Diffusion Coefficient still doesn't make sense in air at STP

Click For Summary

Discussion Overview

The discussion revolves around understanding the diffusion coefficient of tracer gases, such as isoflurane, in air at standard temperature and pressure (STP). Participants explore the relationship between diffusion and advection, the implications of diffusion coefficients, and the mathematical underpinnings of Fick's laws in the context of gas dispersal in indoor environments.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to compare the diffusion of a tracer gas to the advection of air, expressing confusion about the diffusion constant and its implications for transfer rates and velocities.
  • Another participant references Fick's first law, stating that the flux of a substance is proportional to the concentration gradient, suggesting that the diffusion coefficient does not need to include the amount of substance in its units.
  • A third participant provides a breakdown of Fick's law, explaining the dimensions of the diffusion coefficient and the flux, while also expressing a desire for a more intuitive understanding of the topic.
  • Further clarification is offered regarding the concentration gradient and its units, with an emphasis on how to derive the units for the diffusion coefficient from the relationship between flux and concentration gradient.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the diffusion coefficient and its implications. While some agree on the definitions and relationships presented by Fick's laws, others seek a more intuitive explanation, indicating that the discussion remains unresolved with multiple viewpoints on the clarity and applicability of the concepts.

Contextual Notes

Participants highlight limitations in the existing explanations, noting that many discussions on diffusion are either overly simplistic or highly theoretical, which may not adequately address practical applications or intuitive understanding.

Rooner1
Messages
4
Reaction score
1
TL;DR
The units of the Diffusion Coefficient (cm2/sec) don't look like a mass transfer units.
I want to compare diffusion of a tracer gas with a low exposure limit (e.g. isoflurane) to the advection of air by a ventilation system. When will diffusion exceed advection? I can't make sense of diffusion constant to compare transfer rates or velocities.
At room temperature the diffusion coeeficient is generally around 0.2 cm2/sec for many gases. So what does that mean for the dispersal of a tracer gas (like ether vapors or isoflurane) in a calm indoor environment? What are the full units that are cancelling out? I'd love some citations if you have them.
There was a similar post about diffusion coefficient in 2010, and the reply finished with, "I can't get much more intuitive than that", which seems to be circular thinking when his explanation was rather obtuse. He said it was a velocity x density, which would be cm/s x gm/cm3, which would cancel out to be gm/sec.cm2.
I'm a moderately decent chemist, with units anyways, and the explanations of diffusion of gases at tracer levels in air is generally highly simplistic, like the sensing of vailla as it diffuses through a room, or highly theoretical and involving Boltzmann constants, degrees Kelvin, etc. Can this be simplified and still approximate decent rigor?
 
Chemistry news on Phys.org
I am not sure I understand where the problem is. Fick's first law says the flux (amount of the substance that travels) is directly proportional to the gradient of the concentration (amount of substance per volume) - so the amount of substance (in whatever units) is present in nominator on both sides of the equation and the proportionality coefficient doesn't have to contain it.
 
Hello @Rooner1 , :welcome: !

Are you familiar with Fick's law ? The Wiki lemma explains the dimension of the diffusion coefficient ##D##

Wikipedia said:
$$J = - D {d\phi\over dx}$$where
  • J is the diffusion flux, of which the dimension is amount of substance per unit area per unit time. J measures the amount of substance that will flow through a unit area during a unit time interval.
  • D is the diffusion coefficient or diffusivity. Its dimension is area per unit time.
  • φ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume.
  • x is position, the dimension of which is length.
Rooner1 said:
There was a similar post about diffusion coefficient in 2010, and the reply finished with, "I can't get much more intuitive than that"
Pity you don't give the link; I can't find it.

Rooner1 said:
Can this be simplified and still approximate decent rigor?
I like that :smile: !
 
Say mol/cm³ is the concentration φ. You can replace mol by the number of particles.
Then the concentration gradient is of course: φ' = dφ/dx, if we have a one dimensional setting, i.e. the concentration is constant along lines in the y-z-plane.
This yields (mol/cm³) / cm or mol/cm^4 as unit for φ'.
The Flux J is the number of mols or particles, respectively, streaming through a unit area in the y-z-plane, in one time unit, leading to the following unit: mol/(cm² s) as unit for J.
(Actually it is dn/dt/dA, n being the number and A the area, but this leads to the same units of course.)
So to get the diffusion coefficient, being the proportionality J/φ', which division you can hopefully do on your own.