Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Extended Fick-Jacobs equation: variational approach.

P Kalinay1, J K Percus

  • 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Normal and anomalous diffusion in highly confined hard disk fluid mixtures.

The Journal of chemical physics·2009
Same author

Stretched Markov nature of single-file self-dynamics.

Physical review. E, Statistical, nonlinear, and soft matter physics·2007
Same author

Hopping time of a hard disk fluid in a narrow channel.

The Journal of chemical physics·2007
Same author

Hopping times of two hard disks diffusing in a channel.

The Journal of chemical physics·2007
Same author

Corrections to the Fick-Jacobs equation.

Physical review. E, Statistical, nonlinear, and soft matter physics·2006
Same author

Mapping a homopolymer onto a model fluid.

The Journal of chemical physics·2006

We developed a new diffusion equation for particles in channels. This extended Fick-Jacobs equation accurately models particle flux in complex geometries, simplifying transport analysis.

Area of Science:

  • Physics
  • Physical Chemistry

Background:

  • Particle diffusion in confined spaces is crucial in various scientific fields.
  • Existing models may not fully capture diffusion dynamics in channels with varying cross-sections.

Purpose of the Study:

  • To derive an extended Fick-Jacobs equation for noninteracting particles in 2D and 3D channels.
  • To simplify the diffusion process into a single longitudinal coordinate.

Main Methods:

  • Utilized a variational approach to derive the extended Fick-Jacobs equation.
  • Applied the derived equation to calculate stationary flux through a hyperboloidal tube.

Main Results:

  • Successfully derived a second-order diffusion differential equation in one spatial coordinate.

Related Experiment Videos

  • The derived equation provides a simplified yet accurate model for diffusion in channels.

    • Conclusions:

    • The extended Fick-Jacobs equation offers a powerful tool for analyzing particle diffusion in complex channel geometries.
    • The model's accuracy was validated by comparing its solution for a hyperboloidal tube with other established methods.