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Applied Mathematical Sciences #176: Falling Liquid Films

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Synopses & Reviews

Publisher Comments:

This monograph provides a detailed review of the state-of-the-art theoretical (analytical and numerical) methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches, and long-wave expansions. Whenever possible, the link between theory and experiments is illustrated and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics. The book will be of particular interest to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program; researchers working on both applied and fundamental theoretical and experimental aspects of thin film flows; and engineers and technologists dealing with processes involving thin films, either isothermal or heated.   Topics covered include: Detailed derivations of governing equations and wall and free-surface boundary conditions for free-surface thin film flows in the presence of thermocapillary Marangoni effect; linear stability including Orr-Sommerfeld, absolute/convective instability and Floquet analysis of periodic waves; strongly nonlinear analysis including construction of bifurcation diagrams of periodic and solitary waves; weakly nonlinear prototypes such as Kuramoto-Sivashinsky equation; validity domain of the long-wave expansions; kinematic/dynamic waves, connection with shallow water and river flows/hydraulic jumps; dynamical systems approach, local and global bifurcations, homoclinicity and conditions for periodic, subsidiary and secondary homoclinic orbits; modulation instability of solitary waves to transverse perturbations; transition to two-dimensional solitary waves and interaction of two-dimensional solitary waves; and substrate heating and competition between solitary waves and rivulet formation in free-surface flows over heated substrates.   Tutorials and details of computational methodologies including computer programs: Solution of the Orr-Sommerfeld eigenvalue problem; computational search via continuation for traveling wave solutions and their bifurcations; computation of systems of nonlinear pde's using finite differences; spectral representation and aliasing.  

Synopsis:

This research monograph gives a detailed review of the state-of-the-art theoretical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate.

Synopsis:

Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.

Synopsis:

Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.

Table of Contents

Preface. -Acknowledgements. -Nomenclature. -Introduction. -Review of Phenomenology. -Modelling: state-of-the-art. -Structure of the book. -1 Flow and heat transfer. -1.1 Governing equations and boundary conditions. -1.2 Dimensionless equations, scalings and parameters. -1.3 The role of the Biot number. -1.4 Salient features. -1.5 References and further reading. -2 Primary instability. -2.1 Linear stability analysis. -2.2 Transverse disturbances. -2.3 Longtitudinal disturbances. -2.4 Mechanism of the hydrodynamic instability. -2.5 Salient features. -2.6 References and further reading. -3 Boundary layer-like approximation. -3.1 Boundary layer equations. -3.2 2D Boundary Layer Equations. -3.3 Strong surface tension limit. -3.4 Shkadov's scaling. -3.5 Reduction of the governing equations. -3.7 Scalings: three sets of parameters. -3.8 Salient features. -3.9 References and further reading. -3.10 Appendix. -4 Methodologies for flows at low Re. -4.1 Long-wave asymptotic expansion. -4.2 Validity domain of the Benney equation. -4.3 Parametic study for closed and open flows. -4.4 Regularization a la Pade. -4.5 Comparison of the different one-equation models. -4.6 Weakly nonlinear models. -4.7 Salient features. -4.8 References and further reading. -4.9 Appendix. -4.10 Physical parameters. -4.11 Small Biot number, analogy with forced convection. -5 Methodologies for moderate Re. -5.1 Averaged two-equation models. -5.2 Relaxing the self-similar assumption. -5.3 Methods of weighted residuals. -5.4 First-order formulation. -5.5 Comparison of methods of weighted residuals. -5.6 Second-order formulation -5.7 Reduction of the full second order model. -5.8 Salient features. -5.9 References and further reading. -6 Isothermal case: 2D flow. -6.1 Linear stability analysis. -6.2 Travelling waves. -6.3 Spatial evolution of 2D waves. -6.4 Salient features. -6.5 References and further reading. -6.6 Appendix. -7 Isothermal case: 3D flow. -7.1 Phenomenology. -7.2 2D modelling of 3D film flows. -7.3 Floquet Analysis: 3D stability of 2D waves. -7.4 2D simulations of 3D flows. -7.5 Salient features. -7.6 References and further reading. -7.7 Appendix. -8 Interaction of 3D solitary waves. -8.1 A model system for low-dimensional complexity. -8.2 Speed of 3D solitary pulses. -8.4 Approximate analytical solution. -8.5 Coherent structures theory. -8.6 Salient features. -8.7 References and further reading. -9 Heated films. -9.1 Formulation. -9.2 Formulation at first order. -9.3 Reduced models. -9.4 Regularized model. -9.5 Linear stability results. -9.6 Solitary waves. -9.7 Refined models. -9.8 Three-dimensional wave patterns. -9.9 Salient features. -9.10 References and further reading. -9.11 Appendix. -10 Reactive falling films. -10.1 Problem definition and governing equations. -10.2 Long-wave theory. -10.3 Kapita-Shkadov model and weighted residuals. -10.4 Salient features. -10.5 References and further reading. -10.6 Appendix. -11 Outlooks. -11.1 What has been offered/achieved. -11.2 Open questions - Suggestions. -11.3 References and further reading. -Conclusions. -Bibliography. -Index. -Summary.

Product Details

ISBN:
9781848823662
Author:
Kalliadasis, S.
Publisher:
Springer
Author:
Scheid, Benoit
Author:
Velarde, M. G.
Author:
Ruyer-Quil, Christian
Author:
Scheid, B.
Author:
Velarde, Manuel G.
Author:
Kalliadasis, Serafim
Author:
Ruyer-Quil, C.
Location:
London
Subject:
Applied
Subject:
Graphic Methods
Subject:
Mathematical Physics
Subject:
Falling Films
Subject:
Interfacial Flows
Subject:
solitary waves
Subject:
Thermocapillary Marangoni Effects
Subject:
Thin films
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Classical Continuum Physics
Subject:
Statistical Physics, Dynamical Systems and Complexity
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Fluid- and Aerodynamics
Subject:
Visualization
Subject:
Theoretical, Mathematical and Computational Physics Easy access to mathematical models of different degrees of complexity, capable of describing, with controllable accuracy, falling liquid films Gives a detailed review of state-of-the-art theoretical, ana
Subject:
Mathematics-Applied
Subject:
Falling Liquid Films
Subject:
Film Flows
Subject:
Heat -- Transfer.
Subject:
Wave Instabilities
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Engineering mathematics
Copyright:
Edition Description:
2012
Series:
Applied Mathematical Sciences
Series Volume:
176
Publication Date:
20110923
Binding:
HARDCOVER
Language:
English
Pages:
500
Dimensions:
235 x 155 mm

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Applied Mathematical Sciences #176: Falling Liquid Films New Hardcover
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Product details 500 pages Springer - English 9781848823662 Reviews:
"Synopsis" by , This research monograph gives a detailed review of the state-of-the-art theoretical methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate.
"Synopsis" by , Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.
"Synopsis" by , Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.
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