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

• VerfasserIn: 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

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 method of moments. New, consistent approaches for moments' diffusion and the reaction-diffusion system are derived to ensure conservation. Simulations reveal peculiarities of the process such as that, due to drying, polymerisation happens mostly in bulk and monomer evaporation leads to a poor yield. Various process variants and simulation models are discussed. The impact of process parameters is examined by means of numerical DoEs. The second part presents a novel approach for the simulation of structure evolution in suspension drying. The meshfree SPH method is used to model the relevant physical effects on a detailed scale during the first and second drying period. New implementations of physical effects are derived: heat and mass transfer based on linear driving forces, an implicit solution of the heat equation, several approaches for crust formation and a new formulation of surface tension by pairwise forces. The formation of dense structures as well as hollow granules can be simulated. Model parameters influence crust formation during the second drying period concerning shape and microporosity and can be interpreted in a physical sense.

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.