ArticleThe Journal of chemical physics2012
Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation.
Article in The Journal of chemical physics, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Ameboid cell migration through regular arrays of micropillars under confinement.Biophysical journal · 2022Article
- Brownian motion in confined geometries.The European physical journal. Special topics · 2014Article
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5 authors.
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Abstract
The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period.
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