Theory of Multicomponent Fluids

✍ Scribed by Donald A. Drew, Stephen L. Passman (auth.)

• Publisher: Springer-Verlag New York
• Year: 1999
• Tongue: English
• Leaves: 311
• Series: Applied Mathematical Sciences 135
• Edition: 1
• Category: Library

✦ Synopsis

In this book, we give a rational treatment of multicomponent materials as intera- ingcontinua.Weoffertwoderivationsoftheequationsofmotionfortheinteracting continua; one which uses the concepts of continua for the components, and one which applies an averaging operation to the continuum equations for each c- ponent. Arguments are given for constitutive equations appropriate for dispersed multicomponent ?ow. The forms of the constitutive equations are derived from the principles of continuum mechanics applied to the components and their int- actions. The solutions of problems of hydromechanics of ordinary continua are used as motivation for the forms of certain constitutive equations in multicom- nent materials. The balance of the book is devoted to the study of problems of hydrodynamics of multicomponent ?ows. Many materials are homogeneous in the sense that each part of the material has the same response to a given set of stimuli as all of the other parts. An example of such a material is pure water. Formulation of equations describing the behavior of homogeneous materials is well understood, and is described in numerous standard textbooks. Many other materials, both manufactured and occurring in nature, are not - mogeneous. Such materials are often given names such as mixtures or composites.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-9
Front Matter....Pages 11-11
Physical Reality, Corpuscular Models, Continuum Models....Pages 13-19
Classical Continuum Theory....Pages 20-40
Viscous and Inviscid Fluids and Elastic Solids....Pages 41-47
Kinetic Theory....Pages 48-58
Classical Theory of Solutions....Pages 59-61
Front Matter....Pages 63-63
Continuum Balance Equations for Multicomponent Fluids....Pages 65-80
Mixture Equations....Pages 81-84
Front Matter....Pages 85-85
Introduction....Pages 87-91
Ensemble Averaging....Pages 92-104
Other Averages....Pages 105-120
Averaged Equations....Pages 121-130
Postulational and Averaging Approaches....Pages 131-134
Front Matter....Pages 135-135
Introduction....Pages 137-139
Closure Framework....Pages 140-152
Relation of Microstructure to Constitutive Equations....Pages 153-192
Maxwell—Boltzmann Dynamics....Pages 193-198
Interfacial Area....Pages 199-220
Equations of Motion for Dilute Flow....Pages 221-233
Front Matter....Pages 235-235
Nature of the Equations....Pages 237-242
Front Matter....Pages 235-235
Well-Posedness....Pages 243-253
Solutions for Shearing Flows....Pages 254-272
Wave Dynamics....Pages 273-296
Back Matter....Pages 297-310

✦ Subjects

Mathematics, general