We utilize macrotransport theory to compute the effective diffusion coefficient of a point-sized particle in a periodic channel of slowly varying cross-section to the second order in the long-wavelength limit. This asymptotic result serves as a benchmark test for the respective modifications of the Fick–Jacobs equation proposed by Zwanzig [J. Phys. Chem. 96, 3926 (1992)], Reguera and Rubi [Phys. Rev. E 64, 061106 (2001)], and Kalinay and Percus [Phys. Rev. E 74, 041203 (2006)]. While all three modifications result in an identical effective diffusivity at first order, only the model proposed by Kalinay and Percus agrees at second order with our asymptotic result.
REFERENCES
1.
2.
R.
Zwanzig
, J. Phys. Chem.
96
, 3926
(1992
).3.
D.
Reguera
and J. M.
Rubi
, Phys. Rev. E
64
, 061106
(2001
).4.
P.
Kalinay
and J. K.
Percus
, Phys. Rev. E
74
, 041203
(2006
).5.
R.
Festa
and E. G.
d’Agliano
, Physica A
90
, 229
(1978
).6.
H.
Brenner
and D. A.
Edwards
, Macrotransport Theory
(Butterworth-Heinemann
, Boston
, 1993
).7.
E.
Yariv
and K. D.
Dorfman
, Phys. Fluids
19
, 037101
(2007
).8.
L.
Dagdug
, M.-V.
Vazquez
, A. M.
Berezhkovskii
, V. Y.
Zitserman
, and S. M.
Bezrukov
, J. Chem. Phys.
136
, 204106
(2012
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
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