Smart Hydrogel Modelling (eBook)

Preface 5
Authors Brief Biography 8
Foreword 10
Contents 11
1 Introduction 14
1.1 Definition and Application of Hydrogel 14
1.2 Historical Development of Modelling Hydrogel 16
1.2.1 Steady-State Modelling for Equilibrium of Smart Hydrogels 17
1.2.1.1 Mathematical Models and Simulations 18
1.2.1.2 Key Parameters in Steady-State Modelling for Equilibrium of Hydrogels 33
1.2.2 Transient Modelling for Kinetics of Smart Hydrogels 42
1.2.2.1 Mathematical Models and Simulations 44
1.2.2.2 Key Parameters in Transient Modelling for Kinetics of Hydrogels 50
1.2.3 A Theoretical Formalism for Diffusion Coupled with Large Deformation of Hydrogel 56
1.2.4 Remarks 58
1.3 About This Monograph 58
References 60
2 Multi-Effect-Coupling pH-Stimulus (MECpH) Model for pH-Sensitive Hydrogel 69
2.1 Introduction 69
2.2 Development of the MECpH Model 69
2.2.1 Electrochemical Formulation 70
2.2.1.1 Ionic Flux 71
2.2.1.2 Electrical Potential 73
2.2.1.3 Fixed Charge Group 77
2.2.2 Mechanical Formulation 79
2.3 Computational Domain, Boundary Condition and Numerical Implementation 83
2.4 Model Validation with Experiment 88
2.5 Parameter Studies by Steady-State Simulation for Equilibrium of Hydrogel 90
2.5.1 Influence of Initially Fixed Charge Density of Hydrogel 93
2.5.2 Influence of Young's Modulus of Hydrogel 97
2.5.3 Influence of Initial Geometry of Hydrogel 103
2.5.4 Influence of Ionic Strength of Bath Solution 107
2.5.5 Influence of Multivalent Ionic Composition of Bath Solution 114
2.6 Remarks 120
References 123
3 Multi-Effect-Coupling Electric-Stimulus (MECe) Model for Electric-Sensitive Hydrogel 127
3.1 Introduction 127
3.2 Development of the MECe Model 127
3.2.1 Formulation of the MECe Governing Equations 128
3.2.2 Boundary and Initial Conditions 138
3.3 Steady-State Simulation for Equilibrium of Hydrogel 139
3.3.1 Numerical Implementation 139
3.3.2 Model Validation with Experiment 143
3.3.3 Parameter Studies 144
3.3.3.1 Influence of Externally Applied Electric Voltage 146
3.3.3.2 Influence of Initially Fixed Charge Density of Hydrogel 149
3.3.3.3 Influence of Concentration of Bath Solution 154
3.3.3.4 Influence of Ionic Valence of Bath Solution 156
3.4 Transient Simulation for Kinetics of Hydrogel 156
3.4.1 Numerical Implementation 159
3.4.2 Model Validation with Experiment 162
3.4.3 Parameter Studies 163
3.4.3.1 Variation of Ionic Concentration Distribution with Time 164
3.4.3.2 Variation of Electric Potential Distribution with Time 172
3.4.3.3 Variation of Hydrogel Displacement Distribution with Time 172
3.4.3.4 Variation of Hydrogel Average Curvature with Time 179
3.5 Remarks 182
References 183
4 Multi-Effect-Coupling pH-Electric-Stimuli (MECpHe) Model for Smart Hydrogel Responsive to pH-Electric Coupled Stimuli 185
4.1 Introduction 185
4.2 Development of the MECpHe Model 186
4.3 Numerical Implementation 192
4.4 Model Validation with Experiment 194
4.5 Parameter Studies by Steady-State Simulation for Equilibrium of Hydrogel 196
4.5.1 Influence of Solution pH Coupled with External Electric Voltage 196
4.5.2 Influence of Initially Fixed Charge Density of Hydrogel 203
4.5.3 Influence of Ionic Strength 211
4.5.4 Influence of Ionic Valence 221
4.6 Remarks 226
References 229
5 Multi-Effect-Coupling Thermal-Stimulus (MECtherm) Model for Temperature-Sensitive Hydrogel 231
5.1 Introduction 231
5.2 Development of the MECtherm Model 231
5.2.1 Free Energy 232
5.2.2 Poisson--Nernst--Planck Formulation 235
5.3 Numerical Implementation 235
5.4 Model Validation with Experiment 240
5.5 Parameter Studies by Steady-State Simulation for Thermo-Sensitive Ionized Hydrogel 241
5.5.1 Influence of Initially Fixed Charge Density 242
5.5.2 Influence of Bath Solution Concentration 245
5.5.3 Influence of Effective Crosslink Density 249
5.5.4 Influence of Initial Volume Fraction of Polymeric Network 252
5.6 Transient Modelling of Temperature-Sensitive Neutral Hydrogel 255
5.6.1 Model Formulation in Eulerian Frame 258
5.6.1.1 Basics of Two-Phase Mixture Theory 262
5.6.1.2 Governing Equations 262
5.6.1.3 Constitutive Relations 264
5.6.1.4 Boundary and Initial Conditions 272
5.6.2 Analysis 273
5.6.2.1 Non-dimensionalization 273
5.6.2.2 Time Scales 275
5.6.2.3 Momentum Balances 276
5.6.2.4 Parameters and Non-dimensional Numbers 278
5.6.2.5 Mass Balance 279
5.6.2.6 Energy Balance 279
5.6.3 Model Formulation in Lagrangian Frame and Boundary and Initial Conditions 280
5.6.4 Numerical Implementation 282
5.6.5 Simulations and Discussions 284
5.6.5.1 Temperature Dependence of Equilibrium Degree of Swelling 284
5.6.5.2 Permeability for Swelling and Deswelling Kinetics 286
5.6.5.3 Uniform Deformation Behaviour 288
5.6.5.4 Non-uniform Deformation Behaviour 292
5.6.5.5 Deformation Behaviour in a Temperature Gradient 297
5.7 Remarks 298
References 300
6 Novel Models for Smart Hydrogel Responsive to Other Stimuli: Glucose Concentration and Ionic Strength 306
6.1 Introduction 306
6.2 Multi-Effect-Coupling Glucose-Stimulus (MECglu) Model for Glucose-Sensitive Hydrogel 307
6.2.1 Development of the MECglu Model 309
6.2.1.1 Mechanism and Assumptions 310
6.2.1.2 Formulation in Deformed Configuration 312
6.2.1.3 Formulation in Reference Configuration 314
6.2.2 Model Validation with Experiment 317
6.3 Multi-Effect-Coupling Ionic-Strength-Stimulus (MECis) Model for Ionic Strength-Sensitive Hydrogel 321
6.3.1 Development of the MECis Model 323
6.3.1.1 Assumptions 324
6.3.1.2 Formulation with Eulerian Description 324
6.3.1.3 Formulation with Lagrangian Description 334
6.4 Remarks 339
References 340
7 Simulation of Controlled Drug Release from Non-Swellable Micro-Hydrogel Particle 345
7.1 Introduction 345
7.2 Formulation of Model 345
7.3 Numerical Implementation 348
7.4 Comparison with Experiment 349
7.5 Parameter Studies by Transient Simulation 351
7.5.1 Identification of Physical Parameters 351
7.5.2 Influence of Mean Radius of Micro-Hydrogel Particle 354
7.5.3 Influence of Equivalent Drug Saturation Concentration 354
7.5.4 Influence of the First-Order Drug Dissolution Rate 354
7.5.5 Influence of Drug Diffusion Coefficient 355
7.6 Remarks 355
References 355
References 357
Acknowledgements 359
Index 361