Transport Phenomenon

[Nishan]

Hello,

          I am wondering while finding viscosity of gas why do we consider the rate of transfer of momentum in downward direction to be shear strain ?

[exchemist]

Hello,

          I am wondering while finding viscosity of gas why do we consider the rate of transfer of momentum in downward direction to be shear strain ?

This is not very clear to me. I am not sure what you mean by "downward direction".  

 

But let me explain my understanding of the issue and then you can tell me what parts of it give you difficulty.

 

The way gas viscosity has been explained to me is by imagining two trains, running side by side on parallel tracks, one going a bit faster than the other. The passengers amuse themselves by jumping from one train to the other*.

 

Every time a passenger from the faster train jumps onto the slower one, the slower one will be slightly accelerated, due to the extra momentum brought by the jumping passenger. Whereas every time one jumps from the slower train to the faster one, he will slow it down a bit. The net effect, therefore is to produce viscous drag between the trains, due to this exchange of momentum.

 

Similarly, with two adjacent layers of gas moving at different  speeds, the diffusion of molecules between the layers will cause viscous drag between them.  

 

The more frequently the passengers jump, the bigger the drag effect. So with gases the higher the temperature the more rapidly the molecules diffuse between layers and thus the viscosity of gases increases with temperature.  

 

(By the way, this is not true for liquids, for which intermolecular forces, rather than exchange of momentum, play the dominant role.)

 

 

*This analogy is used by W J Moore in his physical chemistry textbook for undergraduate chemists.

Edited June 27, 2019 by exchemist

[Dubbelosix]

Maybe by downwards, he may mean it is direction dependent? Not sure... I'll leave that comment to see.

[Dubbelosix]

Yes, Exchemist, I think you are on the right track. 

[Nishan]

This is not very clear to me. I am not sure what you mean by "downward direction".  

 

But let me explain my understanding of the issue and then you can tell me what parts of it give you difficulty.

 

The way gas viscosity has been explained to me is by imagining two trains, running side by side on parallel tracks, one going a bit faster than the other. The passengers amuse themselves by jumping from one train to the other*.

 

Every time a passenger from the faster train jumps onto the slower one, the slower one will be slightly accelerated, due to the extra momentum brought by the jumping passenger. Whereas every time one jumps from the slower train to the faster one, he will slow it down a bit. The net effect, therefore is to produce viscous drag between the trains, due to this exchange of momentum.

 

Similarly, with two adjacent layers of gas moving at different  speeds, the diffusion of molecules between the layers will cause viscous drag between them.  

 

The more frequently the passengers jump, the bigger the drag effect. So with gases the higher the temperature the more rapidly the molecules diffuse between layers and thus the viscosity of gases increases with temperature.  

 

(By the way, this is not true for liquids, for which intermolecular forces, rather than exchange of momentum, play the dominant role.)

 

 

*This analogy is used by W J Moore in his physical chemistry textbook for undergraduate chemists.

Well I was looking for something like this. Some explanation on this topic that we don't really get. 

 And I have one more question.

Is temperature of gas near the wall of the container lower than that of the middle due to momentum gradient?

[Dubbelosix]

Its due to a thermal pressure gradient, while temperature is also related to kinetic momentum, we tend to think of it more as a pressure, but in a way, it could be related to a momentum gradient.

[exchemist]

Well I was looking for something like this. Some explanation on this topic that we don't really get. 

 And I have one more question.

Is temperature of gas near the wall of the container lower than that of the middle due to momentum gradient?

No. Bulk movement of the entire fluid does not contribute to temperature, but to "normal" kinetic energy of the bulk material instead.

 

After all, a falling apple does not get hotter as it accelerates (!), even though its molecules acquire more kinetic energy.  So if the fluid in the centre of a tube is flowing faster than at the walls, that does not produce a temperature gradient, even though there certainly is a gradient in total kinetic energy. 

[Nishan]

No. Bulk movement of the entire fluid does not contribute to temperature, but to "normal" kinetic energy of the bulk material instead.

 

After all, a falling apple does not get hotter as it accelerates (!), even though its molecules acquire more kinetic energy.  So if the fluid in the centre of a tube is flowing faster than at the walls, that does not produce a temperature gradient, even though there certainly is a gradient in total kinetic energy. 

Ok but then why we consider the momentum of upper layer and lower level level changes oppositely while deriving viscosity.  Or is viscosity so small that the temperature difference is negligible.

And what does normal kinetic energy of the bulk material mean.

[exchemist]

Ok but then why we consider the momentum of upper layer and lower level level changes oppositely while deriving viscosity.  Or is viscosity so small that the temperature difference is negligible.

And what does normal kinetic energy of the bulk material mean.

Whut?

[Nishan]

Whut?

Hope you could take a look.

[exchemist]

Hope you could take a look.rps20190629_180801.jpgrps20190629_180801.jpgrps20190629_180801.jpg

These images do not seem to have come through in a form that I can read. Can you try again? The one on the other thread worked OK. 

[Nishan]

These images do not seem to have come through in a form that I can read. Can you try again? The one on the other thread worked OK.

[exchemist]

 

These images do not seem to have come through in a form that I can read. Can you try again? The one on the other thread worked OK.

 

Thanks that's better. Now at least I understand why you are talking about upper and lower layers, from the orientation used in the diagram.

 

But if you understood the analogy of the train passengers, you should understand why transfer of momentum between the layers leads the slower one to speed up and the faster one to slow down, i.e. to tend to move at the same speed, and thus to resist being made to move at different speeds.

 

Can you not follow this?

[Nishan]

Thanks that's better. Now at least I understand why you are talking about upper and lower layers, from the orientation used in the diagram.

 

But if you understood the analogy of the train passengers, you should understand why transfer of momentum between the layers leads the slower one to speed up and the faster one to slow down, i.e. to tend to move at the same speed, and thus to resist being made to move at different speeds.

 

Can you not follow this?

Yeah i could. thank you  about that.

[Dubbelosix]

 

And what does normal kinetic energy of the bulk material mean.

 

1 He may mean the norm

 

2 He may mean it in a geometrical sense

 

3 He may not even mean the above