© 1993

Fundamentals of Two-Fluid Dynamics

Part II: Lubricated Transport, Drops and Miscible Liquids


Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 4)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 1-16
  3. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 17-113
  4. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 114-225
  5. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 226-287
  6. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 288-323
  7. Daniel D. Joseph, Yuriko Y. Renardy
    Pages 324-395
  8. Back Matter
    Pages 396-445

About this book


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

Authors and affiliations

  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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