Fundamentals of Two-Fluid Dynamics

1. Front Matter

   Pages i-xv

   PDF

2. Introduction to Lubricated Pipelining

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 1-16

3. Lubricated Pipelining: Linear Stability Analysis

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 17-113

4. Core-Annular Flow in Vertical Pipes

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 114-225

5. Nonlinear Stability of Core-Annular Flow

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 226-287

6. Vortex Rings of One Fluid in Another in Free Fall

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 288-323

7. Fluid Dynamics of Two Miscible Liquids with Diffusion and Gradient Stresses

   • Daniel D. Joseph, Yuriko Y. Renardy

   Pages 324-395

8. Back Matter

   Pages 396-445

   PDF

Two-fluid dynamics is a challenging subject rich in physics and prac­ tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu­ ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce­ dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.

• dynamics
• environment
• fluid dynamics
• growth
• iron
• physics
• solution
• stability
• fluid- and aerodynamics

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

  Daniel D. Joseph

• Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

  Yuriko Y. Renardy

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