Projection of two-dimensional diffusion in a narrow channel onto the longitudinal dimension

Kalinay, Pavol; Percus, J. K.

doi:10.1063/1.1899150

Cited by 152 publications

(135 citation statements)

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“…The calculation of the expansion of D(x) (2.22) presented in the Section II also demonstrates how the mapping procedure [4,6] can be applied to diffusion bounded in a channel with hard walls and biased by a transverse force. Other possible extensions are straightforward: we can add also a force acting along the channel, or to go to 3D channels.…”

Section: Discussionmentioning

confidence: 99%

“…The effects of slower transverse relaxation are included in the effective diffusion coefficient D(x). We calculate this function within a recurrence procedure [4]- [6], mapping rigorously the 2D problem onto the longitudinal coordinate x in the limit of the stationary flow, i.e. when the net flux changes very slowly with respect to the relaxation in the transverse direction.…”

Section: Discussionmentioning

confidence: 99%

“…We follow the procedure developed for the diffusion [4,6] and the biased diffusion [17,18], based on introducing a small parameter ǫ into the 2D Smoluchowski equation (1.6). We define it as a parameter of anisotropy of the diffusion constant, D y = D 0 /ǫ, but it can be also imposed by scaling of the transverse lengths [16], y → √ ǫy and the inverse scaling of the force G → G/ √ ǫ.…”

Section: Mapping Proceduresmentioning

confidence: 99%

“…Later Kalinay and Percus [4]- [6] showed, that this function can be found as a series expansion in a small parameter ǫ, representing the ratio of the longitudinal and the transverse diffusion constant, ǫ = D 0 /D y . The anisotropy of the diffusion constant, imposed artificially, causes separation of the modes quickly decaying in the transverse direction from much slower longitudinal ones and formally, it enables us to find a recurrence scheme, generating systematically higher order corrections to the FJ equation (1.1), giving the expansion of the function D(x) in ǫ in the stationary state.…”

Section: Introductionmentioning

confidence: 99%

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Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Kalinay

2011

Phys. Rev. E

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Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Mapping Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Kalinay

2011

Phys. Rev. E

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“…Once the channel radius becomes smaller than the passing threshold, R p = σ, the discs become permanently caged between their neighbours. A Ficks-Jacobs analysis [62] that projects the diffusion of the two discs onto a one-dimensional reaction coordinate predicts [63,64] …”

Section: B Two Dimensional Hard Discsmentioning

confidence: 99%

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

Ahmadi

Bowles

2017

The Journal of Chemical Physics

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Particles confined to a single file, in a narrow quasi-one dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles can begin to pass each other. The long time diffusion coefficient for a system in the crossover regime can be described in terms of a hopping time, which measures the time it takes for a particle to escape the cage formed by its neighbours. In this paper, we develop a transition state theory approach to the calculation of the hopping time, using the small system isobaric-isothermal ensemble to rigorously account for the volume fluctuations associated with the size of the cage. We also describe a Monte Carlo simulation scheme that can be used to calculate the free energy barrier for particle hopping. The theory and simulation method correctly predict the hopping times for a two dimensional confined ideal gas system and a system of confined hard discs over a range of channel radii, but the method breaks down for wide channels in the hard discs case, underestimating the height of the hopping barrier due to the neglect of interactions between the small system and its surroundings.

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Dispersive transport of biomolecules in periodic energy landscapes with application to nanofilter sieving arrays

Liu

Hadjiconstantinou

et al. 2011

Electrophoresis

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We present a theoretical model for describing the electric field-driven migration and dispersion of short anisotropic molecules in nanofluidic filter arrays. The model uses macrotransport theory to derive exact integral-form expressions for the effective mobility and diffusivity of Brownian particles moving in an effective one-dimensional energy landscape. The latter is obtained by modeling the anisotropic molecules as point-sized Brownian particles with their orientational degrees of freedom accounted for by an entropy penalty term, and using a systematic projection procedure for reducing the system dimensionality to the device axial dimension. Our analytical results provide guidance for the design and optimization of nanofluidic separation systems without the need for complex numerical simulations. Comparison with numerical solution of the macrotransport equations in the actual, effectively two-dimensional, geometry shows that the one-dimensional model faithfully describes the field- and size-dependences of mobility and diffusivity, with maximum difference on the order of 10% under the experimentally relevant electric fields.

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Projection of two-dimensional diffusion in a narrow channel onto the longitudinal dimension

Cited by 152 publications

References 6 publications

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Diffusion in quasi-one-dimensional channels: A small system n, p, T, transition state theory for hopping times

Dispersive transport of biomolecules in periodic energy landscapes with application to nanofilter sieving arrays

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