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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.
The flows of thin film form the core of a large number of scientific, technological, and engineering applications. The occurrence of such flows can be observed in nature, for example on the windshield of vehicles in rainy weather. Thin film flows are also found in various engineering, geophysical, and biophysical ap- plications. Specific examples are nanofluidics, microfluidics, coating flows, intensive processing, tear-film rupture, lava flows, and dynamics of continental ice sheets. Important industrial applications of thin films include nuclear fusion research - for cooling the chamber walls surrounding the plasma, complex coating flows - where a thin film adheres to a moving substrate, distillation units, condensers, and heat exchangers, microfluidics, geophysical settings, such as gravity currents, mud, granular and debris flows, snow avalanches, ice sheet models, lava flows, biological and biophysical scenarios, such as flexible tubes, tear-film flows and many more. The dynamics of such films are quite complex and display rich behavior and this attracted many mathematicians, physicists, and engineers to the field. In the past three decades, the work in the area has progressed a lot with considerable stress on revealing the stability and dynamics of the film where the flow is driven by various forces such as gravity, capillarity, thermocapillarity, centrifugation, and inter- molecular. The flow may happen over structured or smooth and impermeable or slippery surfaces. The investigation approaches include modeling and analytical work, numerical simulations, and performing experiments to explain the instabilities that the film can exhibit. Direct analysis of the equations of the model of the interfacial flows is a very complicated mathematical exercise due to the existence of a free, evolving interface that bounds the liquid film. The mathematical complexity emerges from a number of things: (a) The Navier-Stokes (or Stokes or Euler) equations need to be solved in changing domains; (b) In certain applications one has to solve for the temperature or electrostatic or electromagnetic fields apart from the fluid equations; (c) Several nonlinear boundary conditions should be specified at the unknown interface(s) and (d) The solutions may not exist for all times. In fact in thin film problems, one may encounter finite-time singularities accompanied by topological transitions. The breakup of liquid jets is an example of that. However, in the subsequent chapters, we shall see that it is possible to use the different length scales appearing in thin film flows to our advantage. Thin films are characterized by much smaller length scales in the vertical direction as compared to those in the stream-wise direction. This gives rise to a small aspect ratio which makes the problem amenable for small amplitude perturbation expansions.
The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.
Activity in the arena of surface chemistry and adhesion aspects in cosmetics is substantial, but the information is scattered in many diverse publications media and no book exists which discusses surface chemistry and adhesion in cosmetics in unified manner. This book containing 15 chapters written by eminent researchers from academia and industry is divided into three parts: Part 1: General Topics; Part 2: Surface Chemistry Aspects; and Part 3: Wetting and Adhesion Aspects. The topics covered include: Lip biophysical properties and characterization; use of advanced silicone materials in long-lasting cosmetics; non-aqueous dispersions of acrylate copolymers in lipsticks; cosmetic oils in Lipstick structure; chemical structure of the hair surface, surface forces and interactions; AFM for hair surface characterization; application of AFM in characterizing hair, skin and cosmetic deposition; SIMS as a surface analysis method for hair, skin and cosmetics; surface tensiometry approach to characterize cosmetic products; spreading of hairsprays on hair; color transfer from long-wear face foundation products; interaction of polyelectrolytes and surfactants on hair surfaces; cosmetic adhesion to facial skin; and adhesion aspects in semi-permanent mascara; lipstick adhesion measurement.
It is increasingly the case that models of natural phenomena and materials processing systems involve viscous flows with free surfaces. These free boundaries are interfaces of the fluid with either second immiscible fluids or else deformable solid boundaries. The deformation can be due to mechanical displacement or as is the case here, due to phase transformation; the solid can melt or freeze. This volume highlights a broad range of subjects on interfacial phenomena. There is an overview of the mathematical description of viscous free-surface flows, a description of the current understanding of mathematical issues that arise in these models and a discussion of high-order-accuracy boundary-integral methods for the solution of viscous free surface flows. There is the mathematical analysis of particular flows: long-wave instabilities in viscous-film flows, analysis of long-wave instabilities leading to Marangoni convection, and de§ scriptions of the interaction of convection with morphological stability during directional solidification. This book is geared toward anyone with an interest in free-boundary problems, from mathematical analysts to material scientists; it will be useful to applied mathematicians, physicists, and engineers alike.
Advanced Transport Phenomena is ideal as a graduate textbook. It contains a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems, focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory. Also covered are unidirectional flows, lubrication and thin-film theory, creeping flows, boundary layer theory, and convective heat and mass transport at high and low Reynolds numbers. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain solutions that are due either to geometric simplifications, or large or small values of dimensionless parameters. The author emphasizes setting up problems and extracting as much information as possible short of obtaining detailed solutions of differential equations. The book also focuses on the solutions of representative problems. This reflects the book's goal of teaching readers to think about the solution of transport problems.
Specifically focusing on fluid film, hydrodynamic, and elastohydrodynamic lubrication, this edition studies the most important principles of fluid film lubrication for the correct design of bearings, gears, and rolling operations, and for the prevention of friction and wear in engineering designs. It explains various theories, procedures, and equations for improved solutions to machining challenges. Providing more than 1120 display equations and an introductory section in each chapter, Fundamentals of Fluid Film Lubrication, Second Edition facilitates the analysis of any machine element that uses fluid film lubrication and strengthens understanding of critical design concepts.
A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.
Annular Two-Phase Flow presents the wide range of industrial applications of annular two-phase flow regimes. This book discusses the fluid dynamics and heat transfer aspects of the flow pattern. Organized into 12 chapters, this book begins with an overview of the classification of the various types of interface distribution observed in practice. This text then examines the various regimes of two-phase flow with emphasis on the regions of occurrence of the annular flow regime. Other chapters consider the single momentum and energy balances, which illustrate the differences and analogies between single- and two-phase flows. This book discusses as well the simple modes for annular flow with consideration to the calculation of the profile of shear stress in the liquid film. The final chapter deals with the techniques that are developed for the measurement of flow pattern, entrainment, and film thickness. This book is a valuable resource for chemical engineers.