AI Article Synopsis
- The study analyzes the diffusion constant of Brownian particles in a square lattice filled with hard disks, emphasizing the relationship with effective conductivity.
- It utilizes a recently derived Green's function to create a series expansion of the diffusion constant based on the volume fraction of the disks.
- Additionally, a modified Fick-Jacobs approximation is introduced to examine the behavior of the diffusion constant at high volume fractions, resulting in a cohesive analytical framework applicable across various densities.
Article Abstract
We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green's function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk's volume fraction φ. Second, we propose a variant of the Fick-Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.
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| http://dx.doi.org/10.1063/5.0009095 | DOI Listing |
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