Micropolar Fluids

Micropolar fluids are fluids with microstructure. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the well-established Navier-Stokes model of classical fluids that we shall call ordinary fluids. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. The model of micropolar fluids introduced in [65] by C. A. Eringen is worth studying as a very well balanced one. First, it is a well-founded and significant generalization of the classical Navier-Stokes model, covering, both in theory and applications, many more phenomena than the classical one. Moreover, it is elegant and not too complicated, in other words, man ageable to both mathematicians who study its theory and physicists and engineers who apply it. The main aim of this book is to present the theory of micropolar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micropolar fluids, one in the theory of lubrication and the other in the theory of porous media, as well as several exact solutions of particular problems and a numerical method. We took pains to make the presentation both clear and uniform.

Texte du rabat

Micropolar fluids are fluids with microstructure belonging to a class of fluids with nonsymmetrical stress sensor referred to as polar fluids. Physically, they represent fluids consisting of randomly oriented particles suspended in a viscous medium, and they are important to engineers and scientists working with hydrodynamic-fluid problems and phenomena.

The goal of this volume is to provide a comprehensive exposition of the principles and methods of micropolar fluids for a broad readership in the science and engineering of fluid mechanics. Organized into three parts, the first part of the book presents the basic model of micropolar fluids, with necessary background information. Provided in the second part is a thorough presentation of the analysis of the mathematics of motion of micropolar fluids, with many detailed examples. Some select and important applications in the topics of lubrication theory and porous media are discusssed in the third part.

Topics and Features:

• Comprehensive and unified view of the subject, with clear foundations for the basic model

• Chapter exercises and carefully chosen examples to reinforce the material

• Coverage of numerical algorithm for behavior of micropolar fluids in a bounded domain

• Discussions of exact solutions for microrotation and velocity fields for some classical fluids flows

This study serves as an up-to-date and comprehensive reference for mathematicians, scientists, and engineers. Micropolar Fluids is an essential resource for anyone wishing to understand and needing to use concepts and methods when working with the hydrodynamics of miropolar fluids.

Contenu
I Description of the Model.- 1 Ordinary and Polar Fluids.- II Mathematical Analysis.- 1 Mathematical Preliminaries.- 2 Stationary Problems.- 3 Nonstationary Problems.- III Application.- 1 Selected Applications.- References.