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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Republic of Germany).
2001
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ISBN
3-527-29996-3
Con
tents
Preface
xii
Symbols
xu
1
1.1
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.4

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

14
Stress on baffles
14
Stress on stirrer heads
14
Tank vibrations
15
Wear of stirrer heads
15
Shear stress on the particulate material beinig mixed
Flow and Turbulence
20
Introduction
20
Statistical theory of turbulence
21
Description
of
turbulent flow
23
Energy spectra
25
Experimental determination of state
of
flow flow and its mathematical
modeling
27
Homogeneous material systems
27
Heterogeneous

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

vi
I
Contents
1.4.6.4
1.5
1.5.1
1.5.2
1.5.3
1.6
1.6.1
1.6.2
1.6.2.1
1.6.2.2
1.6.2.3
1.6.2.4
1.6.2.5
1.6.2.6
1.6.3
1 h.3.1
1.6.3.2
1.6.3.3
1.6.3.4
1.6.4
1.6.4.1
1.6.4.2
1.6.5
1.6.5.1
1.6.5.2
1.6.5.3
1.6.5.4

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

Dimensional homogeneity of
a
physical relationship 63
The pi theorem 66
Construction of pi sets using matrix transformation
66
Drawing-up of a relevance list for
a
problem
Determination of the characteristic geometric parameter
Constructing and solving of the dimensional matrix
Determination of the process characteristics
Fundamentals of the model theory and scale-up
Model theory 70
Model experiments and scale-up
71
Remarks regarding the relevance list and experimental technique
Taking into consideration of the acceleration due to gravity
g
72
Introduction
of
intermediate quantities
72
Dealing with material systems with
unknown
physical properties
Experimental methods for scale-up 73
Conclusions
73

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

76
3
Homogenization
97
3.1
Definition of macro- and micro-mixing
97
3.2
Definition of degree of mixing
98
3.3
3.3.1
Physical methods
101
Determination of the degree of mixing and the mixing time
100
3.3.2
3.3.3
3.4
3.4.1
3.4.2
3.4.3
3.5
3.6
3.7
3.7.1
3.7.2
3.7.3
4
4.1

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

102
Degree of mixing and molar excess
Homogenization characteristics
104
Material systems without density and viscosity differences
Material systems with density and viscosity differences
Non-Newtonian mixtures
11
2
Optimization to minimum mixing work
Scale-up of the homogenization process
Homogenization in storage tanks
122
Homogenization with propellers
122
Homogenization with liquid jets
123
Homogenization through rising up gas bubbles
102
104
110
116
118
123
Gas-liquid contacting
126
Introduction
126
Physical fundamentals of mass transfer
Determining the driving force

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

136
Sodium sulfite feed technique
137
Hydrogen peroxide method
137
Mass transfer characteristics for the
G/L
system
Establishing mass transfer relationships
138
Mass transfer relationship: experimental data
Sorption characteristics in the coalescing system water/air
Sorption characteristics in coalescence-inhibited systems
Sorption characteristics in rheological material systems
Sorption characteristic in biological material systems
Interfacial area per unit volume
a
Definition of
a
151
Determination of
a
152
Physical methods
152
Chemical methods
152
Process relationships for
a
152

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~

4.8
Gas-absorption in oil/water dispersions
161
4.9
Chemisorption
162
4.10
Bubble coalescence 165
4.11
Foam breaking 175
4.11.1
Methods and devices for foam breaking
176
4.11.2
Foam centrifuge and foam turbine
177
4.11.3
Minimum rotor tip speed
179
4.11.4
4.12
Special gas-liquid contacting techniques
183
4.12.1
Hollow stirrers 183
4.12.1.1
Application areas
183
4.12.1.2
Suction, power and efficiency characteristics

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

4.12.3.3
Funnel shaped nozzle as ejectors
156
Process characteristic of the foam centrifuge and its scale-up
180
185
187
194
mixers 200
205
5
5.1
5.1.1
5.1.2
5.2
5.3
5.3.1
5.3.1.1
5.3.1.2
5.3.2
5.3.2.1
5.3.2.2
5.3.2.3
Suspension
of
Solids in Liquids
(S/L
System)
Classification of the suspension condition
Complete suspension

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

211
211
21
6
Contents
I
ix
5.3.2.4
5.3.2.5
5.3.3
5.3.3.1
5.3.3.2
5.3.3.3
5.3.3.4
5.3.3.5
5.3.4
5.3.5
5.4
5.5
5.5.1
5.5.2
5.6
5.7
6
6.1
6.2
6.2.1
6.2.2
6.2.3
6.2.4

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*

Effect of geometric and device-related factors on the suspension
characteristic 233
Homogenization of the liquid in the
S/L
system
Mass
transfer in the
S/L
system
Physical basis of mass transfer in the
S/L
system
Process characteristics of mass transfer in the
S/L
system
Suspension in the
S/
L/G-system: hydrodynamics and power
requirement
241
Mass transfer in the S/L/G system
217
227
21
7
220
229
231
235
236

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

Effect of stirrer speed 254
Effect of stirrer type and material system
Effect of the mixing time
Stirrer power for dispersion 263
Scaling up of dispersion processes
Mass and heat transfer upon dispersion
Mathematical modeling of the dispersion process
244
250
255
262
263
264
267
7
Intensification
of
heat transfer
by
stirring
272
7.1
Physical fundamentals of heat transfer
272
7.1.1
Determination of
cli
273
7.1.2
Dimensional-analytical description

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

8.2.2
8.3
8.3.1
8.3.2
8.4
8.4.1
8.4.2
8.5
8.5.1
8.5.2
8.5.3
8.6
8.6.1
Heat transfer between a homogeneous liquid and a heat transfer
surface 275
Flow range
Re
=
102-106
Flow range
Re
<
lo2
Generalized representation of the heat transfer characteristic
by
including the stirrer power per unit volume 282
Effect of the Vis-term 284
Taking non-Newtonian viscosity into consideration
Optimization
of

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

299
Mixing and stirring in
pipes
Mixing and homogenization 300
Straight, smooth or rough pipe without fittings
Pipe with a jet mixer or with a Tee piece
302
Jet mixers 302
Tee pieces
304
Flow deflecting fittings (“motionless or static mixers”)
300
300
305
Kenics mixer 307
Sulzer mixers SMV and
SMX
[533]
Ross-ISG mixer 309
G/L-mass transfer 309
Mass transfer in pipe flow
Mass transfer
in
pipe with static mixer
Heat transfer 3
11
Heat transfer in pipe flow 311
Heat transfer in pipe with static mixer
Dispersion in
L/L

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

324
Literature
328
Subject
Index
360
xii
I
Preface
Stirring is one of the unifying processes which form part of the mechanical unit
operations in process technology. It is an important operation which has been used
by man since time immemorial in preparing food and drink and in constructing
his dwelling. Since the emergence of manufacturing and the advent
of
industrial
production, stirring has been used in almost all branches of industry (metallurgy,
building materials, glass, paper, chemicals, food, pharmaceuticals, etc.).
Permeation of scientific method into this field largely took place in the second
half of the twentieth century, during which all the other disciplines in process
technology evolved from “arts into sciences”. Particularly chemical and process
engineers in the chemical industry and in research have studied this topic in-
tensively, since chemical, biochemical and biological processes can only take place
when all the reaction partners are brought into close contact.
This book represents
a
brief summary of the state of the art in the field of stir-
ring technology from the viewpoint of the author. It particularly focuses on recent
research results, account being taken of scientific literature published up to the
summer of
2000.

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

of
Unifying Processes with Regard to the Material
Systems
Involved in the
Unit Operations Mixing, Stirring and Kneading
It
is obvious that mixing of wine with water or the preparation of an aqueous solu-
tion of common salt from powdered or crystalline common salt and water require
different equipment and different procedures from those used for the preparation
of bread dough, modelling paste with coarse or fine clay, or
a
concrete mixture.
It is standard practice to classify mixing operations with regard to the state of
aggregation
of
the major component in the mixture, since the same state of ag-
gregation will generally be present in the final mixture. From the standpoint of
process technology it is relevant, whether
a
gas is sparged into a liquid or a liquid is
sprayed into a gas.
A
further distinction must be made with regard to the degree of uniformity
of
the liquid phase: low viscosity liquids will be much easier to handle than highly
viscous paste-ldce liquids.
In
this respect the classification
of
fields of work given in

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

of a (stochastically or molecularly homogeneous) mixture. Finally one can mix a
heap
on
a pan granulator only by moistening with atomized liquid or in a rotary
furnace preferably by supplying heat. (This is also the case with the English terms
mixing and blending.)
When
a
material system, in which liquid phases predominate,
is
stirred, this
action can result in miscible liquid phases
forming
a molecularly homogeneous
mixture (“solution”). In the case of immiscible liquids,
on
the other hand, a dis-
persion (possibly an “emulsion”) will result.
If
stirring is performed to increase
heat or mass transfer, the purpose is to accelerate this operation and the inherent
mixing of the liquid phases is of secondary importance.
A
similar situation exists in the case
of
the term kneading. There are screw
machines whose primarily task are the mixing or conveying of paste-like compo-
sitions.
In
such cases the kneading itself is of secondary importance, although it

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,

to
honour them properly. This task has already been carried out at reg-
ular intervals in various reviews over the years. It is therefore appropriate, to refer
to these reviews”.
A
researcher is very well advised to consult them before he begins
his own research in
a
special field
of
stirring technology.
1)
Ralf
Weinekotter
-
Hermann Gericke:
Juri
Pawlowski:
Mischen von Feststoffen (Mixing
of
particulate solids)
Springer-Verlag
1995
Salle+Sauerlander
1990
Transportvorgange in Einwellen-Schnecken
(Transfer proceses in single-screw extruders)
ISBN
3-540-58567-2
ISBN

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

&
John
Willey, New
York
1975
ISBN
0-470-62863-4
Kneule,
F.:
Riihren (Stirring)
3.
Adage, Decherna Frankfurt/Main,
1986
Verfahrenstechnische Berechnungsrnethoden
Teil4 Stofiereinigen
in
fluiden Phasen
(Unifying processes
in
fluid phases)
Authors:
F.
Liepe, W. Meusel,
H 0.
M&kel,
B.
Platzer,
H.
WeiBgerber
VCH Verlagsges., Weinheim

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

bubble diameter, usually represented by
d32
mean gas bubble or liquid droplet diameter (“Sauter diameter”; eq. (6.8))
particle or droplet diameter
terminal (final) bubble diameter
inside tank or pipe diameter
diffusion coeficient
effective dispersion coefficient (in axial direction)
difference
enhancement factor in chemisorption; eq. (4.76)
energy spectrum of vortices
energy dissipation density spectrum, eq.
(1.14)
activation energy in chemical reactions
force
mass flow (rate of mass transfer, oxygen uptake)
stirrer distance from bottom of the vessel (bottom clearance)
heat transfer coefficient, definition eq.
(7.1)
total liquid depth (liquid height) in vessel
momentum
mass
flux;
eq.
(4.7)
heat flux, eq. (7.1)
rate constant in eq.
(1.1)
k
k

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

U!
LJ
V
VG
V
WS
ws
s
X
Z
proportionality constant, eq.
(1.45)
thermal conductivity
wave number of vortices
gas side mass transfer coefficient
liquid side mass transfer coefficient
volume-related over-all mass transport coefficient, eq.
(4.9)
base dimension of length
pipe length
mixing length in pipe flow
flow index in pseudoplastic fluids
mass,
rn
=
pV
enhancement factor in physical absorption; eq.
(4.88)
base dimension of mass
degree of mixedness, definition

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)

velocity components in the
x-,
y-,
z-direction
mean flow velocity
mean values of velocity fluctuations
(u;
=
@)
over-all heat transfer coefficient, eq. (7.2)
velocity; superficial velocity
superficial flow velocity
(uG
K
qG/Dz)
liquid volume (ungassed)
sinking velocity of single particles; eq. (5.17)
sinking velocity of
a
particle swarm; eq. (5.20)-(5.22)
chemical conversion
X
=
(co
-
ct)/co
number
Creek
Characters
a

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.

(1.53)
macro-scale of turbulence;
A
K
d
dynamic viscosity
chemical potential
scale factor
p
=
LT/LM
kinematic viscosity
density
I
xvii
List
of
Symbols
heat capacity per unit volume at constant pressure
interfacial, surface tension
standard deviation under given conditions
(,)
variance
variance coefficient
mean residence time
r
=
V/q
shear stress, eq.
(1.41)

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

bulk
of
liquid
kinetic
liquid
minimum
model scale
related to stirrer speed
start condition, initial value
particle (solid or liquid)
related to throughput
I
P'Pe
S
baf
S
foam
t
t
T
voli
W
x.
y.
z
radial
Pipe
saturation value
baffles
solid, solid phase

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

sphere in fluid flow
friction factor in pipe
flow
Deborah number
energy dissipation number
Euler number
Fourier number
Froude number
Froude number, modified by
Ap
Galilei number
Grashof number
Hat1
Hatta number, 1.order reaction
Hat2
Hatta number, 2.order reaction
Ne
Newton number
Nu
Nusselt number
no
Mixing number
Pr
Prandtl number
Pe
PCclet number
Q
Throughput number
Re
Reynolds number

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

d/L
De
=
?/A&
nl
E'
=
(EA~/v~)'/~
Eu
=
Ap/(pv2)
Fo
=
at/d2
Fr
=
n2d/g
Fr'
=
Frp/Ap
Ga
=
Re2/Fr
Gr
=
pATgd3/v2
Hatl
E
m/kL
Hat2

=
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

=
pn2d3/a
We/(FrRe4)
'I3
structure unknown
Q
=
w3)
Sc
=
Sh
Sherwood number
St
Stanton number
Vis
Viscosity number
I'
Sorption number
I
xix
list
of
Symbols
Sh
=
kLdp/D
St
=
Nu/RePr
=

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
heat transfer between a liquid and a heat transfer surface;
-
Suspension (and possible dissolution) of
a
solid
in
a liquid or slurry formation;
-
Dispersion (or sparging) of a gas in a liquid (gas-liquid contacting).
Dispersion (or emulsification) of
two
immiscible liquids;
The term homogenization is used, if
a
uniform liquid phase has to be realized,
e.g. a molecularly homogeneous mixture of several miscible liquids or equalization
of concentration and temperature differences during a chemical reaction in the
liquid phase. (The same term is used in the food industry for
a
completely different
operation, namely for
L/
L
(liquid/liquid) dispersion under extreme shear condi-
tions; e.g. the “homogenization” of
milk).
Intensification of heat transfer in
a
stirred tank can represent, especially in case

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

or
gas bubbles to accelerate
mass transport between the
two
phases.
In
suspension polymerization the stirring
conditions are adjusted
so
that
a
particular desired droplet size distribution results.
Often different stirring operations must be carried out simultaneosly, an example
being solids-catalyzed hydrogenation, in which the stirrer disperses the gas (hydro-
gen) in the liquid phase, swirls up the catalyst particles (e.g. Raney nickel) from the
bottom
of
the reactor and intensifies the removal
of
reaction heat.
In
such cases the
stirring conditions are determined by that stirring operation which is the bottle-
neck in the process.
1.2
Mixing Equipment
1.2.1
Mixing Tanks and Auxiliary Equipment
The mixing tank or stirred vessel
is

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,

5061,
ASME Code
Section
VIII.
Internal fittings include: baffles, coils, probes (e.g. thermometer, level
indicators) and feed and drain pipes. All of these fittings can influence the stirring
process.
If an axially positioned stirrer is operated in a vessel without inserts, the liquid is
set
in
rotation and a vortex is produced. In the case of rapidly rotating stirrers and
low
viscosity liquids, the vortex can reach the stirrer head with the result that the
stirrer entrains the gas in the liquid (see section
1.4.5.2).
This
is
generally unde-
sirable because it results in an extraordinarily high mechanical stress
on
the stirrer
shaft, bearings and seal, due to the absence of the “liquid bearing”. This ofien
leads to the destruction of the stirrer. Even when the vortex formation causes
no
gas entrainment, rotation of the liquid is always undesirable if a two-phase system
with different densities is concerned, since the centrifugal force counteracts the
stirring process.
The rotation of liquid in cylindrical tanks is prevented by the installation of
baffles. So-called “complete baffling” is realized with four baffles (flow interrupting
strips)

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

(Fig. 1.1a).
In
enamel-coated vessels they are attached to the vessel lid. If this
is
not
possible (glass tanks, wooden vats), they are made in the form of a basket with
pressure-fitted rings (Fig. 1.1b).
Baffles are not necessary, if stirring is carried out in a container with rectangular
cross-section (e.g. basins or pits) or when the stirrer
is
mounted laterally in the
tank wall.
In
the case of weak stirring, rotation of the liquid can be prevented even
in cylindrical
tanks
by installing the stirrer eccentrically and/or at an angle to the
tank axis. In this case, however, uneven mechanical stress in the stirrer shaft must
be accepted.
A
jacketed vessel wall is sufficient to supply or remove relatively small quantities
of heat. The usual configurations are shown in Fig.
1.2.
To
transfer larger quantities of heat, the installation
of
coils is necessary.
A
helical
coil (Fig. 1.3a) is only efficient

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

of
the vessel wall for heat transfer
[102].
15
1.2
Mixing
Equipment
6
I
1
Stirring,
General
The heat-exchange tubes can also be arranged into bundles and installed instead
of baffles. (Fig.
1.3~).
These heat exchangers possess
a
particularly large surface
area and are therefore mainly used in biotechnology, e.g. in penicillin and enzyme
production, because the operating temperature in such processes has to be kept
below 40°C, resulting in extremely small temperature differences.
1.2.2
Stirrer Types and Their Operating Characteristics
The stirring operations discussed in the introduction can obviously not be per-
formed with a single type of stirrer. There are many types of stirrers appropriate
for particular stirring operations and particular material systems. In this section
only those stirrer types will be discussed which are widely used in the chemical
industry and for which reliable design guidelines exist. The dimensions of stirrer
types have also been standardized to a large extent
[

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.

It
can be sensibly utilized only with low
viscosity liquids and in baffled tanks. Its diameter ratio Dld is
3-5.
The turbine
stirrer causes high levels of shear and hence is well suited for dispersion processes.
The
PFAUDLER
impeller stirrer was developed for use in enamel-coated vessels
[438]
and thus has rounded stirring arms. It is installed with small bottom clear-
ance at a Dld ratio of
1.5
and can be used both with and without baffles. Due to the
small bottom clearance it can be used with strongly fluctuating filling levels (e.g.
during emptying), since it can efficiently mix even small liquid volumes.
PFAUDLER
[438]
has developed the so-called “Cryo-Lock-System”, enabling enamel-
coated-BE vessels according to
DIN
28136
to be equipped with impellers of
d
>
600
mm via
a
manhole of
I

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

misleading choice of words, since it
is
not the
disk which effects the stirring, but
the
blades
it
supports
[
G37].
17
7.2
Mixing Equipment
c
500
~
P
I
Turbine
'itched blade
Impeller@
(Pfaudler)
4
Propeller
Liquid
viscosity
[m
Pa
s]
500

-
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

Flow patterns in a
;I:
Blade
INERMIG@
(Ekato)
jx
103-5x
104
Anchor
ielical ribbon