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1748

Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo

Michael Ruzicka

Electrorheological Fluids: Modeling and Mathematical Theory

Springer

Author Michael Rt'lzicka Institute of Applied Mathematics University of Freiburg Eckerstr. I 79104 Freiburg, Germany E-mail: [email protected]

Cataloging-in-Publication Data applied for Die Deutsche Bibliothek· CIP-Einheitsaufnahme RuziCka, Michael: Electrorheological fluids: modeling and mathRematical theory I Michael Ruzicka. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo : Springer, 2000 (Lecture notes in mathematics; 1748) ISBN 3-540-41385-5

Mathematics Subject Classification (2000): 76Axx, 35Q35, 76D03, 35Dxx, 35K55, 35J60, 3502 ISSN 0075-8434 ISBN 3-540-41385-5 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the Wholeor part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer- Verlag. Violations are liable for prosecution under the German Copyright Law. Springer- Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science-Business Media GmbH © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany Typesetting: Camera-ready TEX output by the author SPIN: 10724266 41/3142-543210 - Printed on acid-free paper

MEINEN ELTERN

Introduction Electrorheological fluids are special viscous liquids, that are characterized by their ability to undergo significant changes in their mechanical properties when an electric field is applied. This property can be exploited in technological applications, e.g. actuators, clutches, shock absorbers, and rehabilitation equipment to name a few. Winslow [131] is credited for the first observation of the behaviour of electrorheological fluids in 1949. Since then great strides have been made to overcome the impediments of early electrorheological fluids, as the abrasive nature and the instability of the suspension and the enormous voltage requirements that are necessary for a significant change in the material properties. Nowadays existing electrorheological fluids, which make the above mentioned devices possible, are the result of intensive efforts to manufacture materials without these impediments. In this book we present a theoretical investigation of electrorheological fluids. Firstly, we develop a model for these liquids within the framework of Rational Mechanics, which takes into account the complex interactions between the electro­magnetic fields and the moving liquid. Secondly, we carry out a mathematical analysis of the resulting system of partial differential equations which posse