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diffusion convection issues
Posted Jul 1, 2014, 9:31 p.m. EDT Fluid & Heat, Microfluidics Version 4.3b, Version 5.0 12 Replies
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Hi,
I want to simulate the concentration variation of nano-particle in a micro-fluid channel under magnetic field, and to show nano-particle will build up in the region near the magnet. I have built a modeling including transport of diluted species modeling. But the result is not similar to what happened in my experiment. That is, although I can see the concentration variation near the magnet, in the modeling, nano-particles does not have a high build-up that happened in the experiments. The values of the concentration in the modeling just vary from 0.05 to 0.08.
I will briefly introduce the modeling. This modeling includes three modules, magnetic field, laminar flow and transport of diluted species.
For the magnetic field, the big rectangle beside the T-shaped channel is a permanent magnet, which will produce stable magnetic field. Thus, the magnetic field in every point is fixed and then independent of the other two modules, so that we can solve it separately.
Then go to the laminar flow. Actually, the fluid flowing into the T-shaped channel is the ferrofluid, not pure water. I figure you are not very familiar to ferrofluid. Here we go: A ferrofluid is a liquid that gets strongly magnetized in the presence of an external applied magnetic field. Ferrofluids contain magnetic nanoparticles suspended in a carrier fluid usually an organic solvent or water. In general, the nanoparticles in a ferrofluid are suspended by Brownian motion and generally will not settle under standard conditions. However, if applied a magnetic field, some nanoparticles will be attracted by magnetic force. That's why ferrofluid will build up in the area near magnet. And the velocity of those nanoparticles has two components, one is the flow velocity and the other is the velocity induced by magnet.
What you can see in the transport of diluted species module is that I have redefined the nanoparticle velocity as flow velocity plus the velocity induced by magnet. Obviously, the concentration we care is that of nanoparticles. The initial concentration of ferrofluid is 0.05, which means the nanoparticles will take 5 percent of ferrofluid.
I know it's too long. Thanks for your patience. I have checked the modeling for several times and make sure everything should be OK. I don't understand why the transport of diluted species module cannot show the "high" concentration variation well? Is anyone willing to help me? Thank you.
Attached is the modeling.
Regards,
Yilong
I want to simulate the concentration variation of nano-particle in a micro-fluid channel under magnetic field, and to show nano-particle will build up in the region near the magnet. I have built a modeling including transport of diluted species modeling. But the result is not similar to what happened in my experiment. That is, although I can see the concentration variation near the magnet, in the modeling, nano-particles does not have a high build-up that happened in the experiments. The values of the concentration in the modeling just vary from 0.05 to 0.08.
I will briefly introduce the modeling. This modeling includes three modules, magnetic field, laminar flow and transport of diluted species.
For the magnetic field, the big rectangle beside the T-shaped channel is a permanent magnet, which will produce stable magnetic field. Thus, the magnetic field in every point is fixed and then independent of the other two modules, so that we can solve it separately.
Then go to the laminar flow. Actually, the fluid flowing into the T-shaped channel is the ferrofluid, not pure water. I figure you are not very familiar to ferrofluid. Here we go: A ferrofluid is a liquid that gets strongly magnetized in the presence of an external applied magnetic field. Ferrofluids contain magnetic nanoparticles suspended in a carrier fluid usually an organic solvent or water. In general, the nanoparticles in a ferrofluid are suspended by Brownian motion and generally will not settle under standard conditions. However, if applied a magnetic field, some nanoparticles will be attracted by magnetic force. That's why ferrofluid will build up in the area near magnet. And the velocity of those nanoparticles has two components, one is the flow velocity and the other is the velocity induced by magnet.
What you can see in the transport of diluted species module is that I have redefined the nanoparticle velocity as flow velocity plus the velocity induced by magnet. Obviously, the concentration we care is that of nanoparticles. The initial concentration of ferrofluid is 0.05, which means the nanoparticles will take 5 percent of ferrofluid.
I know it's too long. Thanks for your patience. I have checked the modeling for several times and make sure everything should be OK. I don't understand why the transport of diluted species module cannot show the "high" concentration variation well? Is anyone willing to help me? Thank you.
Attached is the modeling.
Regards,
Yilong
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12 Replies Last Post Oct 23, 2014, 9:49 a.m. EDT
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Posted:
10 years ago
I am not 100% sure, but one thing crossed my mind:
In the Transport of Diluted Species node, you have User defined velocity field, and there an expression
u+Vferro*mu0*(1-c*1[m^3/mol]*C1)*(Md*(coth(alfa*P)-1/( alfa*P))* mf.Hx/ P*d(mf.Hx,x)+Md*(coth(alfa*P)-1/( alfa*P))* mf.Hy/ P*d(mf.Hx,y))/3/pi/spf.mu/dnano
But since you have a user defined expression, Comsol does not recognize u (or v) and puts them to zero. I think you should write spf.u and spf.v if you wish to use the velocity field solved in the Laminar Flow node.
Wish this helps
Lasse
In the Transport of Diluted Species node, you have User defined velocity field, and there an expression
u+Vferro*mu0*(1-c*1[m^3/mol]*C1)*(Md*(coth(alfa*P)-1/( alfa*P))* mf.Hx/ P*d(mf.Hx,x)+Md*(coth(alfa*P)-1/( alfa*P))* mf.Hy/ P*d(mf.Hx,y))/3/pi/spf.mu/dnano
But since you have a user defined expression, Comsol does not recognize u (or v) and puts them to zero. I think you should write spf.u and spf.v if you wish to use the velocity field solved in the Laminar Flow node.
Wish this helps
Lasse
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Posted:
10 years ago
Hi Lasse，
Thanks for your reply. When I change u to spf.u, the expression will become yellow. I figure the spf.u would not be suitable. If I set u and v as 0 in the expression, the result will be totally different. And I have draw the streamline for that expression "u+Vferro*mu0*(1-c*1[m^3/mol]*C1)*(Md*(coth(alfa*P)-1/( alfa*P))* mf.Hx/ P*d(mf.Hx,x)+Md*(coth(alfa*P)-1/( alfa*P))* mf.Hy/ P*d(mf.Hx,y))/3/pi/spf.mu/dnano". It turns out Comsol can recognize the u. Thus, this may not be the reason.
Regards,
Yilong
Thanks for your reply. When I change u to spf.u, the expression will become yellow. I figure the spf.u would not be suitable. If I set u and v as 0 in the expression, the result will be totally different. And I have draw the streamline for that expression "u+Vferro*mu0*(1-c*1[m^3/mol]*C1)*(Md*(coth(alfa*P)-1/( alfa*P))* mf.Hx/ P*d(mf.Hx,x)+Md*(coth(alfa*P)-1/( alfa*P))* mf.Hy/ P*d(mf.Hx,y))/3/pi/spf.mu/dnano". It turns out Comsol can recognize the u. Thus, this may not be the reason.
Regards,
Yilong
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Posted:
10 years ago
Is 'diluted species' appropriate if you want such high concentrations?
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Posted:
10 years ago
I think you can use it. Transport of Concentrated Species node is meant for, e.g. mixtures of solvents where the mass fraction of one species is > 0.1.
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Posted:
10 years ago
I am not sure. But if not, does comsol have other module which is appropriate for this issue?
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Posted:
10 years ago
Transport of concentrated species is - in my opinion - the best approach, but the Stefan-Maxwell formalism on which it is based contains so many unknown parameters that it is rather difficult to apply.
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Posted:
10 years ago
Thank you. Recently, I have read some papers, which mention the false-diffusion errors among the numerical approximations. Is that the point of my problem?
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Posted:
10 years ago
Well, is the transport of nanoparticles diffusion in the first place? Diffusion is basicly Brownian motion. But you can estimate the values of the diffusion coefficient with the Stokes-Einstein equation
D = kT/(6·pi·eta·a)
where eta is the viscosity of the solution and a the particle radius.
D = kT/(6·pi·eta·a)
where eta is the viscosity of the solution and a the particle radius.
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Posted:
10 years ago
Thank you. I know this Stokes-Einstein equation and have used it in the modeling. But it not my issue. I think numerical false-diffusion error should be one reason why the result is not as good as expected.
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Posted:
10 years ago
Hi Yilong,
I was curious about this model so I ran it with a minor modification to link Study 1 and Study 2 and I get a peak concentration of 0.46, not 0.08. Is that what you expect?
Nagi Elabbasi
Veryst Engineering
I was curious about this model so I ran it with a minor modification to link Study 1 and Study 2 and I get a peak concentration of 0.46, not 0.08. Is that what you expect?
Nagi Elabbasi
Veryst Engineering
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Posted:
10 years ago
Hi Nagi,
Sorry for such late reply. I just saw your reply.
That is what we expect. Could you tell me which minor modification you did to the modeling? Thanks for your help.
Regards,
Yilong
Sorry for such late reply. I just saw your reply.
That is what we expect. Could you tell me which minor modification you did to the modeling? Thanks for your help.
Regards,
Yilong
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Posted:
10 years ago
Hi Yilong,
I believe I just set the “Values of variables not solved for” setting for Study 2 to point to the solution of Study 1. Otherwise you are not using the flow and magnetic field results in your Study 2!
Nagi Elabbasi
Veryst Engineering
I believe I just set the “Values of variables not solved for” setting for Study 2 to point to the solution of Study 1. Otherwise you are not using the flow and magnetic field results in your Study 2!
Nagi Elabbasi
Veryst Engineering