Modification of classical approximations for diffusion in fluids with density gradients

Aranovich, G. L.; Whitman, Jessica R.; Donohue, Marc D.

doi:10.1039/b924340b

Cited by 1 publication

(1 citation statement)

References 18 publications

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“…A more general treatment could include anisotropy in both the mean free path and the average molecular velocity (i.e., temperature gradient). If V + and V − are average velocities in the + and − directions and λ + and λ − are mean free paths in the + and − directions, then the net flux is represented as F=

V_{+} ρ_{+} - V_{-} ρ_{-}

where ρ + and ρ − are densities at points x + λ + and x − λ − .…”

Section: Relevance To Chemical Engineering Applications and Discussionmentioning

confidence: 99%

Diffusion in fluids between Knudsen and Fickian limits: Departure from classical behavior

Aranovich

Donohue

2015

AIChE Journal

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The finite-difference equation of diffusion (consistent with Einstein's evolution equation of diffusion) without the assumption of small mean free path is discussed. This equation predicts significant deviations from classical behavior for the simplest geometry: fluid in a pipe with a large density gradient, such that one end is at the Fickian limit, the other end is at Knudsen limit and there can be a transition zone between them. This has not been considered in previous studies. The analysis indicates that significant deviations from classical (Fickian) behavior arise due to the large change in mean free path which is important in numerous situations, including vacuum technology and propulsion in space. Other examples of deviations from Fick's law include cases where the mean free path is not small compared to system size (nanoscale systems and low density systems) and cases where there are large gradients. These are important in a variety of practical applications, including vacuum distillation, vacuum pumps, and adsorption measurements. V C 2015 American Institute of Chemical Engineers AIChE J, 61: [3138][3139][3140][3141][3142][3143] 2015

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V_{+} ρ_{+} - V_{-} ρ_{-}

where ρ + and ρ − are densities at points x + λ + and x − λ − .…”

Section: Relevance To Chemical Engineering Applications and Discussionmentioning

confidence: 99%

Diffusion in fluids between Knudsen and Fickian limits: Departure from classical behavior

Aranovich

Donohue

2015

AIChE Journal

View full text Add to dashboard Cite

show abstract

Modification of classical approximations for diffusion in fluids with density gradients

Cited by 1 publication

References 18 publications

Diffusion in fluids between Knudsen and Fickian limits: Departure from classical behavior

Diffusion in fluids between Knudsen and Fickian limits: Departure from classical behavior

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