-79
3
5
-5
5
28-3
2)
Mixing
-
Theory
and
Practice, Vol.
1
+
2
+
3
(Ed.: V.W. Uhl, Y.B.
Gray)
Academic Press, New
York
1966, 1967, 1968
Nagata,
S.:
Mixing
-
Prinaples and
Application
Kodansha Ltd.
Tokyo

1988
ISBN
3-527-26 205-9
ISBN
3-921567-48-3
I
xv
List
of
Symbols
Latin Characters
interfacial area per unit volume,
a
=
A/V
thermal diffusivity;
a
=
k/(pCp)
area, interfacial area
Hamaker constant
height of stirer (paddle) blade
concentration
saturation concentration
drag coefficient of
a
sphere in a fluid flow
pipe flow friction factor
heat capacity at constant pressure
stirrer diameter

R
kG
kL
kLa
L
L
Lrn
m
m
m
M
M
n
N
Nx
P?
AP
4’
Q
P
4
R
S
T
T
Tu
t
U
Ui
U

p.
100
stirrer speed
number of stages
normal stress
(x
=
1
or
2);
eq. (1.50,
1.51)
pressure, pressure difference (pressure drop)
power, stirrer power
volume throughput
liquid throughput, brought about by a stirrer
heat flow (rate of heat transfer)
heat of reaction
surface; cross-sectional area
time
base dimension
of
time
temperature
degree of turbulence, definition p.
23
tip velocity
(u
=
nnd)

angle
/lo
temperaturc coefficient of the density
deformation
shear rate, eq.
(1.41)
temperature coefficient of the viscosity, eq.
(7.6)
thickness (of film, layer, wall)
mixing power per unit mass
e
=
P/pV
gas hold-up (gas fraction in liquid)
mixing time
kinetic energy per unit mass,
Ekin/m
=
(1/2)ma2/m
=
v2/2
Kolmogorods micro-scale
of
turbulence;
2
=
(v3/&)'I4;
eq.
(1.6)
relaxation time, eq.

yield stress
volume or
mass
fraction
Subscripts
0
ax
C
d
F
G
h
i
bulk
kin
L
min
M
n
0
P
'I
outer
axial
continuous phase
dispersed phase
flake
gas, gas phase
hydraulic
inner

foam
terminal (final) value
value
at
the time
t
technological scale, full-scale
vortex
wall
space coordinates in the vessel
Dimensionless
Numbers
Ar
Bd
Bo
cd
Cf
De
E'
Eu
Fo
Fr
Fr'
Ga
Gr
Archimedes number
Bond number
Bodenstein number
drag coefficient of
a

Ri
Richardson number
Wi
Weigenberg number
We
Weber number
cr*
physical properties number
S:
physical properties numbers describing
Sc
Schmidt number
bubble coalescence behaviour
Ar
=
Re2/Fr'
Bd
=
WeFr
Bo
=
nd2/D,tf
and
vD/D,R,
resp.
Cd
E
2Eu
Cf
2Eu

=
dz/kL
Ne
=
P/(pn3d5)
NU
E
hiD/k
Pr
=
v/a
=
C,p/k
Pe
=
RePr
=
nd2/a
=
nd2pCp/k
Re
=
nd2p/p
Ri
=
[Fr'd/H]-'
Wi
=
Nl/r
We

h/(vpCp)
Vis
=
h/p
see
definition
eq.
4.72
Stirring
Theory and Practice
Marko
Zlokarnik
0
Wiley-VCH
Verlag
GmbH,
2001
I’
1
Stirring, General
1.1
Stirring Operations
If the liquid component predominates in the mixture of substances to be mixed,
the mixing operation is named stirring and a stirrer (an impeller) is used as the
mixing device. The following five stimng operations can be distinguished
[Gll]:
-
Homogenization, i.e. equalization of concentration and temperature differences;
-
Intensification

of viscous liquids, an important stimng operation, particularly if a strongly exo-
thermic reaction takes place (e.g. block polymerization).
In
such cases the stimng
operation consists of reducing the thickness of the liquid boundary layer on the
tank wall and realizing liquid transport to and from the heat exchanger surface.
If
particulate matter has to be dissolved in
a
liquid or if a chemical reaction cata-
lyzed by
a
solid is involved, the particles must be suspended from the vessel bottom,
so
that the total surface can participate in the process. In continuous processes a
stochastically homogeneous distribution of the solid in the bulk of the liquid is
required,
so
that the solid particles can be transported with the liquid from stage to
stage (for example in a cascade crystallization process). In this intensive suspen-
sion process, the solid is, as a rule, subjected to high mechanical stress, which can
result in its attrition.
In
the case of dispersion in
a
L/L
or
L/G
(liquid/gas) systems, one fluid phase is
distributed in the other in the form of fine droplets

the most commonly used piece of stirring
equipment. (It is also the most commonly used chemical reactor). This is due to
its considerable flexibility as regards the flow conditions, which can be realized in
it. Mixing tubs and storage tanks are the second most commonly used pieces of
mixing apparatus.
The tank diameter is restricted to
D
5
4.6
m on transport grounds.
A
further
increase in liquid volume is therefore only possible by an enlargement of the vessel
height. Two disadvantages have thereby to be taken into account:
a)
the stirrer shaft
becomes longer and support bearings may be required along its length; b) mixing
times increase (see Fig.
3.6).
(For most stirring operations the most favorable aspect
ratio
HID
(liquid height to vessel diameter) is
HID
z
1).
The design of mixing tanks is standardized
DIN
28
130 [161,

D/10
in width, where
D
is the inner diameter of the vessel, arranged along
the entire vessel wall. Dead zones in the
flow
direction behind the baffles can be
13
7.2
Mixing
Equipment
A
B
Fig.
1.1
Baffle design
A
-
Standard design
B
-
For
glass and coated vessels (baffle basket
with
pressure-
fitted ring)
avoided by using baffles Dl12 in width, set at
a
clearance of D/50 from the vessel
wall. Baffles are usually attached to the vessel wall by means of welded brackets

with
axially working stirrers, since they produce
good liquid circulation in the annular space between the helical coil and the wall.
On
the other hand, the liquid circulation produced by radially working stirrers is
strongly deflected by a helical coil,
so
that the flow through the annulus between
the coil and wall is suppressed. For such stirrer types, it is advantageous to arrange
the coil in vertical loops along the vessel wall (meander coil, Fig. 2b). This arrange-
ment does not deflect the radial flow pattern, but prevents bulk rotation of the liquid
to such an extent that baffles are often superfluous.
Fig.
1.2
A
-
Jacketed vessel
B
-
Cast iron vessel with integral steel tubes
C
-Welded helical coil with intercolated copper plates
D
-Welded half pipe coil
E
-
Welded corner iron channels
F
-Jacketed bolt welding
Design

1611.
In Fig.
1.4
the stirrer types are arranged according to the predominant flow pat-
tern they produce, as well as to the range
of
viscosities over which they can be
effectively used.
90%
of all stirring operations can be carried out with these stan-
dard stirrer types. The flow patterns obtained with typical radially and axially con-
veying stirrers are shown in Fig. 1.5.
Of
the stirrer types which set the liquid in a radlal motion
-
or into a tangential
flow in the case of high viscosities
-
only the turbine stirrer*) (so-called “Rushton
turbine”,
a
disk 2d/3 in diameter supporting
6
blades each
d/5
high and
d/4
wide
[474])
belongs to the high speed stirrers.

600
mm in diameter. It is
a
stirrer with four paddles of
different design (straight, pitched paddles, TurbofoilJ-o) its paddles being arranged
on the hub in an X-configuration rather than in a cross configuration. The fasten-
ing of the impeller hub to the impeller shaft is realized inside the tank by first con-
tracting the shaft in liquid nitrogen
(-196”C),
then mounting the impeller hub and
finally heating to produce the connection
[316].
Cross-beam, grid and blade stirrers are slow-speed stirrers and are used
at
D/d
=
1.5
to
2
both with and (in the case of viscous liquids) without baffles. They
are particularly suitable for homogenization.
*
In the German literature on mixing the
Rushton turbine is referred
to
as
Scheibenriihrer:
“disk stirrer”.
This
is a

-
5
000
CrOS
beam Frame
L
MIG@
(Ekato)
Fig.
1.4
Classification
of
stirrers according to the predominant
flow pattern they produce and
to
the range
of
viscosities over
which they can
be
effectively used
Fig.
1.5
baffled tank, generated by
A
-
axial-flow propeller and a
B
-
radial-flow turbine stirrer