Rosensweig - Ferrohydrodynamics

FERROHYDRODYNAMICS

FERROHYDRODYNAMICS

R. E. Rosensweig

DOVER PUBLICATIONS, INC.

Mineola, New York

Copyright

Copyright 1985 by Cambridge University Press

All rights reserved.

Bibliographical Note

This Dover edition, first published by Dover Publications, Inc., in 2014, is an unabridged republication of Ferrohydrodynamics, published by Dover Publications, Inc., in 1997, which was a slightly corrected edition of the work first published by Cambridge University Press in 1985.

International Standard Book Number

eISBN-13: 978-0-486-78300-0

Manufactured in the United States by Courier Corporation

67834201 2014

www.doverpublications.com

To my wife

RUTH

for her love, devotion, and good spirits

CONTENTS

PREFACE

The forces of ordinary magnetism, transmitted at a distance, are apt to stir wonder in all. Separate curiosity arises concerning the motion and forms of flowing liquid, whether observed in ocean surf or a teacup. Consider then magnetic fluids, in which the features of magnetism and fluid behavior are combined in one medium. These fluids display novel and useful behavior. It is hoped that some of the fascination of such a fluid is expressed in this work.

My initial studies with my colleagues were motivated by engineering endeavors and the hope that adding a magnetic term to the equation of fluid motion would lead to interesting and useful consequences. This hope was quickly substantiated with the realization of a succession of novel equilibrium flows arising in family groups both in theory and in the laboratory. Subsequently, more subtle manifestations of magnetics in fluids made an appearance in the form of striking stability phenomena, some leading to the spontaneous organization of fluid into geometric patterns not seen before. In this context the magnetic surface force density unexpectedly emerges to play a key role. Another broad class of flow phenomena arises as the result of the antisymmetric stress produced by the magnetic body torque present in dynamic flows along with magnetic body force. Interactions in magnetic multiphase flow illustrate the most recent extension of the general principles.

Ferrohydrodynamics is an interdisciplinary topic having inherent interest of a physical and mathematical nature with applications in tribology, separations science, instrumentation, information display, printing, medicine, and other areas. Because practitioners in these pursuits have widely different backgrounds, an effort has been made to produce a work that is sufficiently self-contained to be accessible to , with emphasis on the use of the generalized Bernoulli equation as a unifying concept that is simple to apply yet powerful in the results achieved.

treats the basic instability flows, a more sophisticated topic that repays the effort to understand it. The final chapters broach the more complex topics of flows dominated by asymmetric stress and behavior in magnetic multiphase flow, a topic of developing interest in the processing of chemicals and fossil fuel. In these topics the state of theoretical knowledge is less perfect, and so pains are taken to distinguish those parts of the subject that stand on firm ground from those having a tentative status.

Throughout the work, selected applications of ferrohydrodynamics are discussed, for the most part in places where the subject matter serves to illuminate the theoretical principles and where combined liquid and magnetic behavior is prominent.

The topics of this work were offered in a course presented at the University of Minnesota in 1980, when the author visited as professor in the Department of Chemical Engineering and Materials Science. O. A. Basaran recorded the lectures and assisted in producing bound notes that served as a point of departure for this work. His efforts and contributions are deeply appreciated. I am especially grateful to L. E. Scriven for inviting the visit and encouraging the work as well as for many stimulating discussions, and to H. T. Davis for his support and suggestions. Interactions with M. Zahn of MIT have been unstintingly enthusiastic and productive, and I am appreciative of his reading and commenting on the entire text.

Help in the production of this work has been given through the generosity of my employer Exxon and its Corporate Research organization. The support of F. A. Horowitz has been vital. I thank Carolyn Dupr for her sustained efforts in producing the typed manuscript. It has also been a pleasure to work with the publishers staff and D. Tranah.

Collaboration with many other colleagues over a number of years has been enriching and enjoyable. Most will be identified in this work by citation to their published research. Finally, it is noted that international symposia devoted exclusively to aspects of the subject are being held at three-year intervals. Proceedings of the meetings together with extensive bibliographies of the scientific and patent literature are published as special issues of the Journal of Magnetism and Magnetic Materials (Amsterdam) and provide an important source of recent and archival information.

Ronald E. Rosensweig

INTRODUCTION

Prior to recent years the engineering applications of fluid mechanics were restricted to systems in which electric and magnetic fields play no role. However, the interaction of electromagnetic fields and fluids has been attracting increasing attention with the promise of applications in areas as diverse as controlled nuclear fusion, chemical reactor engineering, medicine, and high-speed silent printing. The study of various field and fluid interactions may be divided into three main categories:

1. electro hydrodynamics (EHD), the branch of fluid mechanics concerned with electric force effects;

2. magnetohydrodynamics (MHD), the study of the interaction between magnetic fields and fluid conductors of electricity; and

3. ferrohydrodynamics (FHD), the subject of this work, which has become of interest owing to the emergence in recent years of magnetic fluids.

1.1 Scope of ferrohydrodynamics

Ferrohydrodynamics deals with the mechanics of fluid motion influenced by strong forces of magnetic polarization. Developing an understanding of the consequences of these forces occupies most of this book. It will be well at the outset to emphasize the difference between ferrohydrodynamics and the relatively better-known discipline of magnetohydrodynamics. In MHD the body force acting on the fluid is the Lorentz force that arises when electric current flows at an angle to the direction of an impressed magnetic field. However, in FHD there need be no electric current flowing in the fluid, and usually there is none. The body force in FHD is due to polarization force, which in turn requires material magnetization in the presence of magnetic field gradients or discontinuities. Likewise, the force interaction arising in EHD is often due to free electric charge acted upon by an electric force field. In comparison, in FHD free electric charge is normally absent, and the analog of electric charge, the monopole, has not been found in nature. An analogy between EHD and FHD arises, however, for charge-free electrically polarizable fluids exposed to a gradient electric field. A major difference from FHD is the magnitude of the effect, which is normally much smaller in the electrically polarizable media. This work is concerned exclusively with FHD; however, the reader interested in EHD or MHD will find excellent starting points in the references cited at the end of this chapter.

Ferrohydrodynamics began to be developed in the early to mid-1960s, motivated initially by the objective of converting heat to work with no mechanical parts. However, as colloidal magnetic fluids (ferrofluids) became available, many other uses of these fascinating liquids were recognized. Many of these ideas are concerned with the remote positioning and control of magnetic fluid using magnetic force fields. An aspect of this behavior is illustrated in the photograph of .