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Über dieses Buch

Fluid flows that transfer heat and mass often involve drops and bubbles, particularly if there are changes of phase in the fluid in the formation or condensation of steam, for example. Such flows pose problems for the chemical and mechanical engineer significantly different from those posed by single-phase flows. This book reviews the current state of the field and will serve as a reference for researchers, engineers, teachers, and students concerned with transport phenomena. It begins with a review of the basics of fluid flow and a discussion of the shapes and sizes of fluid particles and the factors that determine these. The discussion then turns to flows at low Reynolds numbers, including effects due to phase changes or to large radial inertia. Flows at intermediate and high Reynolds numbers are treated from a numerical perspective, with reference to experimental results. The next chapter considers the effects of solid walls on fluid particles, treating both the statics and dynamics of the particle-wall interaction and the effects of phase changes at a solid wall. This is followed by a discussion of the formation and breakup of drops and bubbles, both with and without phase changes. The last two chapters discuss compound drops and bubbles, primarily in three-phase systems, and special topics, such as transport in an electric field.

Inhaltsverzeichnis

Frontmatter

1. Fundamental Principles and Definitions

Abstract
Drops and bubbles exist in a large number of natural as well as man-made systems. In nearly every situation, these fluid particles, which may lie within a continuum of another fluid, or another state of the same fluid, have an important bearing on the physical behavior of the system. For example, clouds are natural assemblages of tiny water droplets which coalesce due to changes in the atmosphere and lead to rainfall or other forms of precipitation. Natural water systems such as lakes and oceans contain air in dissolved form as well as bubbles, and make up a component that is essential to marine life. On the other hand, with industrial systems, such as some nuclear power plants, one encounters bubbles in a boiling water reactor and drops in spray cooling components. In chemical reactors, drops and bubbles commonly occur as carriers of both reactants and products. Internal combustion engines and jet engines utilize sprays of atomized liquid hydrocarbons as fuel. With most of these systems, important physical phenomena arise through the transport of heat and/or mass which may be accompanied by fluid motion which generally serves to enhance the transport. In cases involving phase change, fluid motion may be additionally generated by the transfer process. With most processes involving drops and bubbles, there is relative motion between particles, as well as between the fluid particles and the surrounding medium. In this book, transfer processes associated with drops and bubbles under various physical circumstances will be discussed.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

2. Shape and Size of Fluid Particles

Abstract
The shape and size of a fluid particle (a bubble or a drop) significantly affects its motion as well as the associated heat and mass transfer processes. The drag force depends on the particle shape and it is one of the factors that determines the magnitude of the fluid velocity. The transport depends strongly on the interfacial area which is a function of the size and shape of the particle, as well as the overall fluid motion. At the interface between a particle and the ambient fluid, for particle stability, a balance between the normal force, the shear force, gravity, and the surface tension force must be maintained. This balance governs the shape of the particle. The size would also be influenced, particularly if there is phase change.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

3. Transport at Low Reynolds Numbers

Abstract
As discussed in Chapter 1, fluid dynamics at low Reynolds numbers refers to what is commonly known as creeping flow to chemical engineers, and physically corresponds to motion with little or no inertia. Such motion generally arises in systems involving fluids with high viscosity or interacting particles of small dimension. The inertia in a system can be weak, also due to low fluid density or slow fluid motion. The net effect of these parameters is grouped into a Reynolds number. The magnitude of this quantity is in some sense a measure of the relative importance of the inertia of a given system. This is evident from the behavior of the equations of motion discussed in Chapter 1 on pages 5–6. The earliest work in the regime of noninertial flows appears to be that by Stokes [164] who obtained an expression for the drag force on a solid sphere translating in a viscous fluid. This fundamental solution naturally brought about the problems pertaining to fluid spheres, as well as solid particles of other shapes. The parameter of interest usually has been the drag force on a particle undergoing pure translation in a fluid. The behavior of the flow field arising from such motion has also been of interest. The classical development subsequent to Stokes’ [164] was the solution of the slow motion of a fluid sphere given by Rybczynski [143] and independently by Hadamard [69].
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

4. Transport at Intermediate and High Reynolds Numbers

Abstract
Highly accurate closed-form analytical and perturbation solutions for flow description and transport are available for many low Reynolds number (creeping flow) situations where the nonlinear inertial effects are weak. However, fluid motion and transport at intermediate Reynolds numbers [Re ~ O(1) — O(100)] or even higher values are much more complicated. For example, at higher values of the translational Reynolds number, the external flow may separate as it moves toward the rear of the particle and the internal motion may also consist of secondary vortices. Under such circumstances, various transport mechanisms are set into play and the accurate determination of the magnitude of transport becomes a challenging task. Numerical and experimental studies with a drop have shown that at higher values of the Reynolds number, a recirculatory wake is formed with dimensions that are comparable to the drop size [62,63,87]. In such cases, wake effects may have to be taken into account to ascertain accurately the magnitude of transport quantities. It is well acknowledged that both analytical modeling and numerical evaluations of wake effects are in general difficult due to their elliptic nature. In such situations, we rely on semianalytical or fully numerical solutions to the governing equations. With sophisticated numerical methods and super-computers, it is possible to develop sufficiently accurate and physically realizable solutions to problems in the intermediate and high Reynolds number flow regimes.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

5. Wall Interactions

Abstract
The interaction of drops and bubbles with solid walls affects their motion and the general dynamic behavior. Since the infinite continuous phase is an approximation for a large container, or otherwise distant boundaries, many situations would call for the understanding of the fluid mechanics along with the heat and mass transfer associated with drops and bubbles near boundaries. In particular, the presence of solid boundaries requires serious consideration. Some common examples are the problems associated with dispersed flow in tubes, or interaction of sprays with solid materials. Wall effects in heat transfer are especially important because in many instances the wall is the heat source or the heat sink. The thermal behavior, to a large extent, depends on the fluid flow. There are instances, however, that are weakly dependent on the fluid flow, such as in dropwise condensation. We will first discuss the fluid mechanics concerning the interaction of drops and bubbles with solid walls. Fluid particles near, as well as in contact with, walls are considered in this discussion. The coverage is to the extent of direct application to convective transport of energy or solute. While topics such as cavitation and boiling are discussed briefly, some other areas such as bubble motion in tubes have not been considered. Topics dealing with pure fluid mechanics with inconsequential or undeveloped heat or mass transfer results are not included.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

6. Transport with a Spectrum of Fluid Particles

Abstract
In this chapter, we discuss fluid mechanics and direct-contact transport processes with a swarm of bubbles or drops. The transport processes may involve exchange between streams which are of identical media or of different ones. The treatment of the multiple particle problem is in general very difficult. Interactions between fluid particles are difficult to describe accurately and the evaluation of the associated transport is challenging. However, with meaningful approximations, suitable models with a wide range of applicability can be constructed. Here, the salient features of some of these models and the corresponding results developed are discussed. At the outset, a brief discussion of the particle size and velocity distributions is provided.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

7. Formation and Breakup of Bubbles and Drops

Abstract
In this chapter we are concerned with the mechanisms and the underlying physics of the formation and breakup of bubbles and drops. The mechanisms for formation and breakup (or collapse) are fundamentally different depending on whether the processes involve phase change or not. In this context, we will discuss many processes which do not involve phase transitions, and two important processes which do involve phase change — bubble nucleation and droplet nucleation. Studies of formation and breakup are relevant to many important engineering applications. Most direct-contact heat and/or mass exchange equipment employ bubbles or drops in a suitable environment in order to enhance the rate of transport between the phases. The nucleation process for bubbles or droplets has to be understood to gain insight into boiling or condensation phenomena.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

8. Compound Drops and Bubbles

Abstract
The term compound drops generally refers to fluid particles which consist of at least two phases in yet another distinct continuous phase. Therefore, there are at least three well-defined phases is such a system. Compound drops and bubbles exist in three fundamental forms: a fluid particle entirely within another drop, a fluid particle attached to drop, or two separate fluid particles. The distinction whether a particle is a compound drop or a compound bubble may not be obvious in some cases, especially if the dispersed phase is partially liquid and partially gas. This situation occurs when there is direct-contact heat exchange between two immiscible liquids and the resulting dispersed phase consists of the liquid and the vapor together in the form of compound drops. The fluid dynamics and the heat transfer processes associated with a compound fluid-particle systems are, in general, very complicated and most of the analytical developments are relatively recent. Although the pioneering experimental studies of Sideman & Taitel [90] go back some 30 years, much of the subsequent experimental work has been carried during in the past 15 years.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

9. Special Topics

Abstract
The special topics considered in this chapter are concerned with: (i) transport in the presence of an electric field; (ii) transport with a slurry fuel droplet; and (iii) thermocapillary phenomena and transport under conditions of microgravity. An attempt has been made to succinctly discuss the special features that arise in consideration of these topics, and in this context, very recent studies in the published literature have been critically examined.
S. S. Sadhal, P. S. Ayyaswamy, J. N. Chung

Backmatter

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