The Moving Boundary Problems.

Abstract

The problem of a phase boundary that moves via diffusion in a binary solid is presented in a tutorial format. Particular attention is given to an internally consistent definition of the reference frames in which diffusive fluxes in each phase, the velocities of the relative motion of phases, and the velocities of phase boundaries can be measured. Suitable boundary conditions for the joining of concentration fields between adjacent phases are formulated by transforming into a reference frame in which the interphase boundary is at rest and then requiring continuity of the fluxes of each diffusing species. This entire formalism is then illustrated via analytical solutions of a number of problems involving planar multiphase diffusion couples and constant interdiffusion coefficients. Analytical solutions are then presented for the motion of non-planar boundaries including the circular cylinder, the sphere, the ellipsoid, and the elliptical paraboloid. It is shown briefly how numerical methods can be used to solve problems that involve more complicated initial conditions, geometries, and variable material parameters.

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1975
Accession Number
ADA013123

Entities

People

  • C. L. Jeanfils
  • R. F. Sekerka
  • R. W. Heckel

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Continuity
  • Diffusion
  • Ellipsoids
  • Geometric Forms
  • Geometry
  • Materials
  • Mathematics
  • Relative Motion

Fields of Study

  • Mathematics

Readers

  • Aerosol Science/Aerosol Physics
  • Calculus or Mathematical Analysis
  • Powder metallurgy of Titanium alloys.