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On effective diffusivity of periodic non‐homogeneous solid media
Author(s) -
Mishin Yu. M.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221740204
Subject(s) - thermal diffusivity , homogeneous , diffusion , simple (philosophy) , periodic boundary conditions , boundary (topology) , mathematical analysis , boundary value problem , statistical physics , mathematics , physics , thermodynamics , philosophy , epistemology
Diffusion in a non‐homogeneous medium with periodic spatial variations of diffusivity and driving force is analyzed in detail. After a time t ≪ τ (τ being time to attain local quasi‐stationarity) diffusion proceeds like in a homogeneous medium with an effective diffusivity D̃ ij . Correct procedure of D̃ ij calculation includes solution of a stationary diffusion problem in a periodic unit cell with special boundary conditions. Methods of exact calculation and estimation of D̃ ij are discussed, some simple estimates are presented. Possible applications of the theory are sketched.