Establishment of New Fundamental Theory in Diffusion Phenomena

Takahisa Okino

doi:10.5539/apr.v11n1p82

Abstract

Investigating the elementary process of diffusion revealed that the De Broglie hypothesis is really valid in a material and further that the Schr&ouml;dinger equation is reasonably derived from the diffusion equation. The diffusion equation is thus one of the fundamental equations in physics. The problem between a moving coordinate system and a fixed coordinate system for the diffusion equation had never been discussed until recently in the history of diffusion theory. In that situation, it is revealed that investigating the problem between those coordinate systems is indispensable for understanding the diffusion phenomena. The new findings obtained here, which are revolutionary in the existing diffusion theory, will be not only dominant but also indispensable for further advance in the diffusion study.

Highlights

The solutions of thermal conduction equation proposed by Fourier show that the temperature distribution in a material satisfies the parabolic law (Fourier, 1822)
Based on the fact that the concentration distribution of micro particles resulting from the diffusion experiments satisfies the parabolic law, Fick proposed that the Fourier’s thermal conduction equation is applicable to diffusion phenomena as it is (Fick, 1855)
Under the condition of nonexistence of the sink and source relevant to micro particles concerned, the diffusion flux JF and diffusion equation given by JF = −D ∇ C (t, r )

Summary

Introduction

The solutions of thermal conduction equation proposed by Fourier show that the temperature distribution in a material satisfies the parabolic law (Fourier, 1822). Under the condition of nonexistence of the sink and source relevant to micro particles concerned, the diffusion flux JF and diffusion equation given by JF = −D ∇ C (t, r ) The elementary process of diffusion and the coordinate transformation of diffusion equation were investigated and some dominant findings were obtained (Okino, 2011, 2013, 2015, 2018).

Results

Conclusion