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Theoretical Evidence for Revision of fickian First Law and New Understanding of Diffusion Problems

Journal of Modern Physics 2012年第10期3卷 1388-1393页

作者： Takahisa Okino Department of Applied Mathematics Faculty of Engineering Oita University Oita Japan

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 |J0(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 |J0(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.

关键词： Diffusion Equation fickian First Law Kirkendall Effect

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Transitions between Single-File and fickian Self-Diffusion for Fluids Confined in Carbon Nanotubes,Bundles and Activated Carbons

Transitions between Single-File and Fickian Self-Diffusion f...

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第十届全国计算(机)化学学术会议

作者： Joshua D.Moore Jeremy Palmer Keith E.Gubbins Department of Chemical ＆ Biomolecular Engineering and Center for High Performance Simulation（CHiPS） North Carolina State UniversityRaleighNC 27695-7905 U.S.A

＜正＞Carbon nanotubes are important building blocks for nanocomposite materials and nanomachinery due to their unique physical properties（electronic,optical,thermal,mechanical, etc.） and have received extensive interest in materials science.One possible application is the use of carbon nanotubes as host structures for gas separation as they yield faster diffusion rates of fluid molecules than other widely used materials（e.g.,zeolites）.Several diffusion mechanisms are possible in narrow cylindrical pores,but these are still poorly understood.Among the most important are ballistic motion,fickian diffusion,and single-file diffusion.Ballistic motion occurs for very short times,before the molecule has had a chance to collide with anything. For longer times the motion becomes either fickian or single-file.If the pore is large enough, the molecules will diffuse in 3-dimensions as they would in a bulk fluid（fickian diffusion）,but if the pore diameter becomes small enough the diffusion will crossover from fickian to single-file diffusion,where the molecules can no longer pass each other.Clearly single-file motion is much slower than fickian,which is much slower than ballistic.

关键词： single-file fickian carbon nanotubes bundle diffusion mechanism bimodal diffusion

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Ending of Darken Equation and Intrinsic Diffusion Concept

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Journal of Modern Physics 2013年第11期4卷 1495-1498页

作者： Takahisa Okino Department of Applied Mathematics Faculty of Engineering Oita University Oita Japan

The well-known Darken equation has been widely accepted in analyzing interdiffusion problems since 1948. The diffusion researchers have never conceived a doubt about the validity of Darken equation for such a long time. However, it is revealed that the Darken equation is inconsistent with the fundamental theory in mathematics. At the same time, it is clarified that the well-known intrinsic diffusion concept is an illusion. The present brief report will have a great influence on matters of the research and education relevant to diffusion problems not only in future but also in past, since the accumulated diffusivity data analyzed by the invalid Darken theory and the misjudged descriptions in existing text books should be revised or deleted as soon as possible.

关键词： Darken Equation Kirkendall Effect Intrinsic Diffusion fickian First Law

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