Stability and Dynamics of Systems of Interacting Bubbles with Time-delay and Self-action Due to Liquid Compressibility


Book Description

A Hamiltonian model for the radial and translational dynamics of clusters of coupled bubbles in an incompressible liquid developed by Ilinskii, Hamilton, and Zabolotskaya [J. Acoust. Soc. Am. 121, 786-795 (2007)] is extended to included the effects of compressibility in the host liquid. The bubbles are assumed to remain spherical and translation is allowed. The two principal effects of liquid compressibility are time delay in bubble interaction due to the finite sound speed and radiation damping due to energy lost to acoustic radiation. The incorporation of time delays produces a system of delay differential equations of motion instead of the system of ordinary differential equations in models of bubble interaction in an incompressible medium. The form of the Hamiltonian equations of motion is significantly different from the commonly used models based on Rayleigh-Plesset equations for coupled bubble dynamics, and it provides certain advantages in numerical integration of the time-delayed equations of motion. Corrections for radiation damping in clusters of interacting bubbles are developed in the form of a time-delayed expression for bubble self-action following the method of Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837-2841 (1992)]. A set of approximate series expansions of this delayed expression is calculated to first order in the ratio of bubble radius to the characteristic wavelength of acoustic radiation from the bubble, and to varying orders in the ratio of bubble radius to characteristic bubble separation distance. Stability of the delay differential equations of motion is analyzed with four successive levels of approximation for the effects of radiation damping and time delay. The stability is analyzed with and without the effects of viscous and thermal damping. The effect of time delay and radiation damping on the pressure radiated by small systems of bubbles is considered. An approximate method to account for the delays in bubble interaction in a weakly compressible liquid is presented. This method converts the system of delay differential equations into an approximate system of ordinary differential equations, which may simplify numerical integration. Several sets of model equations incorporating propagation time delay in bubble interactions are solved numerically with existing algorithms specialized for delay differential equations. Numerical simulations of the dynamics of single bubbles, pairs of bubbles, and clusters of bubbles are used to compare the different levels of approximation for compressibility effects for low- and high-amplitude radial motion in systems of bubbles under free response and pulsed excitation by an external pressure source.




Bubbles in Polymeric Liquids


Book Description

From the Authors' Preface The advancements of technology . . . and chemical engineering have brought about extensive use of a wide range of rheologically complex materials, e.g., polymeric solutions and melts, suspensions, mixtures, oil products, fibre-forming substances, etc. that are characterized by diverse and, every so often, significant deviations from classical Newtonian behavior. Such materials are often used in conditions where the formation of vapor-gas bubbles or two-phase flow regimes is possible. This necessitates deep investigations into the thermo-hydrodynamic problems of liquids with bubbles for the case of a continuous phase with anomalous rheological properties. These conditions are typical of a number of applications and manufacturing processes, e.g., gas removal from polymeric solutions or melts in production of film, chemical fibres and other polymeric materials. . . . The bubbles containing gas or vapor-gas mixtures are often present in polymeric systems. This is because of a number of reasons, e.g., a low wettability of solid surfaces by polymers, the use of volatile solvents, abundance of vapor-gas nuclei, the capture of gas by porous or fibre-like polymeric particles during the polymer dissolution or melting, etc. Spontaneous evacuation of bubbles in polymeric media is usually complicated by a high viscosity of the liquid; therefore two-phase polymeric systems possess a higher sedimentation and aggregation stability than bubble mixtures in low-molecular-weight liquids. One of the main problems in the dynamics of vapor-liquid and gas-liquid systems is the investigation of heat and mass transfer and phase interactions in a liquid with bubbles. The decisive importance of this problem in the analysis of various aspects of the bubbly fluid behavior under diverse conditions, in particular, during a sound wave propagation, has given impetus to numerous researches. The current state of art in the investigation of Newtonian liquids with bubbles is described in voluminous literature. However, these problems have been much less studied for non-Newtonian systems. Behavior of bubbles in polymeric liquids is of great interest because of wide application in chemical technology. . . . In a number of processes connected with the application of polymeric fluids, the dynamic interaction of bubbles with liquid phase plays the key role. Such interaction in the case of a polymeric liquid phase are essentially influenced by the specific properties of macromolecular fluids, including primarily the rheological effects. These effects in the bubble dynamics combined with heat and mass transfer between the bubble content and the ambient liquid constitute the main subject of the analysis presented in this book. Macrokinetics Laboratory, and Full Professor at the Byelorussian Polytechnic Institute, Department of Heat and Power Engineering. Dr. Schulman is recognized as a leading authority in his field of investigation. Extensive Bibliography: A valuable feature of this new book is its extensive international bibliography, with 393 references.




Bubble Dynamics and Shock Waves


Book Description

This book explores the interplay of bubble dynamics and shock waves, covering shock wave emission by laser generated bubbles, pulsating bubbles near boundaries, interaction of shock waves with bubble clouds, applications in shock wave lithotripsy, and more.




Bubble Dynamics and Interface Phenomena


Book Description

This volume contains papers presented at the IUTAM Symposium on Bubble Dynamics and Interface Phenomena held at the University of Birmingham from 6-9 September 1993. In many respects it follows on a decade later from the very successful IUTAM Symposium held at CALTECH in June 1981 on the Mechanics and physics of bubbles in liquids which was organised by the late Milton Plesset and Leen van Wijngaarden. The intervening period has seen major development with both experiment and theory. On the experimental side there have been ad vances with very high speed photography and data recording that provide detailed information on fluid and interface motion. Major developments in both computer hardware and software have also led to extensive improvement in our understand ing of bubble and interface dynamics although development is still limited by the sheer complexity of the laminar and turbulent flow regimes often associated with bubbly flows. The symposium attracts wide and extensive interest from engineers, physical, chemical, biological and medical scientists and applied mathematicians. The sci entific committee sought to achieve a balance between theory and experiment over a range of fields in bubble dynamics and interface phenomena. It was our intention to emphasise both the breadth and recent developments in these various fields and to encourage cross-fertilisation of ideas on both experimental techniques and theo retical developments. The programme, and the proceedings recorded herein, cover bubble dynamics, sound and wave propagation, bubbles in flow, sonoluminescence, acoustic cavitation, underwater explosions, bursting bubbles and ESWL.







Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions


Book Description

This book is devoted to a fundamental understanding of the fluid dynamic nature of a bubble wake, more specifically the primary wake, in liquids and liquid-solid suspensions, an dto the role it plays in various important flow phenomena of multiphase systems. Examples of these phenomena are liquid/solids mixing, bubble coalescence and disintergration, particle entrainment to the freeboard, and bed contraction.




Mechanics and Physics of Bubbles in Liquids


Book Description

A IUTAM (International Union of Theoretical and Applied Mechanics) Sympo sium 'Mechanics and Physics of Bubbles in Liquids' was held at Pasadena, Calif., USA from 15 through 19 June 1981. The present volume contains the printed version of nearly all papers read at the Symposium. The study of the behaviour of bubbles in liquids was originally stimu lated by problems in cavitation and in boiling ofliquids. Today research is initiated by problems in many other fields as well. In this respect a growing interest from the side of biomechanics may be mentioned. Ordering of the papers could be done either according to the various mechanical and physical aspects of the subject or according to the fields of application. The presentaton at the Symposium contained a bit of both; there was a session on physico-chemical aspects for example and also a session on biological applications. The subdivision in this volume follows roughly the sessions in the Symposium. Most of them start with a paper of a survey nature, reporting progress made in recent years. Here, as in other fields of engineering science, one notes the important part played by experimental techniques and by numerical analysis.







Bubbles, Drops, and Particles


Book Description

This volume offers a unified treatment and critical review of the literature related to the fluid dynamics, heat transfer, and mass transfer of single bubbles, drops, and particles. 1978 edition.




Particles, Bubbles & Drops


Book Description

The field of multiphase flows has grown by leaps and bounds in the last thirty years and is now regarded as a major discipline. Engineering applications, products and processes with particles, bubbles and drops have consistently grown in number and importance. An increasing number of conferences, scientific fora and archived journals are dedicated to the dissemination of information on flow, heat and mass transfer of fluids with particles, bubbles and drops. Numerical computations and "thought experiments" have supplemented most physical experiments and a great deal of the product design and testing processes. The literature on computational fluid dynamics with particles, bubbles and drops has grown at an exponential rate, giving rise to new results, theories and better understanding of the transport processes with particles, bubbles and drops. This book captures and summarizes all these advances in a unified, succinct and pedagogical way. Contents: Fundamental Equations and Characteristics of Particles, Bubbles and Drops; Low Reynolds Number Flows; High Reynolds Number Flows; Non-Spherical Particles, Bubbles and Drops; Effects of Rotation, Shear and Boundaries; Effects of Turbulence; Electro-Kinetic, Thermo-Kinetic and Porosity Effects; Effects of Higher Concentration and Collisions; Molecular and Statistical Modeling; Numerical Methods-CFD. Key Features Summarizes the recent important results in the theory of transport processes of fluids with particles, bubbles and drops Presents the results in a unified and succinct way Contains more than 600 references where an interested reader may find details of the results Makes connections from all theories and results to physical and engineering applications Readership: Researchers, practicing engineers and physicists that deal with any aspects of Multiphase Flows. It will also be of interest to academics and researchers in the general fields of mechanical and chemical engineering.