Mechanics and Mathematics of Fluids of the Differential Type
This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book. Each part of the book can be considered as being self-contained. The first part
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D. Cioranescu V. Girault K.R. Rajagopal
Mechanics and Mathematics of Fluids of the Differential Type
Advances in Mechanics and Mathematics Volume 35
Series Editors: David Y. Gao, Virginia Polytechnic Institute and State University Tudor Ratiu, École Polytechnique Fédérale Advisory Board: Ivar Ekeland, University of British Columbia Tim Healey, Cornell University Kumbakonam Rajagopal, Texas A&M University David J. Steigmann, University of California, Berkeley
More information about this series at http://www.springer.com/series/5613
D. Cioranescu V. Girault K.R. Rajagopal •
Mechanics and Mathematics of Fluids of the Differential Type
123
D. Cioranescu Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Paris 06 Paris France
K.R. Rajagopal Department of Mechanical Engineering Texas A&M University College Station, TX USA
V. Girault Laboratoire Jacques-Louis Lions Université Pierre et Marie Curie Paris 06 Paris France
ISSN 1571-8689 ISSN 1876-9896 (electronic) Advances in Mechanics and Mathematics ISBN 978-3-319-39329-2 ISBN 978-3-319-39330-8 (eBook) DOI 10.1007/978-3-319-39330-8 Library of Congress Control Number: 2016940108 Mathematics Subject Classification (2010): 35A01, 35A02, 35A15, 35A16, 35A23, 35B35, 35B45, 35D30, 35G60, 35Q30, 35Q35, 35R45, 76A05, 76A10, 76E30 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Non-Newtonian Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Shear-Thinning and Shear-Thickening . . . . . . . . . . 2.2.2 Thixotropy . . .
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