HI Georg,
thank you very much for your explanations. We agree with the second
part of your e-mail. What do you, would we like to meeting us to try to
clarify the open questions? We are still working on similar problems
and we can try to optimize it.
Have a nice weekend,
best wishes,
Rainer
Am 04.12.2015 um 10:29 schrieb [email protected]:
Here is a Mickey Mouse example that shows the what the Dumux diffusion
formulation can produce:
I just plotted an imaginary molfraction gradient and 2 gradient of
molar density over some spatial domain. For an ideal gas, the molar
density is propotional to the gas pressure (ideal gas law).
So the molar density gradient corresponds to a pressure gradient which
is again proportional to 1/K (the permeability).
I also plotted the molar concentration which is rho*x.
If only a gradient of the molfraction drives the diffusion, transport
will be from right to left. However, it is obvious that for case 2
(high pressure gradient), the concentration has its maximum not at the
right boundary but inside the domain. I think this illustrates that
Fickian diffusion breaks down even for a binary system in porous media
if the permeability is low.
A better approach would probably be the dusty gas model
(Stefan-Maxwell + Knudsen diffusion) but I need to check how it is
derived. Maybe the same problem can occur when the dusty gas model is
used.
Best regards
Georg
*Von:*Dumux [mailto:[email protected]] *Im
Auftrag von *Alexander Kissinger
*Gesendet:* Donnerstag, 3. Dezember 2015 16:06
*An:* DuMuX User Forum
*Betreff:* Re: [DuMuX] A fundamental question concerning diffusion in
Dumux
sorry one more clarification to the last post:
I wrote:
Mass or molar gradients are only valid if
I meant:
Mass or molar *concentration* gradients [mol_comp/m3] are only valid if
On 12/03/2015 03:56 PM, Alexander Kissinger wrote:
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
<https://en.wikipedia.org/wiki/Fick%27s_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]
<mailto:[email protected]> wrote:
I forgot the attached file…
*Von:*Dumux
[mailto:[email protected]] *Im
Auftrag von *[email protected] <mailto:[email protected]>
*Gesendet:* Mittwoch, 2. Dezember 2015 10:44
*An:* [email protected]
<mailto:[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]>
www.DLR.de <http://www.DLR.de>
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Institut für Wasser- und Umweltsystemmodellierung
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung
Pfaffenwaldring 61
D-70569 Stuttgart
Telefon: +49 (0) 711 685-64729
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Universitaet Stuttgart, Pfaffenwaldring 61,70569 Stuttgart
email: [email protected]
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