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Contributed papers presented at a seminar held during September 1-4, 2006.
The work considers some free surface problems and attempts to understand the intrinsic complex behavior of waves in thin films down an inclined plane or vertical wall. The viscous Newtonian thin film or non-Newtonian inelastic power-law film or viscoelastic film down an inclined plane or vertical wall is considered and dynamics of waves and stability characteristics of thin film flow systems are analyzed. The investigations are based on the derivation of an amplitude equation of Landau-Stuart type for the evolution of waves for isothermal or non-isothermal films valid in the neighborhood of a neutral curve or on the use of modern bifurcation techniques of dynamical systems theory together with direct numerical integration to construct weakly nonlinear permanent waves on Newtonian / viscoelastic films for moderate to high Reynolds numbers and small to moderate surface tension effects. The work also considers the development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field with or without induced air shear effects. The entire work is divided into seven chapters.
Wave evolution on a falling film is a classical hydrodynamic instability whose rich wave dynamics have been carefully recorded in the last fifty years. Such waves are known to profoundly affect the mass and heat transfer of multi-phase industrial units. This book describes the collective effort of both authors and their students in constructing a comprehensive theory to describe the complex wave evolution from nearly harmonic waves at the inlet to complex spatio-temporal patterns involving solitary waves downstream. The mathematical theory represents a significant breakthrough from classical linear stability theories, which can only describe the inlet harmonic waves and also extends classical soliton theory for integrable systems to real solitrary wave dynamics with dissipation. One unique feature of falling-film solitary wave dynamics, which drives much of the spatio-temporal wave evolution, is the irreversible coalescence of such localized wave structures. It represents the first full description of a hydrodynamic instability from inception to developed chaos. This approach should prove useful for other complex hydrodynamic instabilities and would allow industrial engineers to better design their multi-phase apparati by exploiting the deciphered wave dynamics. This publication gives a comprehensive review of all experimental records and existing theories and significantly advances state of the art on the subject and are complimented by complex and attractive graphics from computational fluid mechanics.
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. 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 experiment 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 basic, underlying physics. This monograph will appeal 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. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.
Providing a comprehensive introduction with the necessary background material to make it accessible for a wide scientific audience, Kinetics of Phase Transitions discusses developments in domain-growth kinetics. This book combines pedagogical chapters from leading experts in this area and focuses on incorporating various experimentally releva
One half of this book focuses on the techniques of scientific computing: domain decomposition, the absorption of boundary conditions and one-way operators, convergence analysis of multi-grid methods and other multi-grid techniques, dynamical systems, and matrix analysis. The remainder of the book is concerned with combining techniques with concrete applications: stochastic differential equations, image processing, and thin films."
Wave Propagation in Gas-Liquid Media (translated from the Russian 2nd Edition, published in 1990) presents the fundamentals of wave dynamics of two-phase gas-liquid systems. The study of multiphase systems is of growing importance in mechanics and thermophysics, particularly for applications in industrial, energy, power, chemical, and aerospace engineering. This book presents investigations of non-linear wave dynamics, as well as practical applications of wave motion. A system of non-stationary gas-dynamics to replace studies of conventional gas-dynamics is constructed by the book's contributors. Topics discussed include acoustics and shock waves in homogenous gas- and vapor-liquid mixtures, dynamics of gas and vapor bubbles, wave processes in gas-liquid systems, wave propagation in a liquid with vapor bubbles, wave processes on the interface of two media, wave flow of liquid films, and basic calculation formulas for wave dynamics of gas- and vapor-liquid media. The book will be a useful reference for thermophysicists, mechanical engineers, and aerospace engineers.
The book covers selected problems in free surface flows. The topics range from linear and nonlinear gravity and capillary waves, thin film dynamics, equilibrium shape, stability, and dynamics of capillary surfaces to thermal Marangoni effects in several geometries. The fluid dynamical problems are supplemented by a review Eulerian based computational methods.