V. Alexiades - UTK and ORNL
Phase Change Processes
The primary focus of my research has been on phase-change processes, in particular melting and solidification, for pure materials and for multicomponent mixtures (alloys).

This is an area of great technological importance in many fields, including

  • materials science ( crystal growth, casting of metals / ceramics / polymers, laser ablation, welding, ... )
  • geology ( volcanic systems, crustal magmas, ore deposits )
  • energy( latent heat thermal energy storage,   gas hydrates )
  • environmental sciences ( freezing of soil, in situ vitrification )
  • food processing ( food freezing/thawing )
  • cryobiology ( tissue freezing/thawing ).

    Such processes are modeled by nonlinear (systems of) partial differential equations. The characteristic feature is the presense of unknown boundaries (separating the phases) which evolve in time, whence they belong to the class of moving boundary problems. The prototype of such problems is the Stefan Problem.

    The objective is to predict the evolution of the phases and of the strongly and nonlinearly coupled temperature, concentration and/or velocity fields.

    The numerical simulations are computationally intensive and parallel computation (using message passing) is often necessary.

    My favored approach is to formulate the problems globally as systems of conservation laws valid in a mathematically weak sense throughout the material (irrespectively of phase), together with appropriate equations of state expressing the thermochemistry of the phases. With such formulations, it becomes possible to numerically simulate the entire process effectively.

    For more information, see the book

    Vasilios Alexiades and Alan D. Solomon
    Mathematical Modeling of Melting and Freezing Processes
    Hemisphere Publ. Co., Washington DC, 1993
    323 pages; Hardcover; ISBN 1-56032-125-3 ; QC303.A38 1993

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