Microcontinuum Field Theories II: Fluent Media

Abstract

1R40. Microcontinuum Field Theories II: Fluent Media. - AC Eringen (15 Red Tail Dr, Littleton CO 80126-5001). Springer-Verlag, New York. 2001. 340 pp. ISBN 0-387-98969-2. $149.00.Reviewed by ME Ryan (Dept of Chem Eng, SUNY, 505 Furnas Hall, Buffalo NY 14260).The book, Microcontinuum Field Theories II. Fluent Media, is a mathematically-based exposition of the continuum mechanics of structured fluid media, such as anisotropic fluids, liquid crystals, suspensions, etc. Volume II builds upon and extends the theoretical foundation of the subject developed in the first volume, Microcontinuum Field Theories I. Foundations and Solids. The development in Volume II extends the classical field theories of elasticity, fluid dynamics, and electromagnetism to continua constituted of material points or internal structures having directors that may be deformable as well as orientable. The book is largely based on the author’s contribution to the subject over the past few decades. The book is a reference source that assumes the reader has sufficient background in the subject to follow the derivation and application of the field equations to a variety of different situations. The book is intended for research scientists and graduate students in the disciplines of mathematics, physics, engineering, and related fields. This volume comprises nine chapters (Chs 9-17) which can be divided into four parts: I) Theory of micropolar fluids (Chs 9-11), II) Liquid crystals (Chs 12-14), III) Microstretch fluids (Chs 15-16), and IV) Micromorphic fluids (Ch 17). Electromag-netic interactions are also incorporated into the first three parts. Chapter 9 introduces basic measures of strain and rotation, constitutive equations, and the basic field equations. Analyses of pipe flow, flow in an orthogonal rheometer, lubrication in a journal bearing, Stokes flow around a sphere, stagnation flow, thermal instability, and boundary layer flow are provided. Mixed convection in vertical flow and a discussion of turbulence are also provided within the context of micropolar fluid dynamics. Chapter 10 develops the constitutive and field equations of magneto-hydrodynamics. Analyses of channel flow, shear flow, and thermal stability are presented. Chapter 11 addresses anisotropic fluids and suspensions. The basic theory is developed and applied to channel and couette flows.Chapter 12 gives a detailed presentation of the kinematics, balance laws, constitutive equations, and field equations of liquid crystals. The electrodynamics of liquid crystals is presented in Chapter 13. A variety of problems involving liquid crystals are analyzed in Chapter 14 including shear flow and heat conduction in a channel. The kinematics, constitutive equations, and field equations relating to microstretch fluids are provided in Chapter 15. Applications to the theory of acoustic waves in bubbly fluids and blood flow in small arteries are presented. Chapter 16 presents a continuum theory of the electrodynamics of polymeric liquid crystals. The last chapter addresses the subject of micromorphic fluids with applications of the theory to channel flow, the rheological behavior of blood in arteries, and the behavior of deformable suspensions. A few problems are briefly stated at the end of each chapter. A list of references, a subject index, and a list of errata for Volume I are provided at the end of the book. The treatment provided in this monograph will serve as a useful reference for the academician or research scientist interested in the fundamental theoretical development of this subject.