Simulation of Spray Polymerisation and Structure Generation in Spray Drying by Single Droplet Models /

Simulation of Spray Polymerisation and Structure Generation in Spray Drying by Single Droplet Models / / Winfried Säckel.

Spray polymerisation has a long time been discussed as a promising process, yet, with little knowledge on cause-and-effect relationships between drying and chemical reactions. This work develops a new single droplet model of combined solution drying and free radical homopolymerisation, based on the...

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Säckel, Winfried,
Place / Publishing House:Berlin, Germany : : Logos Verlag Berlin GmbH,, 2022.
Year of Publication:2022
Language:English
Physical Description:1 online resource (328 pages) :; illustrations
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Table of Contents:
  • List of Symbols xv
  • List of Figures xxi
  • List of Tables xxv
  • 1 Introduction: Spray Drying and Reactive Drying Processes 1
  • 1.1 Spray Polymerisation. 2
  • 1.2 Single Droplet Models for Spray Drying . 3
  • 1.3 Meshfree Methods, Simulation of Structure Evolution4
  • 1.3.1 Previous Applications of SPH to Drying . 5
  • 2 Theoretical Principles 7
  • 2.1 Transport Equations 7
  • 2.1.1 Transport in a Mass Averaged System 9
  • 2.1.2 Transport in a Molar Averaged System . 13
  • 2.1.3 Reference Velocities and Conversion between Systems . 13
  • 2.1.4 Eulerian and Lagrangian Frames of Reference16
  • 2.2 Diffusion . 17
  • 2.2.1 Fickian Diffusion . 17
  • 2.2.2 Maxwell-Stefan Diffusion 19
  • 2.2.3 Determination of Diffusion Coefficients . 21
  • 2.3 Modelling of Free Radical Polymerisation 21
  • 2.3.1 Reactions in Free Radical Polymerisation 22
  • 2.3.2 Quasi-Steady-State Assumption (QSSA) 27
  • 2.3.3 Method of Moments . 28
  • 2.4 Mixture Thermodynamics 31
  • 2.4.1 Vapour Liquid Equilibrium at the Droplet's Surface . 32
  • 2.4.2 Calculation of Activity Coefficients . 33
  • 2.4.3 The UNIFAC Equations . 34
  • 2.5 Spray Drying: Basic Assumptions 35
  • 2.5.1 Approximate Residence Time in a Spray Dryer . 36
  • 2.5.2 Heat and Mass Transfer . 37
  • 2.5.3 Inner Circulation Inside a Droplet 38
  • 2.5.4 Are Droplets Fully Mixed? 40
  • 3 Modelling of Reactive Droplet Drying and Polymerisation 41
  • 3.1 Transport in a Reaction-Diffusion System 42
  • 3.1.1 Constant Physical Properties. 44
  • 3.1.2 Consideration of Mixture Effects . 46
  • 3.1.3 Diffusion and Reaction Driven Convection at Variable
  • Molar Weights47
  • 3.1.4 Transport of Polymer - Quasi-Steady-State Assumption . 50
  • 3.1.5 Transport of Statistical Moments . 52
  • 3.2 Lumped Modelling - 0D approach 56
  • 3.2.1 General Equations for Reactive Spray Drying57
  • 3.2.2 Spray Polymerisation - Quasi-Steady-State Assumption 58
  • 3.2.3 Spray Polymerisation - Method of Moments. 59
  • 3.3 Distributed Modelling - 1D approach. 60
  • 3.3.1 General Equations of the Droplet Continuum60
  • 3.3.2 Boundary Conditions . 62
  • 3.3.3 Spray Polymerisation - QSSA66
  • 3.3.4 Spray Polymerisation - Method of Moments. 68
  • 3.4 Comparison with Existing Models 69
  • 3.5 Implementational Considerations . 70
  • 3.5.1 Implementation of the Moving Boundary Problem . 70
  • 3.5.2 Boundary Conditions . 71
  • 3.5.3 Treatment of Convection Terms . 72
  • 3.5.4 Implementation of Diffusion. 75
  • 3.6 Verification of the Transport Approach76
  • 3.6.1 Diffusion Driven Convection, Constant Properties 76
  • 3.6.2 Diffusion Driven Convection, Variable Molar Weight 79
  • 3.6.3 Diffusion Driven Convection, Excess Volumes . 82
  • 3.6.4 Reaction Induced Convection85
  • 4 Simulation of Spray Polymerisation 87
  • 4.1 Kinetics and Process Conditions . 88
  • 4.2 Lumped Simulation of Droplet Polymerisation 92
  • 4.2.1 Principle Course of the Process -
  • Plain Kinetics, no Monomer Evaporation 92
  • 4.2.2 Effects of Kinetics on the Process 94
  • 4.3 Spatial Effects in Droplet Polymerisation 98
  • 4.3.1 Effect of the Diffusion Coefficient on Concentration Gradients . 99
  • 4.3.2 Inhomogeneities of the Product at Small Diffusion Coefficients, Effect of Moments' Diffusion . 102
  • 4.3.3 Effect of Monomer Evaporation . 106
  • 4.3.4 Pre-polymerisation Before Atomisation . 111
  • 4.3.5 Polymerisation at Elevated Monomer Content in the Drying Gas 116
  • 4.3.6 Influence of Non-Ideality of Activities 122
  • 4.3.7 Interaction with the drying gas125
  • 4.3.8 Applicability of the QSSA model 131
  • 4.4 Summary of Basic Findings on Droplet Polymerisation . 133
  • 4.5 Process Evaluation, Numerical DoEs. 135
  • 4.5.1 DoEs' Setup and Evaluation. 135
  • 4.5.2 Droplet Polymerisation with Solvent in the Feed 138
  • 4.5.3 Bulk Polymerisation within a Droplet 142
  • 4.5.4 Bulk Feed with Pre-Polymerisation before Atomisation . 149
  • 4.6 Discussion and Suggestions for Further Research 153
  • 5 SPH and its Application to Single Droplet Slurry Drying 155
  • 5.1 Mathematical Derivation . 156
  • 5.1.1 SPH Interpolation 156
  • 5.1.2 Integral Approximations . 159
  • 5.1.3 First Derivatives . 160
  • 5.1.4 Laplace-Operator and Divergence of Diffusive Fluxes 162
  • 5.1.5 General Second Derivatives. 165
  • 5.1.6 Choice of Kernel, Smoothing Length and Cut-off Radius 165
  • 5.1.7 Correction of the SPH Approximation 168
  • 5.2 Implementation of Boundary Conditions . 169
  • 5.2.1 Ghost Particles169
  • 5.2.2 Insertion of Boundary Conditions into SPH Equations . 171
  • 5.2.3 Repulsive Forces as Hard Sphere Boundaries172
  • 5.3 Hydrodynamics of an Incompressible Liquid in SPH173
  • 5.3.1 Continuity Equation, Density Evaluation 173
  • 5.3.2 Momentum Balance . 175
  • 5.3.3 Weakly Compressible SPH 178
  • 5.4 Incompressible SPH 179
  • 5.4.1 Boundary Conditions in ISPH182
  • 5.4.2 Boundaries by the Ghost Technique, Wall Boundaries 182
  • 5.4.3 Free Surface Boundaries in ISPH 183
  • 5.4.4 Modifications to ISPH in This Work . 184
  • 5.5 Surface Tension and Wetting . 189
  • 5.5.1 The Interparticle Force Approach 190
  • 5.5.2 The Concept of Surface-Lateral Particle Forces . 195
  • 5.6 Representation of the Solid Phase 200
  • 5.6.1 Primary Particles in the Slurry200
  • 5.6.2 Calculation of Crust Formation . 202
  • 5.7 Modelling of Drying Phenomena in SPH . 205
  • 5.7.1 Heat Conduction . 205
  • 5.7.2 Implementation of Linear Driving Force based Heat and
  • Mass Transfer into SPH . 205
  • 5.7.3 Extension to the Second Drying Period . 208
  • 5.7.4 Treatment of Evaporation Concerning Particle Mass and
  • Deletion 209
  • 5.7.5 Modelling of Diffusion Driven Drying Involving the Gas
  • Phase . 210
  • 5.8 Time Integration 213
  • 5.8.1 Stability Criteria in Explicit Time Stepping. 214
  • 5.8.2 Time Stepping Criteria Employed in This Work and Their
  • Reference Length . 216
  • 5.8.3 Implicit Solution of Diffusive Equations . 218
  • 5.8.4 Initialisation of an SPH Calculation . 220
  • 6 Validation of the SPH Implementation 221
  • 6.1 Implicit Solution of Heat Conduction. 221
  • 6.2 Heat and Mass Transfer by Linear Driving Forces 224
  • 6.2.1 Heat Transfer to a Unilaterally Heated Rod. 224
  • 6.2.2 Coupled Heat and Mass Transfer: Droplet Evaporation . 226
  • 6.3 Diffusion Driven Drying by SPH-Grid Coupling . 228
  • 6.4 SPH Flow Solver . 230
  • 6.4.1 ISPH Solution of a Standing Water Column. 230
  • 6.4.2 Free Surface Flow 231
  • 6.4.3 Surface Tension Approach of Pairwise Forces234
  • 6.4.4 Wetting Phenomena . 237
  • 7 Simulation of Structure Evolution During Drying 243
  • 7.1 Simulation of the First Drying Period243
  • 7.2 Simulation of Crust Formation 245
  • 7.2.1 Simulation of the Second Drying Period without Crust
  • Formation . 245
  • 7.2.2 Crust Formation by Caught on First Touch. 247
  • 7.2.3 Crust Formation Determined by the Water Content . 249
  • 7.2.4 Effect of the Density Correction . 250
  • 7.3 Influence of Adjustable Parameters on the Structure. 251
  • 7.4 Effect of the Temperature . 256
  • 7.5 Variation of the Resolution 259
  • 7.6 Drying of a Microporous Structure 261
  • 7.7 Comments on numerical efficiency 267
  • 8 Conclusion 269
  • A Numerical Regression by Gaussian Processes 273
  • B FVM Implementation of the Droplet Polymerisation Model 277
  • C Implementational Aspects of SPH 281
  • C.1 Neighbourhood Search281
  • C.1.1 Linked List 281
  • C.1.2 Verlet List . 282
  • C.2 Performance Aspects, Memory Alignment 282List of Symbols xv
  • List of Figures xxi
  • List of Tables xxv
  • 1 Introduction: Spray Drying and Reactive Drying Processes 1
  • 1.1 Spray Polymerisation. 2
  • 1.2 Single Droplet Models for Spray Drying . 3
  • 1.3 Meshfree Methods, Simulation of Structure Evolution4
  • 1.3.1 Previous Applications of SPH to Drying . 5
  • 2 Theoretical Principles 7
  • 2.1 Transport Equations 7
  • 2.1.1 Transport in a Mass Averaged System 9
  • 2.1.2 Transport in a Molar Averaged System .
  • 13
  • 2.1.3 Reference Velocities and Conversion between Systems . 13
  • 2.1.4 Eulerian and Lagrangian Frames of Reference16
  • 2.2 Diffusion . 17
  • 2.2.1 Fickian Diffusion . 17
  • 2.2.2 Maxwell-Stefan Diffusion 19
  • 2.2.3 Determination of Diffusion Coefficients . 21
  • 2.3 Modelling of Free Radical Polymerisation 21
  • 2.3.1 Reactions in Free Radical Polymerisation 22
  • 2.3.2 Quasi-Steady-State Assumption (QSSA) 27
  • 2.3.3 Method of Moments .
  • 28
  • 2.4 Mixture Thermodynamics 31
  • 2.4.1 Vapour Liquid Equilibrium at the Droplet's Surface . 32
  • 2.4.2 Calculation of Activity Coefficients . 33
  • 2.4.3 The UNIFAC Equations . 34
  • 2.5 Spray Drying: Basic Assumptions 35
  • 2.5.1 Approximate Residence Time in a Spray Dryer . 36
  • 2.5.2 Heat and Mass Transfer . 37
  • 2.5.3 Inner Circulation Inside a Droplet 38
  • 2.5.4 Are Droplets Fully Mixed? 40
  • 3 Modelling of Reactive Droplet Drying and Polymerisation 41
  • 3.1 Transport in a Reaction-Diffusion System 42
  • 3.1.1 Constant Physical Properties. 44
  • 3.1.2 Consideration of Mixture Effects . 46
  • 3.1.3 Diffusion and Reaction Driven Convection at Variable
  • Molar Weights47
  • 3.1.4 Transport of Polymer - Quasi-Steady-State Assumption . 50
  • 3.1.5 Transport of Statistical Moments . 52
  • 3.2 Lumped Modelling - 0D approach 56
  • 3.2.1 General Equations for Reactive Spray Drying57
  • 3.2.2 Spray Polymerisation - Quasi-Steady-State Assumption 58
  • 3.2.3 Spray Polymerisation - Method of Moments. 59
  • 3.3 Distributed Modelling - 1D approach. 60
  • 3.3.1 General Equations of the Droplet Continuum60
  • 3.3.2 Boundary Conditions . 62
  • 3.3.3 Spray Polymerisation - QSSA66
  • 3.3.4 Spray Polymerisation - Method of Moments. 68
  • 3.4 Comparison with Existing Models 69
  • 3.5 Implementational Considerations . 70
  • 3.5.1 Implementation of the Moving Boundary Problem . 70
  • 3.5.2 Boundary Conditions . 71
  • 3.5.3 Treatment of Convection Terms . 72
  • 3.5.4 Implementation of Diffusion. 75
  • 3.6 Verification of the Transport Approach76
  • 3.6.1 Diffusion Driven Convection, Constant Properties 76
  • 3.6.2 Diffusion Driven Convection, Variable Molar Weight 79
  • 3.6.3 Diffusion Driven Convection, Excess Volumes . 82
  • 3.6.4 Reaction Induced Convection85
  • 4 Simulation of Spray Polymerisation 87
  • 4.1 Kinetics and Process Conditions . 88
  • 4.2 Lumped Simulation of Droplet Polymerisation 92
  • 4.2.1 Principle Course of the Process -
  • Plain Kinetics, no Monomer Evaporation 92
  • 4.2.2 Effects of Kinetics on the Process 94
  • 4.3 Spatial Effects in Droplet Polymerisation 98
  • 4.3.1 Effect of the Diffusion Coefficient on Concentration Gradients . 99
  • 4.3.2 Inhomogeneities of the Product at Small Diffusion Coefficients, Effect of Moments' Diffusion . 102
  • 4.3.3 Effect of Monomer Evaporation . 106
  • 4.3.4 Pre-polymerisation Before Atomisation . 111
  • 4.3.5 Polymerisation at Elevated Monomer Content in the Drying Gas 116
  • 4.3.6 Influence of Non-Ideality of Activities 122
  • 4.3.7 Interaction with the drying gas125
  • 4.3.8 Applicability of the QSSA model 131
  • 4.4 Summary of Basic Findings on Droplet Polymerisation . 133
  • 4.5 Process Evaluation, Numerical DoEs. 135
  • 4.5.1 DoEs' Setup and Evaluation. 135
  • 4.5.2 Droplet Polymerisation with Solvent in the Feed 138
  • 4.5.3 Bulk Polymerisation within a Droplet 142
  • 4.5.4 Bulk Feed with Pre-Polymerisation before Atomisation . 149
  • 4.6 Discussion and Suggestions for Further Research 153
  • 5 SPH and its Application to Single Droplet Slurry Drying 155
  • 5.1 Mathematical Derivation . 156
  • 5.1.1 SPH Interpolation 156
  • 5.1.2 Integral Approximations . 159
  • 5.1.3 First Derivatives . 160
  • 5.1.4 Laplace-Operator and Divergence of Diffusive Fluxes 162
  • 5.1.5 General Second Derivatives. 165
  • 5.1.6 Choice of Kernel, Smoothing Length and Cut-off Radius 165
  • 5.1.7 Correction of the SPH Approximation 168
  • 5.2 Implementation of Boundary Conditions . 169
  • 5.2.1 Ghost Particles169
  • 5.2.2 Insertion of Boundary Conditions into SPH Equations . 171
  • 5.2.3 Repulsive Forces as Hard Sphere Boundaries172
  • 5.3 Hydrodynamics of an Incompressible Liquid in SPH173
  • 5.3.1 Continuity Equation, Density Evaluation 173
  • 5.3.2 Momentum Balance . 175
  • 5.3.3 Weakly Compressible SPH 178
  • 5.4 Incompressible SPH 179
  • 5.4.1 Boundary Conditions in ISPH182
  • 5.4.2 Boundaries by the Ghost Technique, Wall Boundaries 182
  • 5.4.3 Free Surface Boundaries in ISPH 183
  • 5.4.4 Modifications to ISPH in This Work . 184
  • 5.5 Surface Tension and Wetting . 189
  • 5.5.1 The Interparticle Force Approach 190
  • 5.5.2 The Concept of Surface-Lateral Particle Forces . 195
  • 5.6 Representation of the Solid Phase 200
  • 5.6.1 Primary Particles in the Slurry200
  • 5.6.2 Calculation of Crust Formation . 202
  • 5.7 Modelling of Drying Phenomena in SPH . 205
  • 5.7.1 Heat Conduction . 205
  • 5.7.2 Implementation of Linear Driving Force based Heat and
  • Mass Transfer into SPH . 205
  • 5.7.3 Extension to the Second Drying Period . 208
  • 5.7.4 Treatment of Evaporation Concerning Particle Mass and
  • Deletion 209
  • 5.7.5 Modelling of Diffusion Driven Drying Involving the Gas
  • Phase . 210
  • 5.8 Time Integration 213
  • 5.8.1 Stability Criteria in Explicit Time Stepping. 214
  • 5.8.2 Time Stepping Criteria Employed in This Work and Their
  • Reference Length . 216
  • 5.8.3 Implicit Solution of Diffusive Equations . 218
  • 5.8.4 Initialisation of an SPH Calculation . 220
  • 6 Validation of the SPH Implementation 221
  • 6.1 Implicit Solution of Heat Conduction. 221
  • 6.2 Heat and Mass Transfer by Linear Driving Forces 224
  • 6.2.1 Heat Transfer to a Unilaterally Heated Rod. 224
  • 6.2.2 Coupled Heat and Mass Transfer: Droplet Evaporation . 226
  • 6.3 Diffusion Driven Drying by SPH-Grid Coupling . 228
  • 6.4 SPH Flow Solver . 230
  • 6.4.1 ISPH Solution of a Standing Water Column. 230
  • 6.4.2 Free Surface Flow 231
  • 6.4.3 Surface Tension Approach of Pairwise Forces234
  • 6.4.4 Wetting Phenomena . 237
  • 7 Simulation of Structure Evolution During Drying 243
  • 7.1 Simulation of the First Drying Period243
  • 7.2 Simulation of Crust Formation 245
  • 7.2.1 Simulation of the Second Drying Period without Crust
  • Formation . 245
  • 7.2.2 Crust Formation by Caught on First Touch. 247
  • 7.2.3 Crust Formation Determined by the Water Content . 249
  • 7.2.4 Effect of the Density Correction . 250
  • 7.3 Influence of Adjustable Parameters on the Structure. 251
  • 7.4 Effect of the Temperature . 256
  • 7.5 Variation of the Resolution 259
  • 7.6 Drying of a Microporous Structure 261
  • 7.7 Comments on numerical efficiency 267
  • 8 Conclusion 269
  • A Numerical Regression by Gaussian Processes 273
  • B FVM Implementation of the Droplet Polymerisation Model 277
  • C Implementational Aspects of SPH 281
  • C.1 Neighbourhood Search281
  • C.1.1 Linked List 281
  • C.1.2 Verlet List . 282
  • C.2 Performance Aspects, Memory Alignment 282.

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