The Diffusion Coefficient D, for the regular diffusion of a particle in 1 dimension, is defined as
D=sigma2/(2(delta t)), where sigma2 is the standard deviation squared of the particle's position, that takes place in the time interval (delta t).
Is this definition for D true for any dimension of space that the diffusing particle is traveling in, or does D depend in some way on the space dimension d in which the diffusion takes place?
Any information about this question, along with any references that discuss this, would be greatly appreciated.
Yes, it does depend on dimension, Prof. Ron Zamir
Please look at the following external link for the derivation & explanation:
https://physics.stackexchange.com/questions/235126/dependance-of-diffusion-coefficient-on-size
For 3D & 2D, the diffusion D will depend on the viscosity eta which changes with dimension. The link refers to a breakdown of the diffusion approximation in 2D.
Best Regards.
Hi P. Contreras
The diffusion coefficient depends on the dimension of the space in which the diffusion occurs. Whether you are thinking to an ideal case where you have an infinite space surrounding your particle or not, the diffusion will be driver by the solute concentration in the matrix so you can understand that the higher the solute concentration surrounding the particle the lower the diffusion will be.
You can have a look at this paper to go through the different terms affecting the diffusion:
Microstructural Modeling of the α + β Phase in Ti-6Al-4V: A Diffusion-Based Approach
Article Microstructural Modeling of the α + β Phase in Ti-6Al-4V: A ...
Hope this helps.
Best regards
I think I have found the answer to this question.
The Diffusion coefficient (D) for diffusion in spatial dimensions d that are greater than 1 is related to the Diffusion coefficient (D1) when the diffusion occurs in one dimension by the relationship:
D=D1/d.
This is proved in the 2003 lecture notes for MIT course 18.366 - Random Walks and Diffusion (which can be accessed in MIT Open Courseware).
The particular lecture that provides the derivation is Lecture 2, pages 7-8.
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