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Applied Mathematical Sciences

By: Donald A. Drew, Stephen L. Passman

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Hardcover | 6 November 1998

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Hardcover
324 Pages

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23.39 x 15.6 x 1.91

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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.

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Non-Fiction Engineering & Technology Industrial Chemistry & Manufacturing Technologies Industrial Chemistry Chemical Engineering Mathematics Applied Mathematics Science Physics Classical Mathematics Fluid Mechanics Mechanical Engineering & Materials

List of Figures
Introduction	p. 1
Preliminaries	p. 11
Physical Reality, Corpuscular Models, Continuum Models	p. 13
Classical Continuum Theory	p. 20
Viscous and Inviscid Fluids and Elastic Solids	p. 41
Kinetic Theory	p. 48
Classical Theory of Solutions	p. 59
Continuum Theory	p. 63
Continuum Balance Equations for Multicomponent Fluids	p. 65
Mixture Equations	p. 81
Averaging Theory	p. 85
Introduction	p. 87
Ensemble Averaging	p. 92
Other Averages	p. 105
Averaged Equations	p. 121
Postulational and Averaging Approaches	p. 131
Modeling Multicomponent Flows	p. 135
Introduction	p. 137
Closure Framework	p. 140
Relation of Microstructure to Constitutive Equations	p. 153
Maxwell-Boltzmann Dynamics	p. 193
Interfacial Area	p. 199
Equations of Motion for Dilute Flow	p. 221
Consequences	p. 235
Nature of the Equations	p. 237
Well-Posedness	p. 243
Solutions for Shearing Flows	p. 254
Wave Dynamics	p. 273
References	p. 297
Index	p. 303
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematical Sciences

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Hardcover

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