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MECHANICS AND PHYSICS OF POROUS SOLIDS
MECHANICS AND PHYSICS OF POROUS SOLIDS Olivier Coussy Laboratoire Central des Ponts et Chauss´ees Ecole des Ponts ParisTech Universit´e Paris-Est http://navier.enpc.fr/˜ coussy/
A John Wiley and Sons, Ltd., Publication
This edition first published 2010 C 2010 John Wiley & Sons, Ltd Registered Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Coussy, Olivier. Mechanics and physics of porous solids / Olivier Coussy. p. cm. Includes bibliographical references and index. ISBN 978-0-470-72135-3 (cloth) 1. Porous materials. I. Title. TA418.9.P6C683 2010 2009049316 620.1 16–dc22
A catalogue record for this book is available from the British Library. ISBN: 978-0-47072135-3 (Hbk) Typeset in 10/12pt Times by Aptara Inc., New Delhi, India Printed in Singapore by Markono Print Media Pte Ltd
To my wife Sandra for putting up with it
Contents Preface
xiii
1
The Strange World of Porous Solids
2 2.1
Fluid Mixtures Chemical Potential 2.1.1 Free energy and chemical potential 2.1.2 Equilibrium of mixture composition Gibbs–Duhem Equation 2.2.1 Derivation of the Gibbs–Duhem equation 2.2.2 Molar Gibbs–Duhem equation 2.2.3 Ideal gases 2.2.4 Real gases 2.2.5 Partial molar property Ideal Mixtures 2.3.1 Ideal gas mixture 2.3.2 Ideal mixture definition 2.3.3 Entropy of mixing 2.3.4 Ideal solution – Raoult’s law 2.3.5 Dilute ideal solution – Henry’s law 2.3.6 Osmotic pressure 2.3.7 Electrostatics and excess of osmotic pressure 2.3.8 Reactive ideal mixture 2.3.9 Unconditional stability of ideal solutions Regular Solutions 2.4.1 Regular solutions and the interaction between molecules 2.4.2 Conditional stability of regular solutions Further Reading
11 11 11 13 13 13 14 15 16 16 17 17 19 19 21 21 23 25 32 34 36
The Deformable Porous Solid Strain 3.1.1 Deformation gradient and displacement
41 42 42
2.2
2.3
2.4
3 3.1
1
36 37 40
viii
3.2
3.3
3.4
4 4.1
4.2
4.3
4.4
5 5.1
5.2
5.3
Contents
3.1.2 Strain tensor Stress 3.2.1 The hypothesis of local contact forces 3.2.2 The action–reaction law 3