Theoretical Evidence for Revision of Fickian First Law and New Understanding of Diffusion Problems
- 1 Department of Applied Mathematics, Faculty of Engineering, Oita University, Oita, Japan
Abstract
Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux | J(t,x,y,z) > in the time and space is incomplete without an integral constant | J 0 (t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by | J 0 (t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.
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