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Mathematical Description of Viscous Free Surface Flows

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Free Boundaries in Viscous Flows

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 61))

Abstract

Mathematical formulations for three distinct systems which involve viscous free surface flows are presented. The first model describes boundary conditions posed at a moving contact line formed at the tri-junction of a gas/liquid/solid system. In particular the unification of mass flux conditions is highlighted. The second and third models are solidification systems. Formulations of both models examine the use of asymptotic methods to isolate a mathematical description of the free solidifying surface. In one case evolution equations for solidifying fronts are developed. These equations allow one to investigate micro scale morphology of the interface. In the other model, the influence of macroscopic heat, mass, and momentum transport on the solidifying front is examined. A reduced model is developed which is simpler for analysis yet retains the relevant physics.

This work is supported by NSF Grant DMS-89-57534 and by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Akron, Akron, Ohio, 44325-4002, USA

    Gerald W. Young

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  1. Gerald W. Young
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Room 66-353, Cambridge, MA, 02139, USA

    Robert A. Brown

  2. Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Stephen H. Davis

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© 1994 Springer-Verlag New York, Inc.

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Young, G.W. (1994). Mathematical Description of Viscous Free Surface Flows. In: Brown, R.A., Davis, S.H. (eds) Free Boundaries in Viscous Flows. The IMA Volumes in Mathematics and its Applications, vol 61. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8413-7_1

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  • DOI: https://doi.org/10.1007/978-1-4613-8413-7_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8415-1

  • Online ISBN: 978-1-4613-8413-7

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