Microhydrodynamics and complex fluids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references (p. 227-230) and index |
| Beschreibung: | XXI, 233 S. Ill., graph. Darst. |
| ISBN: | 9781439881965 1439881960 |
Internformat
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| 020 | |a 1439881960 |c hardcover : alk. paper |9 1-439-88196-0 | ||
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| 100 | 1 | |a Barthès-Biesel, Dominique |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Microhydrodynamics and complex fluids |c Dominique Barthès-Biesel |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2012 | |
| 300 | |a XXI, 233 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 227-230) and index | ||
| 650 | 4 | |a Hydrodynamics | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Complex fluids | |
| 650 | 4 | |a Viscous flow | |
| 650 | 0 | 7 | |a Hydrodynamik |0 (DE-588)4026302-2 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025236610 | ||
Datensatz im Suchindex
| _version_ | 1804149426018582528 |
|---|---|
| adam_text | Contents
List of Figures
ix
List of Tables
xv
Foreword
xvii
About the Author xjx
Symbol Description
xxi
1
Fundamental Principles
1
1.1
Mass Conservation
........................ 1
1.2
Equation of Motion
....................... 2
1.3
Newtonian Fluid
......................... 3
1.4
Navier-Stokes Equations
.................... 4
1.5
Energy Dissipation
....................... 4
1.6
Dimensional Analysis
......................
б
2
General Properties of Stokes Flows
7
2.1
Stationary Stokes Equations
.................. 8
2.1.1
Pressure-Velocity Relation
............... 8
2.1.2
Pressure-Vorticity Relation
............... 9
2.1.3
Boundary Conditions on a Solid Surface
........ 9
2.2
Simple Stokes Flow Problem
.................. 10
2.3
Linearity and Reversibility
...................
И
2.3.1
Linearity Theorem
.................... 11
2.3.2
Reversibility
....................... 12
2.4
Uniqueness
............................ 12
2.4.1
Uniqueness Theorem
................... 12
2.4.2
Demonstration
...................... 12
2.5
Minimum Energy Dissipation
.................. 14
2.5.1
Minimum Energy Theorem
............... 14
2.5.2
Demonstration
...................... 15
2.6
Reciprocal Theorem
....................... 15
2.6.1
Reciprocal Theorem
................... 16
Ш
IV
2.6.2 Demonstration...................... 16
2.6.3
Particular
Cases of the Reciprocal Theorem
...... 17
2.7
Solution in Terms of Harmonic Functions
........... 17
2.8
Problems
............................. 19
2.8.1
Symmetry of Stokes Flow
................ 19
2.8.2
Energy Dissipation Due to the Motion of a Solid Particle
in a Quiescent Fluid
................... 19
2.8.3
Drag on a Particle in a Reservoir
............ 20
3
Two-Dimensional Stokes Flows
21
3.1
Stream Function
......................... 21
3.1.1
Cartesian Coordinates
.................. 21
3.1.2
Cylindrical Coordinates
................. 23
3.2
Two-Dimensional Stokes Momentum Equation
........ 23
3.3
Wedge with a Moving Boundary
................ 24
3.3.1
Velocity Field
....................... 25
3.3.2
Pressure Field
...................... 28
3.3.3
Force on the Scraper
................... 28
3.3.4
Other Wedge Flows with Moving Boundary
...... 29
3.4
Flow in Fixed Wedges
...................... 30
3.4.1
Large Wedge Angle (2a
> 146.3°) ........... 32
3.4.2
Small Wedge Angle (2a
< 146.3°) ........... 34
3.5
Problems
............................. 37
3.5.1
Closing
а
Wedge
..................... 37
3.5.2
Flow in an Unbounded Cavity
............. 38
3.5.3
Flow near a Stagnation Point on a Plane Wall
.... 38
4
Lubrification
Flows
41
4.1
Two-Dimensional Lubrication Flows
.............. 42
4.1.1
Orders of Magnitude and Approximations
....... 42
4.1.2
Velocity Field
....................... 44
4.1.3
Mass Balance
....................... 45
4.1.4
Two-Dimensional Reynolds Equation
.......... 45
4.1.5
Example: Slider Bearing
................. 46
4.2
Three-Dimensional Lubrication Flows
............. 49
4.2.1
Three-Dimensional Reynolds Equation
......... 49
4.2.2
Example: Squeezing a Drop
............... 51
4.3
Flow between Fixed Solid Boundaries
............. 53
4.3.1
Hele-Shaw Flow
..................... 53
4.3.2
Flow in Microfluidic Channels
.............. 55
4.4
Flow in Porous Media
...................... 58
4.4.1
Definition of a Porous Medium
............. 59
4.4.2
Flow in a Porous Medium
................ 60
4.5
Problems
............................. 63
4.5.1
Lubrication Flow in a Journal Bearing
........ 63
4.5.2
Flow in an Ideal Porous Membrane
........... 64
4.5.3
Flow along a Porous Wall
................ 66
4.5.4
Motion of a Cylinder between Two Parallel Walls
... 67
5
Free Surface Films
71
5.1
Interface between Two Immiscible Fluids
........... 72
5.1.1
Geometry of a Free Surface
............... 72
5.1.2
Kinematic Conditions
.................. 73
5.1.3
Dynamic Conditions: Laplace s Law
.......... 73
5.1.4
Air-Liquid Interface
................... 74
5.2
Gravity Spreading of a Fluid on a Horizontal Plane
..... 74
5.2.1
Spreading with No Surface Tension
........... 75
5.2.2
Effect of Surface Tension
................ 78
5.3
Stability of a Film Flowing Down an Inclined Plane
..... 79
5.4
Problems
............................. 82
5.4.1
Gravity Spreading of a Film with Continuous Flux
. . 82
5.4.2
Two-Dimensional Thermocapillary Flow
....... 83
5.4.3
Motion of a Contact Lens on the Eye
......... 84
6
Motion of a Solid Particle in a Fluid
87
6.1
Motion of a Solid Particle in a Quiescent Fluid
........ 88
6.1.1
Resistance and Mobility Tensors
............ 89
6.1.2
Relations between the Resistance and Mobility Tensors
90
6.1.3
Translation without Rotation
.............. 92
6.1.4
Rotation without Translation
.............. 93
6.2 Isotropie
Particles
........................ 93
6.3
Flow around a Translating Sphere
............... 95
6.3.1
Stream Function
..................... 96
6.3.2
Velocity and Vorticity
.................. 98
6.3.3
Force Exerted on the Sphere
.............. 98
6.3.4
Streamline Pattern
.................... 100
6.4
Flow around a Rotating Sphere
................ 101
6.5
Slender Particles
......................... 102
6.5.1
Rod
............................ 102
6.5.2
Helix
............................ 103
6.6
Problems
............................. 105
6.6.1
Sedimentation of a Particle with a Symmetry Plane
. 105
6.6.2
Swimming Motion of Spheres and Bacteria
...... 105
6.6.3
Micro-Organism Propulsion by Means of a Flagellum
. 107
6.6.4
Solid Particle in a General Flow Field
......... 109
VI
7
Flow of Bubbles and Droplets
щ
7.1
Freely Suspended Liquid Drop
................. 112
7.1.1
General Problem Statement
............... 112
7.1.2
Dimensional Analysis
.................. 113
7.2
Translation of a Bubble in a Quiescent Fluid
......... 114
7.2.1
Problem Equations
.................... 114
7.2.2
Solution in Terms of a Stream Function
........ 115
7.2.3
Shape of the Bubble
................... 116
7.3
Translation of a Liquid Drop in a Quiescent Fluid
...... 117
7.3.1
Hadamard-Rybczynski Drag on a Drop
........ 117
7.3.2
Stability of the Stokes Solution
............. 119
7.3.3
Validity Limits of the Stokes Solution
......... 119
7.4
Problems
............................. 122
7.4.1
Thermocapillary Motion of a Gas Bubble
....... 122
7.4.2
Flow in a Droplet Due to an Electric Field
...... 123
8
General Solutions of the Stokes Equations
127
8.1
Flow Due to a Point Force
................... 128
8.1.1
Stokeslet
......................... 128
8.1.1.1
Demonstration
................. 129
8.1.2
Stokeslet Properties
................... 130
8.1.3
Correspondence with the Flow around a Sphere
.... 131
8.1.4
Solutions Derived from a Stokeslet
........... 132
8.2
Irrotationa] Solutions
...................... 134
8.3
Series of Fundamental Solutions: Singularity Method
.... 135
8.3.1
Singularities for External Flows
............. 136
8.3.2
Singularities for Internal Flows
............. 137
8.3.3
Example: Translating Gas Bubble
........... 140
8.3.4
Applications of the Singularity Method
........ 141
8.4
Integral Form of the Stokes Equations
............. 142
8.4.1
Velocity Field in V
.................... 143
8.4.2
Velocity Field on the Boundary &D
........... 144
8.4.2.1
Demonstration
................. 145
8.4.3
Boundary Integral Method
............... 145
8.4.4
Motion of a Solid Particle
................ 146
8.4.5
Applications of the Boundary Integral Method
.... 147
8.5
Problems
.............. ............... 150
8.5.1
Liquid Droplet Translating in a Quiescent Liquid
. . . 150
8.5.2
Solid Sphere Freely Suspended in a Linear Shear Flow
150
8.5.3
Hydrodynamic Interaction between Three Spheres
. . 151
8.5.4
Integral Equation for the Flow around a Solid Particle
153
8.5.5
Integral Equation for the Flow around a Liquid Drop
154
Vil
9
Introduction
to Suspension Mechanics
155
9.1
Homogenisation of a Suspension
................ 156
9.2
Micro-Macro Relationship
................... 157
9.3
Dilute Suspension
........................ 160
9.3.1
Dilute Suspension of Identical Spheres
......... 160
9.3.2
Dilute Suspension of
Anisotropie
Particles
....... 161
9.3.3
Approximation
O(c2)
to the Viscosity of a Suspension
of Spheres
......................... 163
9.4
Highly Concentrated Suspension of Spheres
.......... 165
9.5
Numerical Modelling of a Suspension
............. 166
9.5.1
Global Mobility and Resistance Tensors
........ 167
9.5.2
Application to a Suspension of Spherical Particles
. . 168
9.6
Conclusion
............................ 170
9.7
Problems
............................. 172
9.7.1
Constitutive Law of a Suspension of Spheres
..... 172
9.7.2
Intrinsic Convection in a Suspension
.......... 173
10
0(Re) Correction to Some Stokes Solutions
177
10.1
Translation of a Sphere:
Oseen
Correction
........... 177
10.2
Translation of a Cylinder: Stokes Paradox
........... 180
10.3
Validity Limits of the Stokes Approximation
......... 182
10.4
Problem
............................. 183
10.4.1
Evaluation of the Reynolds Number
.......... 183
11
Non-Newtonian Fluids
185
11.1
Introduction
........................... 186
11.2
Non-Newtonian Fluid Mechanics
................ 187
11.2.1
Equations of Motion
................... 187
11.2.2
Formulation of a Constitutive Law
........... 188
11.2.3
Viscometric Parameters in Simple Shear Flow
..... 190
11.3
Viscous Non-Newtonian Liquid
................. 191
11.3.1
Reiner-Rivlin Fluid
................... 191
11.3.2
Fluid with a Yield Stress
................ 193
11.4
Viscoelastic fluid
......................... 195
11.4.1
Relative Deformation
.................. 195
11.4.2
General Constitutive Law
................ 197
11.5
Linear Viscoelastic Laws
.................... 197
11.5.1
Maxwell Fluid
...................... 197
11.5.2
Generalised Maxwell Fluid
............... 199
11.5.2.1
Proof of Equation
(11.39)........... 200
11.5.3
Linear Viscoelastic Law: Integral Form
........ 201
11.6
Non-Linear Viscoelastic Laws
.................. 202
Vlil
11.6.1
Non-
Linear
Integral
Laws
................ 202
11.6.2
Non-Linear Differential Laws
.............. 203
11.7
Non-Newtonian Flow Examples
................ 204
11.7.1
Stationary 2D Flow between Two Parallel Plates
... 204
11.7.1.1
Example (a): Power Law Fluid
........ 205
11.7.1.2
Example (b): Bingham Fluid
......... 207
11.7.1.3
Example (c): Unknown Constitutive Law
. . 208
11.7.2
Oscillatory Flow of a Viscoelastic Liquid
........ 209
11.8
Conclusion
............................ 211
11.9
Problems
............................. 212
11.9.1
Flow of a Bingham Fluid in a Cylindrical Tube
.... 212
11.9.2
Weissenberg Effect
.................... 213
Appendix A Notations
217
A.I Vectors and Tensors
....................... 217
A.2 Einstein Summation Convention
................ 218
A.3 Integration on a Sphere
..................... 219
Appendix
В
Curvilinear Coordinates
221
B.I Cylindrical Coordinates
..................... 221
B.2 Spherical Coordinates
...................... 224
Bibliography
227
Index
231
Mechanical Engineering
Microhydrodynamics
and Complex Fluids
A self-contained textbook, Microhydrodynamics and Complex
Fluids deals with the main phenomena that occur in slow,
inertialess viscous flows often encountered in various industrial,
biophysical and natural processes. It examines a wide range of
situations, from flows in thin films, porous media and narrow
channels to flows around suspended particles. Each situation is
illustrated with examples that can be solved analytically so that
the main physical phenomena are clear. It also discusses a range
of numerical modelling techniques.
Two chapters deal with the flow of complex fluids, presented
first with the formal analysis developed for the mechanics of
suspensions and then with the phenomenological tools of non-
Newtonian fluid mechanics. All concepts are presented simply,
with no need for complex mathematical tools. End-of-chapter
exercises and exam problems help you test yourself.
Dominique
Barthès-Biesel
has taught this subject for over
15
years and is well known for her contributions to low Reynolds
number hydrodynamics. Building on the basics of continuum
mechanics, this book is ideal for graduate students specializing
in chemical or mechanical engineering, material science,
bioengineering, and physics of condensed matter.
|
| any_adam_object | 1 |
| author | Barthès-Biesel, Dominique |
| author_facet | Barthès-Biesel, Dominique |
| author_role | aut |
| author_sort | Barthès-Biesel, Dominique |
| author_variant | d b b dbb |
| building | Verbundindex |
| bvnumber | BV040383126 |
| callnumber-first | Q - Science |
| callnumber-label | QA911 |
| callnumber-raw | QA911 |
| callnumber-search | QA911 |
| callnumber-sort | QA 3911 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4000 |
| ctrlnum | (OCoLC)812243419 (DE-599)BVBBV040383126 |
| dewey-full | 532/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.5 |
| dewey-search | 532/.5 |
| dewey-sort | 3532 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV040383126 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:22:50Z |
| institution | BVB |
| isbn | 9781439881965 1439881960 |
| language | English |
| lccn | 2012013484 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025236610 |
| oclc_num | 812243419 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XXI, 233 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Barthès-Biesel, Dominique Verfasser aut Microhydrodynamics and complex fluids Dominique Barthès-Biesel Boca Raton [u.a.] CRC Press 2012 XXI, 233 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 227-230) and index Hydrodynamics Fluid dynamics Complex fluids Viscous flow Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Komplexe Flüssigkeit (DE-588)4311495-7 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Komplexe Flüssigkeit (DE-588)4311495-7 s Hydrodynamik (DE-588)4026302-2 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025236610&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025236610&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Barthès-Biesel, Dominique Microhydrodynamics and complex fluids Hydrodynamics Fluid dynamics Complex fluids Viscous flow Hydrodynamik (DE-588)4026302-2 gnd Komplexe Flüssigkeit (DE-588)4311495-7 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4311495-7 (DE-588)4077970-1 |
| title | Microhydrodynamics and complex fluids |
| title_auth | Microhydrodynamics and complex fluids |
| title_exact_search | Microhydrodynamics and complex fluids |
| title_full | Microhydrodynamics and complex fluids Dominique Barthès-Biesel |
| title_fullStr | Microhydrodynamics and complex fluids Dominique Barthès-Biesel |
| title_full_unstemmed | Microhydrodynamics and complex fluids Dominique Barthès-Biesel |
| title_short | Microhydrodynamics and complex fluids |
| title_sort | microhydrodynamics and complex fluids |
| topic | Hydrodynamics Fluid dynamics Complex fluids Viscous flow Hydrodynamik (DE-588)4026302-2 gnd Komplexe Flüssigkeit (DE-588)4311495-7 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Hydrodynamics Fluid dynamics Complex fluids Viscous flow Hydrodynamik Komplexe Flüssigkeit Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025236610&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025236610&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT barthesbieseldominique microhydrodynamicsandcomplexfluids |