: Douglas N. Arnold, Arnd Scheel, Maria-Carme T. Calderer, Eugene M. Terentjev
: Maria-Carme T. Calderer, Eugene M. Terentjev
: Modeling of Soft Matter
: Springer-Verlag
: 9780387321530
: 1
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: Sonstiges
: English
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This IMA Volume in Mathematics and its Applications MODELING OF SOFT MATTER contains papers presented at a very successful workshop with the same ti­ tle. The event, which was held on September 27-October 1, 2004, was an integral part of the 2004-2005 IMA Thematic Year on 'Mathematics of Ma­ terials and Macromolecules: Multiple Scales, Disorder, and Singularities. ' We would like to thank Maria-Carme T. Calderer (School of Mathematics, University of Minnesota) and Eugene M. Terentjev (Cavendish Laboratory, University of Cambridge) for their superb role as workshop organizers and editors of the proceedings. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Arnd Scheel, Deputy Director of the IMA PREFACE The physics of soft matter in particular, focusing on such materials as complex fluids, liquid crystals, elastomers, soft ferroelectrics, foams, gels and particulate systems is an area of intense interest and contemporary study. Soft matter plays a role in a wide variety of important processes and application, as well as in living systems. For example, gel swelling is an essential part of many biological processes such as motility mecha­ nisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switch­ ing devices. Experiments of the last decade have provided a great deal of detailed information on structures and properties of soft matter.
FOREWORD6
PREFACE7
CONTENTS9
AN ENERGETIC VARIATIONAL FORMULATION WITH PHASE FIELD METHODS FOR INTERFACIAL DYNAMICS OF COMPLEX FLUIDS: ADVANTAGES AND CHALLENGES11
1. Introduction11
2. An energy-based phsuse-field theory.13
3. Numerical scheme.16
4. Advantages of the diffuse-interface model.18
5. Physical and numerical subtleties.22
6. Concluding remarks.31
7. Acknowledgments.32
REFERENCES32
NON-EQUILIBRIUM STATISTICAL MECHANICS OF NEMATIC LIQUIDS37
1. Introduction.37
2. Kinetic equation.40
3. Viscous stress tensor.51
4. Microscopic viscosity coefficients.58
5. Rotational friction constant.72
6. Spatial inhomogeneities and domain structure.85
REFERENCES92
ANISOTROPY AND HETEROGENEITY OF NEMATIC POLYMER NANO-COMPOSITE FILM PROPERTIES95
1. Introduction.95
2. Plane Couette film flow of nematic polymers.96
3. Conductivity properties across the phase diagram of flowinduced film structures.99
REFERENCES107
NON-NEWTONIAN CONSTITUTIVE EQUATIONS USING THE ORIENTATIONAL ORDER PARAMETER108
1. Introduction.108
2. Dynamics of the orientational order parameter tensor.109
3. Stress tensor.111
4. Dynamic stress tensor equation.112
6. Summary.116
REFERENCES116
SURFACE ORDER FORCES IN NEMATIC LIQUID CRYSTALS119
1. Introduction.119
2. Energy and stresses.122
3. Twist cell125
4. Torque and force.129
5. Surface biaxial force.135
6. Conclusion.137
REFERENCES139
MODELLING LINE TENSION IN WETTING141
1. Introduction.141
2. Line tension effects on equilibria.144
3. Modelling surface tension.147
4. Modelling line tension.153
5. Line tension elSects on stability.157
6. Wetting transition.166
7. Dewetting Transition.170
8. Conclusions.172
REFERENCES173
VARIATIONAL PROBLEMS AND MODELING OF FERROELECTRICITY IN CHIRAL SMECTIC C LIQUID CRYSTALS177
1. Introduction.177
2. Free energy functions of smectic materials.179
4. Asymptotic form of the energy minimizers.186
5. Applied constant electric fields and boundary conditions.190
6. Variable electric fields.193
7. Conclusions.194
REFERENCES195
STRIPE-DOMAINS IN NEMATIC ELASTOMERS: OLD AND NEW197
1. Introduction.197
2. A minimalist model.198
3. Stripe - domain patterns: the classics.203
4. Stripe-domain patterns: recent observations.205
5. Conclusions and Outlook.209
REFERENCES210
NUMERICAL SIMULATION FOR THE MESOSCALE DEFORMATION OF DISORDERED REINFORCED ELASTOMERS212
1. Introduction.212
2. Description of the model.214
4. Results.222
5. Conclusion.232
6. Acknowledgments.235
APPENDIX235
REFERENCES238
STRESS TRANSMISSION AND ISOSTATIC STATES OF NON-RIGID PARTICULATE SYSTEMS241
1. Introduction.241
LIST OF WORKSHOP PARTICIPANTS253
IMA SUMMER PROGRAMS257
IMA257
IMA257
258257