Continuum mechanics of viscoelastic liquids

THE PURPOSE OF THIS BOOK IS TO ENABLE A DEEPER UNDERSTANDING TO BE OBTAINED OF THE PHENOMENA INVOLVED IN THE FLOW OF LIQUIDS AND, IN PARTICULAR, OF THE FLOW OF NON-NEWTONIAN LIQUIDS, BY THE APPLICATION OF NON-LINEAR CONTINUUM MECHANICS TO THE STUDY OF THIS SUBJECT.THE SUBJECT MATTER WILL BE OF INTEREST TO RESEARCH WORKERS IN THIS FIELD, TO THOSE ENGAGED IN RHEOLOGY AND ALSO TO ENGINEERS WHO BECOME INVOLVED IN THE MORE COMPLEX PROBLEMS OF FLUID HANDLING.IT MUST BE STRESSED, HOWEVER, THAT OF NECESSITY THE TREATMENT IS HIGHLY MATHEMATICAL IN CHARACTER AND A GOOD KNOWLEDGE OF THIS DISCIPLINE IS THEREFORE NECESSARY -TENSOR CALCULUS, LINEAR VECTOR AND MATRIX ALGEBRA AND SO ON.THE TEXT IS BASED ON THE CONCEPT OF A SIMPLE LIQUID, AND THE FIRST TWO CHAPTERS ARE DEVOTED TO A STUDY OF THE STRAIN HISTORY WHICH HAS BEEN EXPERIENCED BY A LIQUID PARTICLE.THE BASIC THEORY IS GIVEN, TOGETHER WITH THE METHOD OF CARRYING OUT THE CALCULATIONS.THE FIRST CHAPTER CONCLUDES WITH AN APENDIX ON SOME BASIC RESULTS OF TENSOR ANALYSIS, AND THE SECOND CHAPTER, WITH AN APPENDIX ON NOLL'S PROOF OF HIS THEOREM ON MOTIONS WITH A CONSTANT STRETCH HISTORY.CHAPTER THREE INTRODUCES THE CONCEPT OF OBSERVER TRANSFORMATIONS - THE COMPONENTS OF THE VARIOUS KINEMATIC AND STRAIN CONDITIONS AS THEY ARE SEEN BY A SECOND OBSERVER IN RELATIVE MOTION TO THE FIRST.IT ALSO DEALS WITH TWO THEOREMS ON STEADY MOTION, AND THE CONCEPT OF SYMMETRY THROUGH CHANGE IN SECONDS LOCAL CONFIGURATIONSECONDS .CHAPTER FOUR DISCUSSES EQUATIONS FOR THE CONS ERVATION OF MASS, BALANCED LINEAR AND ANGULAR MOMENTA, AND BALANCE OF ENERGY.EQUATIONS OF STATE FOR SIMPLE FLUIDS, I.E.INCOMPRESSIBLE LIQUIDS, ARE CONSIDERED IN CHAPTER FIVE, WHICH ALSO INCLUDES AN APPENDIX ON THE FORMULATION OF THREE EQUATIONS, WHILE CHAPTER SIX IS CONCERNED WITH ISOTROPY AND EQUATIONS OF MOTION FOR NON-STEADY HELICAL FLOW, PARALLEL PLATE SYSTEM (TORSIONAL) FLOW, AND CONE-AND-PLATE FLOW, WITH AN APPENDIXLISTING EQUATIONS OF MOTION IN CURVILINEAR CO-ORDINATES AND ACCELERATION FIELDS.THE DATA IN THIS CHAPTER ARE EXPLAINED IN CHAPTER SEVEN TO DEAL WITH VISCOUS FLOWS, PIPE FLOWS, AND OTHER MOTIONS WITH ACOUSTIC STRETCH HISTORY - AN APPENDIX CONSIDERS THE REINER-RIVLIN PARADOX APPROXIMATE EQUATIONS OF STATE (CONSTITUTIVE EQUATIONS) ARE INTENDED TO DEAL WITH A WIDE CLASS OF STRAIN HISTORIES IN CHAPTER EIGHT, CONSIDERATION BEING GIVEN TO INTEGRAL MODELS, THE BERNSTEIN-KEARSLEY-ZAPAS THEORY, ETC.THIS CHAPTER CONCLUDES WITH AN APPENDIX ON INSTABILITY, UNIQUENESS AND NON-EXISTENCE OF SOLUTIONS TO FLOWS OF SECOND-ORDER FLUIDS.CHAPTER NINE IS CONCERNED WITH NEARLY VISCOMETRIC-FLOWS WHILE CHAPTER TWN DEALS WITH PERTERBATIONS ABOUT A REST STATE AND INCLUDES FLOWS OVER AND ALONG SLOTS, THROUGH TROUGHS, ETC.THE FINAL CHAPTER DESCRIBES THE THEORETICAL BASIS FOR THE TECHNIQUES USED TO MEASURE VISCOSITY, NORMAL STRESS DIFFERENCIES, VISCOELASTIC FLOW OF JETS, AND SO ON.AREAS ARE DEFINED WHERE NEW TECHNIQUES ARE REQUIRED AND SOME EXPERIMENTAL RESULTS ARE GIVEN.REFERENCES TO THE BIBLIOGRAPHY, IN DATE ORDER, ARE GIVEN THROUGHOUT THE BOOK, AND THERE IS A COMPREHENSIVE LIST OF SYMBOLS.(A.L.)