Dear Dumux,
one clarification to the last post:
The driving force for Fickian diffusion is a gradient in the mole
fractions x [mol_comp/mol_total] as implemented in the Dumux models:
Diffusive flux: J_D = -rho_molar [mol_total/m3] * D * grad x
Mass or molar gradients are only valid if
- the volume of the solute is much smaller than the total concentration
or molar density [mol_total/m3] and
- isothermal conditions prevail, i.e. no volume change due to changes in
temperature
A detailed explanation can be found in:
Taylor, Ross, and Rajamani Krishna. /Multicomponent mass transfer/. Vol.
2. John Wiley & Sons, 1993.
Chapter 3.1 and 3.1.1
Best regards
Alex
On 12/03/2015 01:40 PM, Bernd Flemisch wrote:
Hi,
I discussed this a bit here with Alex, Holger and Rainer. The main
point is that Fickian diffusion is described by _molar_ concentrations
[mol/m3], not _mass_ concentrations [kg/m3],
https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion
The multiplication by molar/mass density comes then from the fact that
we balance moles/mass. But it happens outside of the gradient.
This indeed allows diffusion to occur against the mass concentration
gradient, if that differs from the molar concentration gradient like
in the setup that you prescribe.
Kind regards
Bernd
On 12/02/2015 10:45 AM, [email protected] wrote:
I forgot the attached file…
*Von:*Dumux [mailto:[email protected]] *Im
Auftrag von *[email protected]
*Gesendet:* Mittwoch, 2. Dezember 2015 10:44
*An:* [email protected]
*Betreff:* Re: [DuMuX] A fundamental question concerning diffusion in
Dumux
Hello Dumux,
I am back with the same question and some more infos. The modeling
approach for diffusion in Dumux is (in my opinion) wrong and gives
unphysical results. This is most pronounced for diffusion in a gas
phase and when the intrinsic permeability is low.
Consider the model setup depicted in Figure1.jpg. In this setup the
only transport mechanism for H2O from the right boundary is diffusion
because the sink of N2 is high and the advective flow is from left to
right. In this setup, the pressure will drop to the right while the
gradient of x_g^H2O is vice versa. However, the concentration of H2O
will be lower at the right boundary and *diffusion will occur from a
lower to a higher concentration!*
This is completely unphysical. There is no reason why the component
should flow against its concentration gradient. The reason for this
lies in the formulation of the diffusive fluxes:
Where
In the Dumux formulation, the second (pressure dependent) term on the
very right is neglected resulting in the possibility that species
diffuse against their concentration gradient.
The density gradient is proportional to the pressure gradient from
left to right while the molfraction gradient is vice versa.
I hope this made things more clear.
I would recommend to use grad(rho*x) instead of grad(x) for the
calculation of the diffusive fluxes.
I am always open for discussion.
Kind regards
Georg
*Von:*Dumux [mailto:[email protected]] *Im
Auftrag von *[email protected] <mailto:[email protected]>
*Gesendet:* Mittwoch, 25. November 2015 14:30
*An:* [email protected]
<mailto:[email protected]>
*Betreff:* [DuMuX] A fundamental question concerning diffusion in Dumux
Hello Dumuxers,
I was wondering why the diffusive fluxes in Dumux are defined as
D*rho*grad(mol-or-massfraction). Typically one would use D*grad(c)
(e.g. Ficks law) where c=rho*mol-or-massfraction. Using the Dumux
equation means that local differences in the density are neglected
for diffusive fluxes. Is there any reason/justification for this? Or
is my thinking just wrong?
Best regards
Georg Futter
——————————————————————————
*German Aerospace Center *(DLR)
Institute of Engineering Thermodynamics | Computational
Electrochemistry | Pfaffenwaldring 38-40 | 70569 Stuttgart
Dipl.-Ing. *Georg Futter* | Ph.D. student
Telefon 0711/6862-8135 | [email protected] <mailto:[email protected]>
<http://www.dlr.de/>www.DLR.de
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Telefon: +49 (0) 711 685-64729
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