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9780387954806

Interfacial Instabilities

by ;
  • ISBN13:

    9780387954806

  • ISBN10:

    0387954805

  • Format: Hardcover
  • Copyright: 2002-10-01
  • Publisher: Springer Verlag
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Summary

This book presents a set of essays on interfacial instability, essays on such topics as jets, solidification and melting, precipitation, and electrodeposition. The book deals with the linear theory; as a result, pencil and paper suffice to work through the material. The first two essays provide the necessary background: the first is an introduction to jets; the second explains how to solve a problem in interfacial instability, where the boundary separating two phases can be displaced. The authors approach interfacial instabilities through their physical origins. These lie in the effect of surface displacements on gradients of pressure, temperature, and composition and on whether or not a perturbed gradient reinforces the displacement causing the perturbation. Intended for graduate students, the discussions are not mathematically demanding, but they do rely on an understanding of fluid flow, heat conduction, and diffusion. Students will find that the book deepens their understanding of problems in which deflecting surfaces are important; instructors will find in the essays useful material to enrich their lectures. Contents: - Domain and Surface Perturbations - Applications to the Stefan Problems - Jets and Bridges - Spinning Jets - Rayleigh-Taylor and Saffman-Taylor Problems - Solidification and Precipitation - Electrodeposition

Table of Contents

Preface: A Guide for the Reader vii
The Stability of Liquid Jets by Rayleigh's Work Principle
1(15)
The Stability of Liquid Jets
1(6)
The Physics of the Instability
2(1)
Rayleigh's Work Principle
3(4)
The Stability of Liquid Bridges
7(1)
Some Unanswered Questions and the Direction Our Work Will Take
8(2)
Discussion Notes
10(6)
The Displacement r = R + εf(z)
10(3)
The Annular Jet
13(3)
An Explanation of the Basic Formulas Required to Carry Out the Work of the Remaining Essays
16(43)
Introduction and Plan
16(4)
The Expansion of a Domain Variable and Its Derivatives Along the Mapping
20(7)
The Equations Satisfied by u0,u1,u2, etc. on the Reference Domain and at Its Boundary
27(7)
The Rule
31(1)
Equations at the Boundary
32(2)
How to Determine u(x, y, ε)
34(4)
Endnotes
38(9)
Vector Formulas
38(4)
The Expansion of Integrals Along the Mapping
42(2)
Expanding the Normal Velocity of a Fluid at a Moving Surface
44(3)
Discussion Notes
47(12)
A Justification of the Rule
47(9)
A Justification of the Rule Under a Little More General Mapping
56(3)
The Stability of a Liquid Jet by a Perturbation Calculation
59(24)
The Nonlinear Equations
59(3)
The Perturbation Equations
62(5)
The Equations on the Reference Domain
63(1)
The Equations on the Boundary of the Reference Domain
64(3)
The Stability of Liquid Jets
67(6)
Discussion Notes
73(10)
The Effect of Streaming on the Stability of a Liquid Jet
73(5)
The Two-Fluid Jet
78(5)
The Stability of a Liquid Bridge Lying Between Two Plane Walls
83(31)
The End Conditions
83(4)
The Fixed-Volume Requirement
87(1)
What Can Be Said Short of Solving the Perturbation Problem?
87(2)
The Solution to the Perturbation Equations
89(8)
Free-Free End Conditions
90(5)
Other End Conditions
95(2)
The Critical Length of a Bridge
97(4)
Free-Free End Conditions
98(1)
Free-Fixed End Conditions
98(1)
Fixed-Fixed End Conditions
99(2)
Rough Estimates of σ2
101(5)
The Case m = 0
101(3)
The Case m = 1
104(2)
What Can Be Said About Viscosity?
106(8)
The Stability of a Spinning Jet in Rigid Rotation
114(25)
The Physics of the Instability
114(1)
The Nonlinear Equations
115(2)
The Perturbation Equations
117(2)
The Critical Condition
119(1)
An Integral Formula for σ2
120(8)
Endnote
128(4)
The Stability of Circular Couette Flow Confined by Two Rigid Walls
128(4)
Discussion Notes
132(7)
Rayleigh's Work Principle
132(4)
The Case Where m Is Not Zero
136(3)
The Stability of a Heavy Fluid Lying over a Light Fluid: The Rayleigh-Taylor Instability
139(49)
Rayleigh's Work Principle
142(2)
The Nonlinear Equations
144(2)
The Perturbation Equations
146(2)
The Solution to the Perturbation Equations
148(5)
The Critical Condition
151(1)
The Dispersion Formula: ε2 versus k2
152(1)
An Observation Made
153(1)
G.I. Taylor
The Stability of an Advancing Interface: The Saffman-Taylor Problem
154(9)
Discussion Notes
163(25)
The Energy Associated with the Motion of a Fluid
163(3)
Other End Conditions: Rough Estimates of σ
166(5)
The Fixed-Volume Requirement
171(4)
The Effect of Viscosity
175(5)
The Three-Dimensional Case
180(3)
What Rayleigh's Work Principle Tells Us About Three Fluid Layers
183(2)
The Loss of Stability When an Oscillation Is Imposed on Two Fluids: A Light Fluid Lying Above a Heavy Fluid
185(3)
Solidification
188(39)
The Physics of the Instability
190(4)
Solidification: Rejecting the Latent Heat to the Solid
194(8)
The Nonlinear Equations
194(2)
The Base Solution
196(2)
The Perturbation Equations
198(4)
Solidification: Rejecting the Latent Heat to the Liquid
202(6)
Solidification and Melting: Is It Important to Account for the Change in the Latent Heat as a Solidification Front Is Displaced?
208(9)
The Nonlinear Equations
210(1)
The Base Solution
210(2)
The Perturbation Problem and Its Solution
212(5)
Endnotes
217(5)
A Few Equilibrium Formulas
217(2)
Equations Holding Across Phase Boundaries
219(3)
Discussion Note
222(5)
Solidification, Heat Rejected to the Liquid, Two Special Cases: Equilibrium and k2 = 0
222(5)
Precipitation
227(17)
The Physics of the Instability
228(3)
The Nonlinear Equations
231(1)
The Base Solution
232(1)
The Perturbation Problem and Its Solution
233(9)
Endnote
242(2)
The Solubility of a Solid
242(2)
Electrodeposition
244(51)
The Physics of the Instability
247(2)
The Electron Transfer Reaction
249(3)
The Nonlinear Equations
252(2)
The Nonlinear Equations Simplified by Local Electroneutrality
254(3)
The Base Solution
257(4)
The Perturbation Problem
261(6)
The Total Current Drawn by the Cell
263(2)
The Perturbation Equations at Fixed Values of L0, c and Vc
265(2)
The Stability of the Equilibrium Base Solution
267(7)
The Stability when Current Passes Through the Cell
274(10)
The Case Where U Is Near Ulim
280(1)
The Case Where U Is Near Zero
280(4)
Endnotes
284(4)
Putting the Butler-Volmer Equation into a Little More Useful Form
284(2)
The Perturbation Equations at the Boundary of the Reference Domain
286(2)
Discussion Notes
288(7)
The Special Case k2 Equal to Zero
288(1)
Uniform Solution Density and Local Electrical Neutrality
289(3)
Limitations on the Admissible Class of Perturbations
292(3)
The Last Word
295(2)
A The Application of the Expansion Formulas of the Second Essay to Some Physical Problems 297(30)
The Shape of the Surface of a Spinning Beaker
297(9)
The Position of a Melting Front
306(7)
Carrying the Melting Front Forward in Time
313(7)
Laminar Flow Through an Off-centered Annulus
320(7)
B The Curvature of Surfaces 327(13)
Background
327(4)
Curvature
331(3)
Some Examples
334(6)
The Normal Speed of a Surface 340(3)
Index 343

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