This page intentionally left blank Theory of Solidification The processes of freezing and melting were present at the beginnings of the Earthandcontinuetoaffectthenaturalandindustrialworlds.Thesolidification ofaliquidorthemeltingofasolidinvolvesacomplexinterplayofmanyphysical effects.Thisbooksystematicallypresentsthefieldofcontinuumsolidification theorybasedoninstabilityphenomena.Anunderstandingofthephysicsisde- velopedbyusingexamplesofincreasingcomplexitywiththeobjectofcreating adeepphysicalinsightapplicabletomorecomplexproblems. Appliedmathematicians,engineers,physicistsandmaterialsscientistswill allfindthisvolumeofinterest. StephenH.DavisisMcCormickProfessorandWalterP.MurphyProfessorof AppliedMathematicsatNorthwesternUniversity. i ii CAMBRIDGEMONOGRAPHSONMECHANICS FOUNDINGEDITOR G.K.Batchelor GENERALEDITORS S.H.Davis McCormickProfessorandWalterP.MurphyProfessor AppliedMathematics NorthwesternUniversity L.B.Freund HenryLedyardGoddardUniversityProfessor DivisionofEngineering BrownUniversity S.Leibovich SibleySchoolofMechanicalandAerospaceEngineering CornellUniversity V.Tvergaard DepartmentofSolidMechanics TheTechnicalUniversityofDenmark iii iv THEORY OF SOLIDIFICATION STEPHEN H. DAVIS NorthwesternUniversity v           The Pitt Building, Trumpington Street, Cambridge, United Kingdom    The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org ©Cambridge University Press 2004 First published in printed format 2001 ISBN 0-511-03696-5 eBook (Adobe Reader) ISBN 0-521-65080-1 hardback Idedicatethisbooktothewonderfulwomeninmylife, mymotherEva and mywifeSuellen vii viii