Kinetic theory of diffusion in a channel of varying cross section
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909243090665472 |
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| author | Brey, J. Javier de Soria, M. I. García Maynar, P. |
| author_facet | Brey, J. Javier de Soria, M. I. García Maynar, P. |
| contents | Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is integrated over the transversal coordinate to get an approximated one-dimensional kinetic equation, keeping the relevant properties of the original one. Then, a macroscopic equation for the time evolution of the longitudinal density is derived, by means of a modified Chapman-Enskog expansion method, that takes into account the inhomogeneity of the equilibrium longitudinal density. This transport equation has the form of the phenomenological Ficks-Jacobs equation, but with an effective diffusion coefficient that contains corrections associated to the variation of the slope of the equilibrium longitudinal density profile. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_04300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kinetic theory of diffusion in a channel of varying cross section Brey, J. Javier de Soria, M. I. García Maynar, P. Statistical Mechanics Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is integrated over the transversal coordinate to get an approximated one-dimensional kinetic equation, keeping the relevant properties of the original one. Then, a macroscopic equation for the time evolution of the longitudinal density is derived, by means of a modified Chapman-Enskog expansion method, that takes into account the inhomogeneity of the equilibrium longitudinal density. This transport equation has the form of the phenomenological Ficks-Jacobs equation, but with an effective diffusion coefficient that contains corrections associated to the variation of the slope of the equilibrium longitudinal density profile. |
| title | Kinetic theory of diffusion in a channel of varying cross section |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.04300 |