Free Boundaries in Viscous Flows

1. Front Matter

   Pages i-xv

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2. Mathematical Description of Viscous Free Surface Flows

   • Gerald W. Young

   Pages 1-27

3. Theoretical Issues Arising in the Modeling of Viscous Free-Surface Flows

   • W. G. Pritchard, Patricia Saavedra, L. Ridgway Scott, S. J. Tavener

   Pages 29-48

4. High Order Boundary Integral Methods for Viscous Free Surface Flows

   • J. J. L. Higdon, C. A. Schnepper

   Pages 49-66

5. Long Wave Instability of Viscous Liquid Free Surface Due to Anomalous Marangoni Effect

   • V. V. Pukhnachov

   Pages 67-77

6. Long-Wave Interfacial Instabilities in Viscous Liquid Films

   • Marc K. Smith

   Pages 79-97

7. Convective and Morphological Stability during Directional Solidification of the Succinonitrile-Acetone System

   • S. R. Coriell, B. T. Murray, G. B. McFadden, K. Leonartz

   Pages 99-112

It is increasingly the case that models of natural phenomena and materials processing systems involve viscous flows with free surfaces. These free boundaries are interfaces of the fluid with either second immiscible fluids or else deformable solid boundaries. The deformation can be due to mechanical displacement or as is the case here, due to phase transformation; the solid can melt or freeze. This volume highlights a broad range of subjects on interfacial phenomena. There is an overview of the mathematical description of viscous free-surface flows, a description of the current understanding of mathematical issues that arise in these models and a discussion of high-order-accuracy boundary-integral methods for the solution of viscous free surface flows. There is the mathematical analysis of particular flows: long-wave instabilities in viscous-film flows, analysis of long-wave instabilities leading to Marangoni convection, and de§ scriptions of the interaction of convection with morphological stability during directional solidification. This book is geared toward anyone with an interest in free-boundary problems, from mathematical analysts to material scientists; it will be useful to applied mathematicians, physicists, and engineers alike.

• Mathematica
• convection
• flow
• material
• stability

• Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, USA

  Robert A. Brown

• Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, USA

  Stephen H. Davis

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