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 This book was carefully produced. Nevertheless, editors, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek - CIP Cataloguing-in-Publication-Data A catalogue record for this publication is available from Die Deutsche Bibliothek 0 Wiley-VCH Verlag GmbH, D-69469 Weinheim (Federal Republic of Germany). 2001 All rights reserved (including those of translation in other languages). 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KG, 67269 Griinstadt 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 [...]... number Sh = kLdp/D St = Nu/RePr = h / ( v p C p ) Vis = h / p see definition eq 4.72 Stirring Theory and Practice Marko Zlokarnik 0Wiley-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... can be concluded that in bubble columns and in stirred tanks the same shear stress is present, if in small and in large vessels the geometric similarity and E = P/pV = idem (1.4) are ensured This is consistent with the Kolmogorov’s theory of locally homogeneous and isotropic turbulence [289], see section 1.4 In turbulent flow range, turbulence exists on the micro- and the macro-scale The micro-scale3,...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... 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... 1.2.2 Stirrer Types and Their Operating Characteristics The stirring operations discussed in the introduction can obviously not be performed 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... 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... from EKATO [0.14]; Alpham, Sigma" (Fig 1.11) and Zeta@stirrers and coaxial stirrers (in different combina- + Fig 1.9 Hollow stirrer, type pipe stirrer [252] 10 I I Stirring, General Fig 1.10 Isojet'" and Interprop" of EKATO[0.14] PR - propeller, EIPR- EKATO Interprop" tions) from Stelzer RLihrtechnik [ 5261; Turbofoilc (Fig 1.12) from Pfaudler-Werke GmbH [438] and Maxilo T-Hydrofoil-Impeller@ (PMD) from... (internal and external single and double mechanical seals; with and without throttle bushing, with or without pressure relief) Some of them can be dismantled and replaced in filled tanks under pres- 1 Immersion seal Labytinth seal c3 ’ < 300 < 25 Stuffing or packing box Lip seal Mechanical seal Magnetic clutch Fig 1.14 Classification of shaft sealing devices with regard to system pressure and the shaft... lime particles than with corundum, with the corresponding values for glass and quartz being 3 and 1.1 16 I 7 Stirring, General respectively Kipke [274] recommended, in the case of stirrers vulnerable to wear, that pilot plant experiments be carried out with the original material system and the stirrers be made out of acrylic glass and that the results be converted with his formulas 1.3.5 Shear Stress on... 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 . Stirring: Theory and Practice Marko Zlokarnik Murk0 Zlokurnik Stirring Theory and Practice @WILEY-VCH Weinheim - New York - Chichester - Brisbane - Singapore - Toronto. Transportvorgange in Einwellen-Schnecken (Transfer proceses in single-screw extruders) ISBN 3-5 4 0-5 856 7-2 ISBN 3-7 9 3 5 -5 5 2 8-3 2) Mixing - Theory and Practice, Vol. 1 + 2 +. 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