[mohsenclick]

dear reader,
I have a basic question about mass diffusion,,,,,as i know temperature gradient, concentration gradient, pressure gradient are the main reasons to create the mass diffusion... as a mechanical engineer I analyze any motion with the newton's second law of motion.....now I want to know how these reasons to create the mass diffusion governed by the newton's second law?????????????????????????????????????????( what is the external force and the way these forces are activated to accelerate the fluid particles????))))
I am looking forward to hearing from you.

[FMDenaro]

Originally Posted by mohsenclick

dear reader,
I have a basic question about mass diffusion,,,,,as i know temperature gradient, concentration gradient, pressure gradient are the main reasons to create the mass diffusion... as a mechanical engineer I analyze any motion with the newton's second law of motion.....now I want to know how these reasons to create the mass diffusion governed by the newton's second law?????????????????????????????????????????( what is the external force and the way these forces are activated to accelerate the fluid particles????))))
I am looking forward to hearing from you.

The law you cited must be written for a fluid system, the way being addressed by the Reynolds transport theorem.
It states (in the Eulerian) that the time variation of the mass in a volume is balanced by the total convective fluxes through the surfaces of the volume. In the Lagrangian formulation, the total time variation of mass vanishes.
Now, total mass diffusion is alway zero (if no chemical reaction), but you can have diffusion of partial concentration of species. The sum must however be zero to fulfill conservation of mass.

Be careful that external forces enter into the momentum equation, they do not enter into the mass equation

[Simbelmynë]

The driving force for mass diffusion is often the concentration gradient or chemical potential. For the concentration gradient we use Fick's law.

Mass diffusion happens in all fluids, but in single component single phase fluids there is no net diffusion.

Mass diffusion can cause convection in non-dilute systems, depending on your frame of reference (e.g. volume average or mass average).

[pswpswpsw]

THE ABOVE ANSWERS ARE USELESS.

Hi,

I like the way you think. Yes. For diffusion, we don't need relative theory. We just need statistic theormodynamics.

However, in theory, we can only use statistic approach to determine the mass diffusion is happening. For example, the mass diffusion is nothing but the process of entropy increase. It is natural in physics. But it is hard to determine the exact relationship just using theory.

But, what I really want to mention is that if we only use newton second law, we can reproduce the diffusion phenomena. Like using DSMC or MD method. Many papers have mentioned they had accurately predict diffusion rate just by computer. Of course, it uses computer. But it is a highly complex process so no one can tell you what exactly the mechanism through simple newton second law. Because diffusion is a macroscopic and statistic term right?

[FMDenaro]

what we call "diffusion" is a macroscopic model for microscopic mass, momentum and energy transport, residual of the statistical average of the transport associated to the velocity (macroscopic model for convection).
We agree. But I do not understand your observation ... Using NS equations means using a continous model, using particle interaction is a different apporach.
So what do you mean?

[mohsenclick]

Originally Posted by FMDenaro

The law you cited must be written for a fluid system, the way being addressed by the Reynolds transport theorem.
It states (in the Eulerian) that the time variation of the mass in a volume is balanced by the total convective fluxes through the surfaces of the volume. In the Lagrangian formulation, the total time variation of mass vanishes.
Now, total mass diffusion is alway zero (if no chemical reaction), but you can have diffusion of partial concentration of species. The sum must however be zero to fulfill conservation of mass.

Be careful that external forces enter into the momentum equation, they do not enter into the mass equation

would you please tell me about species: what is the net force that make them move ....lets forget the bulk motion of fluid and focus on the molecular movemet .....how temperature gradient and pressure gradient leads to the required force for molecular movement? ....this force would be the force that we are looking for satisfying newton second law....
on the other hand in macroscopic scale how we can satisfy the newton second law when we have chemical reaction????

[mohsenclick]

Originally Posted by pswpswpsw

THE ABOVE ANSWERS ARE USELESS.

Hi,

I like the way you think. Yes. For diffusion, we don't need relative theory. We just need statistic theormodynamics.

However, in theory, we can only use statistic approach to determine the mass diffusion is happening. For example, the mass diffusion is nothing but the process of entropy increase. It is natural in physics. But it is hard to determine the exact relationship just using theory.

But, what I really want to mention is that if we only use newton second law, we can reproduce the diffusion phenomena. Like using DSMC or MD method. Many papers have mentioned they had accurately predict diffusion rate just by computer. Of course, it uses computer. But it is a highly complex process so no one can tell you what exactly the mechanism through simple newton second law. Because diffusion is a macroscopic and statistic term right?

what i exactly want to know is that how the mechanisms to create mass diffusion like pressure and temperature and concentration gradient would create the necessary force to make the molecules move?( how a gradient can make force?????) ...it is clear that in macroscopic view the net transport from the boundaries of the control volume is zero but what would happen in microscopic scale when we consider the molecules....
on the other hand in macroscopic scale how we can satisfy the newton second law when we have chemical reaction????

[FMDenaro]

http://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion

[DaveyBaby]

This might be too simple an answer for your liking, FMDenaro covers it more precisely, but it seems like you might be stuck in a certain way of thinking. Maybe it's worth starting by asking yourself what Fick may have been thinking when he wrote his law for diffusion. This is my guess:

- I can't model every particle, so Newton's second law of motion is not directly applicable, therefore I can't rely on it
- I still need a useful, implementable model
- I have observed that a concentration gradient may smooth itself out with time
- This seems to be a passive process, not requiring energy input
- So it's NOT due to the implementation of any outside force!
- The particles are already moving on their own
- Maybe they just "prefer" to be arranged in a particular way and move there on their own??
- As they can't "prefer" anything, maybe it's actually a completely random process??

Following on from this, reading the section on derivation of Fick's law in the link FMDenaro posted will help, explaining how a random process can result in a seemingly non-random outcome for a large number of particles. What pswpswpsw said is also all interesting, EXCLUDING what he said about the other answers being useless. His approach is more fundamental, but exceedingly computationally costly for many applications, so it has merits and faults.