Fluid Dynamics of Viscoelastic Liquids

  • Daniel D. Joseph

Part of the Applied Mathematical Sciences book series (AMS, volume 84)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Daniel D. Joseph
    Pages 1-34
  3. Daniel D. Joseph
    Pages 35-43
  4. Daniel D. Joseph
    Pages 44-68
  5. Daniel D. Joseph
    Pages 69-100
  6. Daniel D. Joseph
    Pages 101-126
  7. Daniel D. Joseph
    Pages 127-163
  8. Daniel D. Joseph
    Pages 164-208
  9. Daniel D. Joseph
    Pages 249-272
  10. Daniel D. Joseph
    Pages 273-295
  11. Daniel D. Joseph
    Pages 328-364
  12. Daniel D. Joseph
    Pages 365-409
  13. Daniel D. Joseph
    Pages 421-438
  14. Daniel D. Joseph
    Pages 439-480
  15. Daniel D. Joseph
    Pages 481-538
  16. Daniel D. Joseph
    Pages 539-572
  17. Daniel D. Joseph
    Pages 573-604

About this book

Introduction

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.

Keywords

differential equation dynamics elasticity fluid dynamics partial differential equation

Authors and affiliations

  • Daniel D. Joseph
    • 1
  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4462-2
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8785-8
  • Online ISBN 978-1-4612-4462-2
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book
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