Dynamics of Polymeric Liquids, Volume 1 Fluid Mechanics

by Bird, R. Byron; Armstrong, Robert C.; Hassager, Ole

• ISBN13: 9780471802457
• ISBN10: 047180245X
• Edition: 2nd
• Format: Hardcover
• Copyright: 1987-05-27
• Publisher: Wiley-Interscience

Summary

Dynamics of Polymeric Liquids, Second Edition Volume 2: Kinetic Theory R. Byron Bird, Charles F. Curtiss, Robert C. Armstrong and Ole Hassager Volume Two deals with the molecular aspects of polymer rheology and fluid dynamics. It is the only book currently available dealing with kinetic theory and its relation to nonlinear rheological properties. Considerable emphasis is given to the connection between kinetic theory results and experimental data. The second edition contains new material on the basis for molecular modeling, the application of phase-space theory to dilute solutions, kinetic theory of melts and melt mixtures, and network theories. 1987 (0 471-80244-1) 450 pp.

Author Biography

About the authors R. Byron Bird is Vilas Professor of Chemical Engineering at the University of Wisconsin-Madison. He is a coauthor of Dynamics of Polymeric Liquids, 2nd Edition, Volume 2 (Wiley 1987), Molecular Theory of Gases and Liquids, (Wiley, 1954), Transport Phenomena, (Wiley, 1960), and several other books. He received his BS in chemical engineering at the University of Illinois in 1947, and his PhD in physical chemistry at the University of Wisconsin in 1950. Robert C. Armstrong is Associate Professor of Chemical Engineering at the Massachusetts Institute of Technology. He is a coauthor of Dynamics of Polymeric Liquids, 2nd Edition, Volume 2 (Wiley, 1987). He received his BChE at Georgia Institute of Technology in 1970 and his PhD at the University of Wisconsin in 1973. Ole Hassager is Lektor at the Danmarks tekniske Højskole in Lyngby, Denmark. He is a coauthor of Dynamics of Polymeric Liquids, 2nd Edition, Volume 2 (Wiley, 1987). He received his MSc in chemical engineering at the Danmarks tekniske Højskole in 1970 and his PhD in chemical engineering at the University of Wisconsin in 1973.

Table of Contents

Notes on Notation for Volume 1	xix
PART I NEWTONIAN VERSUS NON-NEWTONIAN BEHAVIOR
Review of Newtonian Fluid Dynamics	3	(52)
The Equations of Change in Terms of the Fluxes	3	(7)
The Equations of Change in Terms of the Transport Properties	10	(2)
Proof that Normal Stresses of Incompressible Newtonian Fluids Are Zero at Solid Surfaces	12	(1)
Solutions of Isothermal Flow Problems	12	(10)
Laminar Flow between Parallel Plane Surfaces	13	(1)
Laminar Flow in a Circular Tube	14	(2)
Flow in a Slightly Tapered Tube	16	(2)
The Cone-and-Plate Viscometer	18	(2)
Squeezing Flow between Two Parallel Disks	20	(2)
Solution of Isothermal Flow Problems by Use of the Stream Function	22	(33)
Flow around a Translating Sphere	23	(6)
Flow around a Rising Bubble	29	(2)
Rotating Sphere in a Viscous Liquid	31	(24)
Flow Phenomena in Polymeric Liquids	55	(44)
The Chemical Nature of Polymeric Liquids	56	(4)
Non-Newtonian Viscosity	60	(2)
Normal Stress Effects	62	(7)
Interpretation of Free-Surface Shapes in the Rod-Climbing Experiment	64	(2)
Interpretation of Free-Surface Shapes in the Titled Trough Experiment	66	(3)
Secondary Flows	69	(3)
Other Elastic Effects	72	(11)
Bubbles and Particles	83	(4)
Effects of Polymer Additives in Turbulent Flow	87	(5)
Dimensions Groups in Non-Newtonian Fluid Mechanics	92	(7)
Material Functions for Polymeric Liquids	99	(70)
Shear and Shearfree Flows	100	(3)
The Stress Tensor for Shear and Shearfree Flows	103	(1)
Steady Shear Flow Material Functions	104	(8)
Unsteady Shear Flow Material Functions	112	(20)
Shearfree Flow Material Functions	132	(7)
Useful Correlations for Material Functions	139	(14)
Kinematics and Classification of Shear and Shearfree Flows	153	(16)
Kinematics of Steady to Tube Flow, Steady Tangential Annular Flow, and Steady Helical Flow	160	(2)
Kinematics of Flow into a Line Sink	162	(7)
PART II ELEMENTARY CONSTITUTIVE EQUATIONS AND THEIR USE IN SOLVING FLUID DYNAMICS PROBLEMS
The Generalized Newtonian Fluid	169	(86)
The Generalized Newtonian Fluid and Useful Empiricisms for the Non-Newtonian Viscosity	169	(6)
Isothermal Flow Problems	175	(17)
Flow of a Power-Law Fluid in a Straight Circular Tube and in a Slightly Tapered Tube	175	(4)
Thickness of a Film of Polymer Solution Flowing Down an Inclined Plate	179	(1)
Plane Couette Flow	180	(1)
Axial Annular Flow	181	(3)
Enhancement of Axial Annular Flow by Rotating Inner Cylinder (Helical Flow of a Power-Law Fluid)	184	(3)
Flow Enhancement Produced by a Pulsatile Pressure Drop in a Circular Tube (Quasi-Steady-State Approximation)	187	(2)
Squeezing Flow between Two Parallel Circular Disks (Lubrication Approximation and Quasi-Steady-State Approximation)	189	(3)
Isothermal Flow Problems by the Calculus of Variations and Weighted Residual Methods	192	(13)
Axial Annular Flow of a Power-Law Fluid	202	(2)
Estimation of Velocity Distribution for Axial Eccentric Annular Flow (e.g., in a Wire-Coating Device)	204	(1)
Nonisothermal Flow Problems	205	(22)
Flow in Tubes with Constant Wall Temperature (Asymptotic Solution for Small z)	210	(6)
Flow in Tubes with Constant Wall Temperature (Asymptotic Solution for Large z)	216	(2)
Flow in a Circular Die with Viscous Heating	218	(5)
Viscous Heating in a Cone-and-Plate Viscometer	223	(4)
Other Empirical Non-Newtonian Viscosity Functions for Use in the Generalized Newtonian Fluid Model	227	(6)
Tangential Flow of a Bingham Fluid in an Annulus	228	(3)
An Approximate Solution for Axial Annular Flow to Account for the Zero-Shear-Rate Region of the Non-Newtonian Viscosity	231	(2)
Limitations of Generalized Newtonian Fluid Models and Recommendations for Their Use	233	(22)
The General Linear Viscoelastic Fluid	255	(40)
Newtonian Fluids and Hookean Solids	256	(2)
Linear Viscoelastic Fluids	258	(6)
Linear Viscoelastic Rheological Properties	264	(11)
Small-Amplitude Oscillatory Motion	264	(2)
Stress Relaxation after a Sudden Shearing Displacement	266	(1)
Stress Relaxation after Cessation of Steady Shear Flow	267	(1)
Stress Growth at Inception of Steady Shear Flow	268	(1)
Constrained Recoil after Cessation of Steady Shear Flow	269	(1)
Creep after Imposition of Constant Shear Stress	270	(3)
Determination of the Relaxation Spectrum from Linear Viscoelastic Data	273	(2)
Linear Viscoelastic Flow Problems	275	(7)
Wave Transmission in a Semi-Infinite Viscoelastic Liquid	275	(2)
Motion of a Viscoelastic Fluid Pulsating in a Tube	277	(2)
Analysis of a Torsional Oscillatory Viscometer with Small Slit Width	279	(3)
Limitations of Linear Viscoelasticity and Recommendations for Its Use	282	(13)
Illustrations that the General Linear Viscoelastic Model Is Restricted to Motions with Small Displacement Gradients	283	(12)
PART III NONLINEAR VISCOELASTIC CONSTITUTIVE EQUATIONS AND THEIR USE IN SOLVING FLUID DYNAMICS PROBLEMS
The Retarded-Motion Expansion	295	(46)
Convected Derivatives of the Rate-of-Strain Tensor	296	(2)
The Rate-of-Strain Tensors in Simple Shear Flow	297	(1)
The Retarded-Motion Expansion	298	(6)
Viscometric Functions for the Third-Order Fluid	299	(5)
Useful Theorems for the Second-Order Fluid	304	(7)
Force Exerted on a Solid Surface by a Second-Order Fluid in Steady Plane Flow	307	(2)
Force Exerted on a Solid Surface by a Second-Order Fluid in Steady Rectilinear Flow	309	(2)
Two-Dimensional and Rectilinear Flow Problems for the Second-Order Fluid	311	(5)
Axial Eccentric Annular Flow	311	(3)
Tangential Eccentric Annular Flow (Journal Bearing Flow)	314	(2)
Perturbation Technique for Creeping Flows	316	(9)
Flow Near a Rotating Sphere	318	(3)
Flow Near a Translating Bubble	321	(4)
Limitations of the Retarded-Motion Expansion and Recommendations for Its Use	325	(16)
Differential Constitutive Equations	341	(84)
The Convected Derivative of the Stress Tensor	342	(3)
The Convected Derivative of the Stress Tensor for Simple Shear Flow	343	(1)
Calculation of τ(1) for Flow between Parallel Disks	343	(1)
Evaluation of τ(1) for Steady Shear Flow Plus Superposed Rotation	344	(1)
Quasi-liner Differential Models	345	(5)
Time-Dependent shearing flows of the Convected Jeffreys Model	346	(3)
Time-Dependent Shearfree Flows of the Convected Jeffreys Model	349	(1)
Nonlinear Differential Models	350	(19)
Flow Problems in One Spatial Variable	369	(17)
The Rayleigh Problem for a Convected Jeffreys Fluid	369	(2)
Tube Flow of a White-Metzner Fluid with a Pulsatile Pressure Gradient	371	(6)
Fiber Spinning of a White-Metzner Fluid	377	(9)
Flow Problems in Two or three Spatial Variables	386	(22)
Viscoelastic Flow in a Journal Bearing	387	(13)
Torsional Flow of a Convected Jeffreys Fluid between Parallel Disks	400	(8)
Limitations of Differential Models and Recommendations for Their Use	408	(17)
Single-Integral Constitutive Equations	425	(54)
The Finite Strain Tensors	425	(6)
Evaluation of kinematic Tensors	429	(1)
Evaluation of Strain Tensors for a Steady Shear Flow with a Superposed Rotation	430	(1)
Quasi-linear Integral Models	431	(3)
Simple Shear Flow of the Lodge Rubberlike Liquid	432	(2)
Nonlinear Integral Constitutive Equations	434	(21)
A Nonlinear Single-Integral Constitutive Equation	442	(9)
The Wagner Model	451	(2)
The Doi-Edwards Constitutive Equation	453	(1)
The Approximate Currie Potential for the Doi-Edwards Model	454	(1)
Flow Problems in One Spatial Variable	455	(6)
Flow of a Viscoelastic Fluid into a Line Sink	456	(2)
Transient Inflation of a Spherical Viscoelastic Film	458	(3)
Flow Problems in Two or Three Spatial Variables	461	(5)
The Hole Pressure Effect for Flow Across a Transverse Slot	462	(2)
Flow Around a Rigid Sphere Moving along the Axis of a Cylindrical Tube	464	(2)
Limitations of single-Integral Models and Recommendations for Their Use	466	(13)
PART IV CONTINUUM MECHANICS AND ITS USE IN SOLVING FLUID DYNAMICS PROBLEMS
Continuum-Mechanics Concepts	479	(30)
Oldroyd's Criteria for Admissibility of Constitutive Equations	480	(3)
Convected Coordinates and Convected Base Vectors	483	(5)
Change of Convected Base Vectors with Time	486	(2)
Transformation Rules for the Strain Tensor and Its Time Derivatives	488	(5)
The Relation of the Relative Strain Tensors to the Infinitesimal Strain Tensor	489	(4)
Transformation Rules for the Stress Tensor and Its Time Derivatives	493	(4)
The Integral Form of the Convected Jeffreys Model (Oldroyd-B Model)	496	(1)
Construction of Admissible Constitutive Equations in Terms of Fixed Components	497	(1)
Memory-Integral Expansions	498	(11)
Relation of the Memory-Integral Expansion to the Retarded-Motion Expansion	501	(1)
Development of the Oldroyd 6-Constant Model in Memory-Integral Expansion	502	(1)
The Criminale-Ericksen-Filbey (CEF) Equation and the Reiner-Rivlin Equation	503	(6)
Fluid Dynamics of Rheometry	509	(118)
Linear Viscoelastic Measurements	510	(7)
The Parallel-Disk Viscometer	510	(2)
The Eccentric Rotating Disk Rheometer	512	(5)
Steady-State Shear Flows	517	(12)
Measurement of Viscosity and Normal Stress Coefficients in the Cone-and-Plate Instrument	521	(3)
Measurement of the Viscometric Functions in the Parallel-Disk Instrument	524	(3)
Obtaining the Non-Newtonian Viscosity from the Capillary Rheometer	527	(2)
Shearfree Flows	529	(6)
Complex Flows	535	(20)
Squeezing Flow of Viscoelastic Fluids between Parallel Disks	539	(16)
APPENDICES
Appendix A Vector and Tensor Notation	555	(56)
A.1 Vector Operations from a Geometrical Viewpoint	556	(3)
A.2 Vector Operations from an Analytical Viewpoint	559	(5)
A.3 Tensor Operations	564	(7)
A.4 The Vector and Tensor Differential Operations	571	(5)
A.5 Vector and Tensor Integral Theorems	576	(1)
A.6 Vector and Tensor Algebra in Curvilinear Coordinates	577	(5)
A.7 Differential Operations in Curvilinear Coordinates	582	(15)
A.8 Nonorthogonal Curvilinear Coordinates	597	(10)
A.9 Further Comments on Vector-Tensor Notation	607	(4)
Appendix B Components of the Equation of Motion and Kinematic Tensors	611	(10)
B.1 The Equation of Motion in Terms of τ	612	(1)
B.2 The Equation of Motion for a Newtonian Fluid with Constant Density (ρ) and Constant Viscosity (μ)	613	(1)
B.3 The Rate of Strain Tensor γ=Δv + (Δv)†	614	(1)
B.4 The Vorticity Tensor ω = Δv - (Δv)†	615	(1)
B.5 The Relative Strain Tensor γ[0]	616	(2)
B.6 The Relative Strain Tensor γ[0]	618	(2)
B.7 The Displacement Gradient Tensors Δ and E	620	(1)
Appendix C Equations and Tensors Specialized for Homogeneous Shear and Shearfree Flows	621	(6)
C.1 Continuum-Mechanics Tensors	622	(3)
C.2 Oldroyd 8-Constant and Giesekus Equations (Eqs. 7.3-2 and 4)	625	(2)
Author Index	627	(6)
Subject Index	633