Bubbles, Drops, and Particles

R. Clift, J. R. Grace, M. E. Weber

• Publisher: Dover Publications
• Year: 2013
• ISBN:
  9780486317748
• Topic: Technology & Engineering
• Subtopic: Applied Sciences
• Index: Technology & Engineering

This volume offers a critical review of the literature concerning the fluid dynamics, heat transfer, and mass transfer of single bubbles, drops, and particles. Upper-level undergraduates and graduate students, as well as professionals in the fields of engineering, physics, chemistry, geophysics, and applied mathematics, will find it a unified treatment of solid particles, liquid drops, and gas bubbles.
Starting with a summary of the fundamental principles and equations governing the behavior of bubbles, drops, and solid particles in Newtonian fluids, the text proceeds to a survey of the parameters used to characterize the shape of rigid particles, and of the factors that determine the shape of bubbles and drops. Succeeding chapters examine the behavior of solid and fluid particles under steady incompressible flow in an extended external phase. The text concludes with an exploration of effects that complicate the relatively simple case of a particle moving steadily through an unbounded fluid.

Chapter 1

Basic Principles

I. INTRODUCTION AND TERMINOLOGY

Bubbles, drops, and particles are ubiquitous. They are of fundamental importance in many natural physical processes and in a host of industrial and man-related activities. Rainfall, air pollution, boiling, flotation, fermentation, liquid-liquid extraction, and spray drying are only a few of the phenomena and operations in which particles play a primary role. Meteorologists and geophysicists study the behavior of raindrops and hailstones, and of solid particles transported by rivers. Applied mathematicians and applied physicists have long been concerned with fundamental aspects of fluid-particle interactions. Chemical and metallurgical engineers rely on bubbles and drops for such operations as distillation, absorption, flotation, and spray drying, while using solid particles as catalysts or chemical reactants. Mechanical engineers have studied droplet behavior in connection with combustion operations, and bubbles in electromachining and boiling. In all these phenomena and processes, there is relative motion between bubbles, drops, or particles on the one hand, and surrounding fluid on the other. In many cases, transfer of mass and/or heat is also of importance. Interactions between particles and fluids form the subject of this book.

Before turning to the principles involved, the reader should be aware of certain terminology which is basic to understanding the material presented in later chapters. Science is full of words which have very different connotations in the jargon of different disciplines. The present book is about particles and the term particle needs to be defined carefully within our context, to distinguish it from the way in which the nuclear physicist, for example, might use the word. For our purposes a “particle” is a self-contained body with maximum dimension between about 0.5 µm and 10 cm, separated from the surrounding medium by a recognizable interface. The material forming the particle will be termed the “dispersed phase.” We refer to particles whose dispersed phases are composed of solid matter as “solid particles.” If the dispersed phase is in the liquid state, the particle is called a “drop.” The term “droplet” is often used to refer to small drops. The dispersed phase liquid is taken to be Newtonian. If the dispersed phase is a gas, the particle is referred to as a bubble. Together, drops and bubbles comprise “fluid particles.” Following common usage, we use “continuous phase” to refer to the medium surrounding the particles. In this book we consider only cases in which the continuous phase is a Newtonian fluid (liquid or gas). In subsequent chapters we distinguish properties of the dispersed (or particle) phase by a subscript ρ from properties of the continuous phase which are unsubscripted. Occasionally the dispersed and continuous phases are referred to as the “inner” and “outer” phases, respectively.

Another distinction we use throughout the book is between rigid, non-circulating, and circulating particles. “Rigid particles,” comprising most solid particles, can withstand large normal and shearing stresses without appreciable deformation or flow. “Noncirculating fluid particles” are those in which there is no internal motion relative to a coordinate system fixed to the particle. “Circulating particles” contain fluid which has motion of its own relative to any fixed coordinate system. We consider only cases in which the dispersed phase is continuous. Hence the scale of the particle must be large compared to the scale of molecular processes in the dispersed phase.

In this book we consider as particles only those bodies which are biologically inert and which are not self-propelling. To give some specific examples, raindrops, hailstones, river-borne gravel, and pockets of gas formed by cavitation or electrolysis are all considered to be particles. However, insects and microorganisms are excluded by their life, weather balloons and neutrons by their size, homogeneous vortices by the lack of a clearly defined interface, and rockets and airplanes by their self-propelling nature and size. Our attention is concentrated on particles which are free to move through the continuous phase under the action of some body force such as gravity. Thus heat exchanger tubes, for example, are not considered—not only because of their size but also because they are fixed in position. Some elements of our definitions are of necessity arbitrary. For example, a golf ball satisfies our definition of a particle while a football does not. In most cases, there is little ambiguity, however, so long as these general guidelines regarding terminology are borne in mind.

Other terms which can be defined quantitatively are introduced in the following sections. Some other terms, such as “turbulence,” “viscosity,” and “diffusivity” are used without definition. For a full explanation of these terms, we refer the reader to standard texts in fluid mechanics, heat transfer, and mass transfer.

II. THEORETICAL BASIS

The fundamental physical laws governing motion of and transfer to particles immersed in fluids a...