Fluid Dynamics of Viscoelastic Liquids

1. Front Matter

   Pages i-xvii

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2. Models Like Maxwell’s and Boltzmann’s

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   Pages 1-34

3. Models Like Jeffreys’

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   Pages 35-43

4. Equations of Motion

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   Pages 44-68

5. Hadamard Instability and Frozen Coefficients

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   Pages 69-100

6. Characteristics and Classification of Type

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   Pages 101-126

7. Hyperbolicity and Change of Type in Steady Flow

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   Pages 127-163

8. Supercritical Flow Past Bodies

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   Pages 164-208

9. Mach Wedges and Upstream Influence in the Partly Hyperbolic Flow Over a Flat Plate

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   Pages 209-248

10. Hyperbolicity and Change of Type in Sink Flow

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    Pages 249-272

11. Anomalous Elongational Flows and Change of Type

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    Pages 273-295

12. Similarity Solutions that Give Rise to Hyperbolicity and Change of Type in Steady Flows of Viscoelastic Fluids

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    Pages 296-327

13. Poiseuille Flows

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    Pages 328-364

14. Die Swell and Delayed Die Swell

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    Pages 365-409

15. Hyperbolicity and Change of Type in the Flow Between Rotating Cylinders When the Inner Cylinder Is Corrugated

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    Pages 410-420

16. Simple Fluids and Fading Memory

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    Pages 421-438

17. Asymptotic Theories for Simple Fluids

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    Pages 439-480

18. Second Order Fluids

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    Pages 481-538

19. Elasticity and Viscosity of Liquids

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    Pages 539-572

20. Wave Propagation in Linear Viscoelastic Fluids

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    Pages 573-604

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.

• differential equation
• dynamics
• elasticity
• fluid dynamics
• partial differential equation
• fluid- and aerodynamics

• Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

  Daniel D. Joseph

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