Li Smart Hydrogel Modelling

1. Auflage 2010
ISBN: 978-3-642-02368-2
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 359 Seiten

The science of mathematical modelling and numerical simulation is generally accepted as the third mode of scienti?c discovery (with the other two modes being experiment and analysis), making this ?eld an integral component of c- ting edge scienti?c and industrial research in most domains. This is especially so in advanced biomaterials such as polymeric hydrogels responsive to biostimuli for a wide range of potential BioMEMS applications, where multiphysics and mul- phase are common requirements. These environmental stimuli-responsive hydrogels are often known as smart hydrogels. In the published studies on the smart or stimu- responsive hydrogels, the literature search clearly indicates that the vast majority are experimental based. In particular, although there are a few published books on the smart hydrogels, none is involved in the modelling of smart hydrogels. For the few published journal papers that conducted mathematical modelling and numerical simulation, results were far from satisfactory, and showed signi?cant d- crepancies when compared with existing experimental data. This has resulted in ad hoc studies of these hydrogel materials mainly conducted by trial and error. This is a very time-consuming and inef?cient process, and certain aspects of fun- mental knowledge are often missed or overlooked, resulting in off-tangent research directions.

Autoren/Hrsg.

Li, Hua

Inhaltsverzeichnis

1;Preface;5
2;Authors Brief Biography;8
3;Foreword;10
4;Contents;11
5;1 Introduction;14
5.1;1.1 Definition and Application of Hydrogel;14
5.2;1.2 Historical Development of Modelling Hydrogel;16
5.2.1;1.2.1 Steady-State Modelling for Equilibrium of Smart Hydrogels;17
5.2.1.1;1.2.1.1 Mathematical Models and Simulations;18
5.2.1.2;1.2.1.2 Key Parameters in Steady-State Modelling for Equilibrium of Hydrogels;33
5.2.2;1.2.2 Transient Modelling for Kinetics of Smart Hydrogels;42
5.2.2.1;1.2.2.1 Mathematical Models and Simulations;44
5.2.2.2;1.2.2.2 Key Parameters in Transient Modelling for Kinetics of Hydrogels;50
5.2.3;1.2.3 A Theoretical Formalism for Diffusion Coupled with Large Deformation of Hydrogel;56
5.2.4;1.2.4 Remarks;58
5.3;1.3 About This Monograph;58
5.4;References;60
6;2 Multi-Effect-Coupling pH-Stimulus (MECpH) Model for pH-Sensitive Hydrogel;69
6.1;2.1 Introduction;69
6.2;2.2 Development of the MECpH Model;69
6.2.1;2.2.1 Electrochemical Formulation;70
6.2.1.1;2.2.1.1 Ionic Flux;71
6.2.1.2;2.2.1.2 Electrical Potential;73
6.2.1.3;2.2.1.3 Fixed Charge Group;77
6.2.2;2.2.2 Mechanical Formulation;79
6.3;2.3 Computational Domain, Boundary Condition and Numerical Implementation;83
6.4;2.4 Model Validation with Experiment;88
6.5;2.5 Parameter Studies by Steady-State Simulation for Equilibrium of Hydrogel;90
6.5.1;2.5.1 Influence of Initially Fixed Charge Density of Hydrogel;93
6.5.2;2.5.2 Influence of Young's Modulus of Hydrogel;97
6.5.3;2.5.3 Influence of Initial Geometry of Hydrogel;103
6.5.4;2.5.4 Influence of Ionic Strength of Bath Solution;107
6.5.5;2.5.5 Influence of Multivalent Ionic Composition of Bath Solution;114
6.6;2.6 Remarks;120
6.7;References;123
7;3 Multi-Effect-Coupling Electric-Stimulus (MECe) Model for Electric-Sensitive Hydrogel;127
7.1;3.1 Introduction;127
7.2;3.2 Development of the MECe Model;127
7.2.1;3.2.1 Formulation of the MECe Governing Equations;128
7.2.2;3.2.2 Boundary and Initial Conditions;138
7.3;3.3 Steady-State Simulation for Equilibrium of Hydrogel;139
7.3.1;3.3.1 Numerical Implementation;139
7.3.2;3.3.2 Model Validation with Experiment;143
7.3.3;3.3.3 Parameter Studies;144
7.3.3.1;3.3.3.1 Influence of Externally Applied Electric Voltage;146
7.3.3.2;3.3.3.2 Influence of Initially Fixed Charge Density of Hydrogel;149
7.3.3.3;3.3.3.3 Influence of Concentration of Bath Solution;154
7.3.3.4;3.3.3.4 Influence of Ionic Valence of Bath Solution;156
7.4;3.4 Transient Simulation for Kinetics of Hydrogel;156
7.4.1;3.4.1 Numerical Implementation;159
7.4.2;3.4.2 Model Validation with Experiment;162
7.4.3;3.4.3 Parameter Studies;163
7.4.3.1;3.4.3.1 Variation of Ionic Concentration Distribution with Time;164
7.4.3.2;3.4.3.2 Variation of Electric Potential Distribution with Time;172
7.4.3.3;3.4.3.3 Variation of Hydrogel Displacement Distribution with Time;172
7.4.3.4;3.4.3.4 Variation of Hydrogel Average Curvature with Time;179
7.5;3.5 Remarks;182
7.6;References;183
8;4 Multi-Effect-Coupling pH-Electric-Stimuli (MECpHe) Model for Smart Hydrogel Responsive to pH-Electric Coupled Stimuli;185
8.1;4.1 Introduction;185
8.2;4.2 Development of the MECpHe Model;186
8.3;4.3 Numerical Implementation;192
8.4;4.4 Model Validation with Experiment;194
8.5;4.5 Parameter Studies by Steady-State Simulation for Equilibrium of Hydrogel;196
8.5.1;4.5.1 Influence of Solution pH Coupled with External Electric Voltage;196
8.5.2;4.5.2 Influence of Initially Fixed Charge Density of Hydrogel;203
8.5.3;4.5.3 Influence of Ionic Strength;211
8.5.4;4.5.4 Influence of Ionic Valence;221
8.6;4.6 Remarks;226
8.7;References;229
9;5 Multi-Effect-Coupling Thermal-Stimulus (MECtherm) Model for Temperature-Sensitive Hydrogel;231
9.1;5.1 Introduction;231
9.2;5.2 Development of the MECtherm Model;231
9.2.1;5.2.1 Free Energy;232
9.2.2;5.2.2 Poisson--Nernst--Planck Formulation;235
9.3;5.3 Numerical Implementation;235
9.4;5.4 Model Validation with Experiment;240
9.5;5.5 Parameter Studies by Steady-State Simulation for Thermo-Sensitive Ionized Hydrogel;241
9.5.1;5.5.1 Influence of Initially Fixed Charge Density;242
9.5.2;5.5.2 Influence of Bath Solution Concentration;245
9.5.3;5.5.3 Influence of Effective Crosslink Density;249
9.5.4;5.5.4 Influence of Initial Volume Fraction of Polymeric Network;252
9.6;5.6 Transient Modelling of Temperature-Sensitive Neutral Hydrogel;255
9.6.1;5.6.1 Model Formulation in Eulerian Frame;258
9.6.1.1;5.6.1.1 Basics of Two-Phase Mixture Theory;262
9.6.1.2;5.6.1.2 Governing Equations;262
9.6.1.3;5.6.1.3 Constitutive Relations;264
9.6.1.4;5.6.1.4 Boundary and Initial Conditions;272
9.6.2;5.6.2 Analysis;273
9.6.2.1;5.6.2.1 Non-dimensionalization;273
9.6.2.2;5.6.2.2 Time Scales;275
9.6.2.3;5.6.2.3 Momentum Balances;276
9.6.2.4;5.6.2.4 Parameters and Non-dimensional Numbers;278
9.6.2.5;5.6.2.5 Mass Balance;279
9.6.2.6;5.6.2.6 Energy Balance;279
9.6.3;5.6.3 Model Formulation in Lagrangian Frame and Boundary and Initial Conditions;280
9.6.4;5.6.4 Numerical Implementation;282
9.6.5;5.6.5 Simulations and Discussions;284
9.6.5.1;5.6.5.1 Temperature Dependence of Equilibrium Degree of Swelling;284
9.6.5.2;5.6.5.2 Permeability for Swelling and Deswelling Kinetics;286
9.6.5.3;5.6.5.3 Uniform Deformation Behaviour;288
9.6.5.4;5.6.5.4 Non-uniform Deformation Behaviour;292
9.6.5.5;5.6.5.5 Deformation Behaviour in a Temperature Gradient;297
9.7;5.7 Remarks;298
9.8;References;300
10;6 Novel Models for Smart Hydrogel Responsive to Other Stimuli: Glucose Concentration and Ionic Strength;306
10.1;6.1 Introduction;306
10.2;6.2 Multi-Effect-Coupling Glucose-Stimulus (MECglu) Model for Glucose-Sensitive Hydrogel;307
10.2.1;6.2.1 Development of the MECglu Model;309
10.2.1.1;6.2.1.1 Mechanism and Assumptions;310
10.2.1.2;6.2.1.2 Formulation in Deformed Configuration;312
10.2.1.3;6.2.1.3 Formulation in Reference Configuration;314
10.2.2;6.2.2 Model Validation with Experiment;317
10.3;6.3 Multi-Effect-Coupling Ionic-Strength-Stimulus (MECis) Model for Ionic Strength-Sensitive Hydrogel;321
10.3.1;6.3.1 Development of the MECis Model;323
10.3.1.1;6.3.1.1 Assumptions;324
10.3.1.2;6.3.1.2 Formulation with Eulerian Description;324
10.3.1.3;6.3.1.3 Formulation with Lagrangian Description;334
10.4;6.4 Remarks;339
10.5;References;340
11;7 Simulation of Controlled Drug Release from Non-Swellable Micro-Hydrogel Particle;345
11.1;7.1 Introduction;345
11.2;7.2 Formulation of Model;345
11.3;7.3 Numerical Implementation;348
11.4;7.4 Comparison with Experiment;349
11.5;7.5 Parameter Studies by Transient Simulation;351
11.5.1;7.5.1 Identification of Physical Parameters;351
11.5.2;7.5.2 Influence of Mean Radius of Micro-Hydrogel Particle;354
11.5.3;7.5.3 Influence of Equivalent Drug Saturation Concentration;354
11.5.4;7.5.4 Influence of the First-Order Drug Dissolution Rate;354
11.5.5;7.5.5 Influence of Drug Diffusion Coefficient;355
11.6;7.6 Remarks;355
11.7;References;355
12;References;357
13;Acknowledgements;359
14;Index;361