Bubbles, Drops, and Particles in Non-Newtonian Fluids

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Authors
Introduction
1. Non-Newtonian Fluid Behavior
	1.1 Introduction
	1.2 Definition of a Newtonian Fluid
	1.3 Non-Newtonian Fluids
		1.3.1 Time-Independent Fluid Behavior
			1.3.1.1 Shear-Thinning or Pseudoplastic Fluids
			1.3.1.2 Visco-Plastic Fluids
			1.3.1.3 Shear-Thickening Fluids
		1.3.2 Time-Dependent Behavior
			1.3.2.1 Thixotropy
			1.3.2.2 Rheopexy or Negative Thixotropy
		1.3.3 Visco-Elastic Behavior
			1.3.3.1 Normal-Stress Effects in Steady Shearing Flows
			1.3.3.2 Elongational Flow
			1.3.3.3 Small-Amplitude Oscillatory Shearing Motion
			1.3.3.4 Mathematical Models for Visco-Elastic Behavior
	1.4 Dimensional Considerations in the Fluid Mechanics of Visco-Elastic Fluids
	1.5 Experimental Techniques: Rheometry
	1.6 Concluding Remarks
	Nomenclature
	Greek Symbols
	Subscripts
	Superscripts
2. Rigid Particles in Time-Independent Liquids Without a Yield Stress
	2.1 Introduction
	2.2 Governing Equations for a Sphere
	2.3 Spherical Particles in Newtonian Fluids
		2.3.1 Drag Force
		2.3.2 Free-Fall Velocity
		2.3.3 Flow Regimes
		2.3.4 Unsteady Motion
	2.4 Spheres in Shear-Thinning Liquids
		2.4.1 Drag Force
			2.4.1.1 Theoretical Developments in Creeping Flow Region
			2.4.1.2 Experimental Results
			2.4.1.3 Drag Force at High Reynolds Numbers
		2.4.2 Free-Fall Velocity
		2.4.3 Flow Field and Flow Regimes
		2.4.4 Unsteady Motion
		2.4.5 Effect of Imposed Fluid Motion
	2.5 Spheres in Shear-Thickening Liquids
	2.6 Drag on Light Spheres Rising in Pseudoplastic Media
	2.7 Pressure Drop Due to a Settling Sphere
	2.8 Nonspherical Particles
		2.8.1 Introduction
		2.8.2 Drag Force
			2.8.2.1 Newtonian Fluids
			2.8.2.2 Shear-Thinning Liquids
	2.9 Conclusions
	Nomenclature
	Greek Symbols
	Superscript
3. Rigid Particles in Visco-Plastic Liquids
	3.1 Introduction
	3.2 Spheres in Visco-Plastic Liquids
		3.2.1 Static Equilibrium
		3.2.2 Flow Field
		3.2.3 Drag Force
			3.2.3.1 Theoretical Developments
			3.2.3.2 Experimental Drag Correlations
		3.2.4 Values of Yield Stress Used in Correlations
		3.2.5 Time Dependence of Velocity in Visco-Plastic Fluids
	3.3 Flow Past a Circular Cylinder
	3.4 Flow Normal to a Plate
	3.5 Nonspherical Particles
	3.6 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
4. Rigid Particles in Visco-Elastic Fluids
	4.1 Introduction
	4.2 Flow Over a Sphere
		4.2.1 Theoretical Developments
			4.2.1.1 Drag Force on an Unbounded (β = 0) Sphere in Creeping Region (Re → 0)
			4.2.1.2 Drag Force on a Sphere for β = 0.5 and Re → 0: The Benchmark Problem
			4.2.1.3 Wake Phenomenon
		4.2.2 Experimental Results
			4.2.2.1 Shear-Thinning Visco-Elastic Liquids
			4.2.2.2 Nonshear-Thinning Visco-Elastic Liquids (Boger Fluids)
		4.2.3 The Time Effect
		4.2.4 Velocity Overshoot
		4.2.5 Drag-Reducing Fluids
		4.2.6 Sphere in Mixed Flows
	4.3 Flow Over a Long Circular Cylinder
	4.4 Interaction Between Visco-Elasticity, Particle Shape, Multiple Particles, Confining Boundaries, and Imposed Fluid Motion
	4.5 Conclusions
	Nomenclature
	Greek Symbols
5. Fluid Particles in Non-Newtonian Media
	5.1 Introduction
	5.2 Formation of Fluid Particles
		5.2.1 Bubbles
			5.2.1.1 Davidson–Schuler Model
			5.2.1.2 Kumar–Kuloor Model
		5.2.2 Drops
			5.2.2.1 Criterion I: Low-Viscosity Systems
			5.2.2.2 Criterion II: High-Viscosity Systems
		5.2.3 Disintegration (or Breakup) of Jets and Sheets
		5.2.4 Growth or Collapse of Bubbles
	5.3 Shapes of Bubbles and Drops in Free Rise or Fall
		5.3.1 Newtonian Continuous Media
		5.3.2 Non-Newtonian Continuous Media
	5.4 Terminal Velocity–Volume Behavior in Free Motion
	5.5 Drag Behavior of Single Particles
		5.5.1 Theoretical Developments
			5.5.1.1 Newtonian Continuous Phase
			5.5.1.2 Shear-Thinning Continuous Phase
			5.5.1.3 Visco-Elastic Continuous Phase
			5.5.1.4 Non-Newtonian Drops
		5.5.2 Experimental Results
	5.6 Bubble and Drop Ensembles in Free Motion
	5.7 Coalescence of Bubbles and Drops
		5.7.1 Bubble Coalescence
		5.7.2 Drop Coalescence
	5.8 Breakage of Drops
	5.9 Motion and Deformation of Bubbles and Drops in Confined Flows
	5.10 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
6. Non-Newtonian Fluid Flow in Porous Media and Packed Beds
	6.1 Introduction
	6.2 Porous Medium
		6.2.1 Definition of a Porous Medium, its Classification, and Examples
		6.2.2 Description of a Porous Medium
	6.3 Newtonian Liquids
		6.3.1 Flow Regimes
		6.3.2 Pressure Loss–Throughput Relationship
			6.3.2.1 Dimensionless Empirical Correlations
			6.3.2.2 The Conduit or Capillary Models
			6.3.2.3 The Submerged Objects Models or Drag Theories
			6.3.2.4 Use of the Field Equations for Flow Through a Porous Medium
			6.3.2.5 Flow in Periodically Constricted Tubes (PCTs)
			6.3.2.6 Volume Averaging of the Navier–Stokes Equations
		6.3.3 Wall Effects
		6.3.4 Effects of Particle Shape, Particle Roughness, and Size Distribution
		6.3.5 Fibrous Porous Media
		6.3.6 Theoretical Treatments
			6.3.6.1 Flow Parallel to an Array of Rods
			6.3.6.2 Transverse Flow Over an Array of Rods
			6.3.6.3 Creeping Flow Region
			6.3.6.4 Inertial Effects
	6.4 Non-Newtonian Fluids
		6.4.1 Flow Regimes
		6.4.2 Pressure Loss for Generalized Newtonian Fluids
			6.4.2.1 The Capillary Model
			6.4.2.2 Submerged Object Models or Drag Theories
			6.4.2.3 Volume Averaging of Equations
			6.4.2.4 Other Methods
		6.4.3 Visco-Elastic Effects in Porous Media
		6.4.4 Dilute/Semidilute Drag Reducing Polymer Solutions
		6.4.5 Wall Effects
		6.4.6 Effect of Particle Shape and Size Distribution
		6.4.7 Flow in Fibrous Media
			6.4.7.1 Generalized Newtonian Fluids
			6.4.7.2 Visco-Elastic Fluids
		6.4.8 Mixing in Packed Beds
	6.5 Miscellaneous Effects
		6.5.1 Polymer Retention in Porous Media
		6.5.2 Slip Effects
		6.5.3 Flow-Induced Mechanical Degradation of Flexible Molecules in Solutions
	6.6 Two-Phase Gas/Liquid Flow
	6.7 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
	Superscript
7. Fluidization and Hindered Settling
	7.1 Introduction
	7.2 Two-Phase Fluidization
		7.2.1 Minimum Fluidization Velocity
			7.2.1.1 Definition
			7.2.1.2 Prediction of V[sub(mf)]
			7.2.1.3 Non-Newtonian Systems
		7.2.2 Bed Expansion Behavior
			7.2.2.1 Inelastic Non-Newtonian Systems
		7.2.3 Effect of Visco-Elasticity
	7.3 Three-Phase Fluidized Beds
		7.3.1 Introduction
		7.3.2 Minimum Fluidization Velocity
		7.3.3 Bed Expansion Behavior
			7.3.4 Gas Holdup
	7.4 Sedimentation or Hindered Settling
		7.4.1 Non-Newtonian Studies
	7.5 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
8. Heat and Mass Transfer in Particulate Systems: Forced Convection
	8.1 Introduction
	8.2 Boundary Layer Flows
		8.2.1 Plates
		8.2.2 Cylinders
		8.2.3 Spheres
	8.3 Visco-Elastic Effects in Boundary Layers
	8.4 Bubbles
		8.4.1 Large Peclet Number (Pe >> 1)
		8.4.2 Small Peclet Number (Pe <<1)
	8.5 Drops
	8.6 Ensemble of Bubbles and Drops
	8.7 Fixed Beds
	8.8 Liquid–Solid Fluidized Beds
	8.9 Three-Phase Fluidized Bed Systems
	8.10 Heat Transfer From Tube Bundles
	8.11 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
9. Heat and Mass Transfer in Particulate Systems: Free and Mixed Convection
	9.1 Introduction
	9.2 Governing Equations
	9.3 Vertical Plate
		9.3.1 Free Convection
			9.3.1.1 Newtonian Fluids
			9.3.1.2 Power-Law Fluids
			9.3.1.3 Bingham Plastic Fluids
		9.3.2 Mixed Convection
			9.3.2.1 Newtonian Fluids
			9.3.2.2 Power-law Fluids
			9.3.2.3 Visco-plastic Fluids
	9.4 Horizontal Cylinders
		9.4.1 Free Convection
			9.4.1.1 Newtonian Fluids
			9.4.1.2 Power-Law Fluids
			9.4.1.3 Bingham Plastic Fluids
		9.4.2 Mixed Convection
			9.4.2.1 Newtonian Fluids
			9.4.2.2 Power-Law Fluids
			9.4.2.3 Bingham Plastic Fluids
	9.5 Spheres
		9.5.1 Free Convection
			9.5.1.1 Newtonian Fluids
			9.5.1.2 Power-Law Fluids
			9.5.1.3 Bingham Plastic Fluids
		9.5.2 Mixed Convection
			9.5.2.1 Newtonian Fluids
			9.5.2.2 Power-Law Fluids
			9.5.2.3 Bingham Plastic Fluids
	9.6 Visco-Elastic Effects in Boundary Layers
	9.7 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
10. Wall Effects
	10.1 Introduction
	10.2 Definition
	10.3 Rigid Spheres
		10.3.1 Newtonian Fluids
			10.3.1.1 Theoretical Treatments
			10.3.1.2 Experimental Results and Correlations
		10.3.2 Inelastic Non-Newtonian Liquids
			10.3.2.1 Theoretical and Numerical Treatments
			10.3.2.2 Experimental Studies
		10.3.3 Visco-plastic Liquids
		10.3.4 Visco-Elastic Liquids
			10.3.4.1 Boger Fluids
	10.4 Nonspherical Rigid Particles
		10.4.1 Newtonian Liquids
		10.4.2 Inelastic Non-Newtonian Liquids
	10.5 Effect of Blockage on Heat Transfer From a Sphere
	10.6 Drops and Bubbles
		10.6.1 Newtonian Continuous Phase
			10.6.1.1 Low Reynolds Number Regime
			10.6.1.2 High Reynolds Number Regime
		10.6.2 Non-Newtonian Continuous Phase
	10.7 Conclusions
	Nomenclature
	Greek Symbols
	Subscripts
11. Falling Object Rheometry
	11.1 Introduction
	11.2 Falling Ball Method
		11.2.1 Newtonian Fluids
		11.2.2 Non-Newtonian Fluids
			11.2.2.1 Zero-Shear Viscosity
			11.2.2.2 Shear-Dependent Viscosity
			11.2.2.3 Yield Stress
			11.2.2.4 Characteristic Time for Visco-Elastic Fluids
	11.3 Rolling Ball Method
		11.3.1 Newtonian Fluids
		11.3.2 Non-Newtonian Fluids (Shear-Dependent Viscosity)
		11.3.3 Yield Stress
	11.4 Rotating Sphere Viscometer
	11.5 Falling Cylinder Viscometer
		11.5.1 Newtonian Fluids
		11.5.2 Non-Newtonian Fluids
			11.5.2.1 Shear-Dependent Viscosity
			11.5.2.2 Yield Stress
	11.6 Concluding Summary
	Nomenclature
	Greek Symbols
	Subscripts
References
Author Index
Subject Index