Book contents
- Frontmatter
- Contents
- List of Figures and Tables
- Preface
- 1 Preliminaries
- 2 Conservation Equations
- 3 Rigid-Particle Heat Transfer at Re ≪ 1
- 4 Translational Motion at Re ≪ 1
- 5 Shape Deformations
- 6 Volume Pulsations
- 7 Thermodynamics of Suspensions
- 8 The Two-Phase Model
- 9 Sound Propagation in Suspensions
- 10 Applications and Extensions
- Appendix A Material and Transport Properties of Some Substances at 1 atm and 20°C
- Appendix B Useful Formulas from Vector Analysis
- Appendix C Explicit Expressions for Some Quantities in Spherical Polar Coordinates
- Appendix D Some Properties of the Spherical Bessel Functions
- Appendix E Legendre Polynomials
- Bibliography
- Author Index
- Subject Index
- Symbol Index
2 - Conservation Equations
Published online by Cambridge University Press: 25 August 2009
- Frontmatter
- Contents
- List of Figures and Tables
- Preface
- 1 Preliminaries
- 2 Conservation Equations
- 3 Rigid-Particle Heat Transfer at Re ≪ 1
- 4 Translational Motion at Re ≪ 1
- 5 Shape Deformations
- 6 Volume Pulsations
- 7 Thermodynamics of Suspensions
- 8 The Two-Phase Model
- 9 Sound Propagation in Suspensions
- 10 Applications and Extensions
- Appendix A Material and Transport Properties of Some Substances at 1 atm and 20°C
- Appendix B Useful Formulas from Vector Analysis
- Appendix C Explicit Expressions for Some Quantities in Spherical Polar Coordinates
- Appendix D Some Properties of the Spherical Bessel Functions
- Appendix E Legendre Polynomials
- Bibliography
- Author Index
- Subject Index
- Symbol Index
Summary
Introduction
We begin our study by considering suspensions so dilute that each particle behaves independently of others. In this situation, the dynamic behavior of a particle is determined by its physical properties and by the pressure, velocity, and temperature fields in the fluid surrounding it. When no particles are present, those fields may be regarded as known. But particles introduce generally unknown disturbances that modify them and that obey the same equations as the main, or background, field. These are the equations of fluid mechanics; they will be needed throughout the book and are presented herein without derivation.
Equations of Motion
The equations of fluid mechanics are based on conservation laws of mass, momentum, and energy – supplemented by an equation of state and by a relation between the stress and the rate of strain. To express these laws mathematically, we will usually use the Eulerian, or field, description, in which the quantities describing the motion of the fluid are specified at a fixed point in space. For example, pf(x, t), uf(x, t), pf(x, t), and Tf(x, t) denote the fluid's density, velocity, pressure, and temperature, respectively, at time t, at a point whose position vector – relative to the origin of a system of coordinates – is x. When necessary, the Lagrangian description will also be used. Here, the conservation equations are written for an element of fluid composed of the same molecules, whose volume, momentum, and energy; but, not its mass, can change as the element moves.
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- Information
- Suspension AcousticsAn Introduction to the Physics of Suspensions, pp. 15 - 36Publisher: Cambridge University PressPrint publication year: 2005