Reynolds number may have a similar effect to the Knudsen number

In summary: Your Name]In summary, the slip/stick behavior of gases on walls is determined by both the Reynolds number and Knudsen number. At high Reynolds numbers, the gas tends to stick to the wall, while at low Knudsen numbers, the slip effects are negligible. However, at intermediate values of Knudsen number, slip effects become prominent and can be intensified or mitigated by the Reynolds number. Ultimately, the interaction between fluid inertia and slip rarefaction effects determines the slip/stick behavior of gases on walls.
  • #1
Goodman
2
0
Reynolds number prominence to slip/stick the gases on the walls
Dears

A major question has arisen during the comparison of experimental evidence and numerical results. The problem is also recognized by some of the researchers but it’s not fully exhausted yet [1,2]. I know from the slip flow experiment that the high Reynolds numbers enforce the gas to stick to the wall as the no-slip condition stands while the Knudsen number has a value between 0.01 and 0.1. So, I cannot have a turbulent and slip flow at the same time [3]. This means that the gas inertia (Reynolds number) is able to intensify or mitigate the slip rarefaction effects. Therefore, opposite to the Knudsen number, I think that the Reynolds number represents two different physics, one is the fluid inertia and the other is the slip rarefaction effects.

1) If the Reynolds number can intensify and mitigate the slip effects, reducing the Knudsen number to zero may not be the only condition required to reaching the continuum regime. Here, an extra condition for Reynolds number and a new nonzero value for Knudsen number are needed to reduce the slip regime to the continuum one.

2) The second issue which is more acceptable in my view is that the Reynolds number can only mitigate the slip rarefaction effect when it is increased. The converse effect (intensifying the fluid slip on walls) cannot be justified physically when I imagine the diffuse reflection of gas particles from the wall and regarding the interaction of Reynolds number on the tangential momentum of incident/reflected particles. In this case, the Kn=0 is the only condition which reduces the slip regime to the continuum one. Moreover, that high value of Reynolds number at where the slip regime vanishes is not definite and should be determined practically or numerically.

Regarding these views, I shall be greatly indebted to you if you clarify the problem to me.

Yours
Goodman

[1] Zuppardi, G. et al. (2007) Quantifying the Effects of Rarefaction in High Velocity, Slip-Flow Regime. Rarefied Gas Dynamics: 25-th International Symposium, Russia.
[2] Kavehpour, H.P., Faghri, M. and Asako, Y. (1997) Effects of Compressibility and Rarefaction on Gaseous Flows in Microchannels. Numerical Heat Transfer, Part A: Applications, 32, pp. 677 – 696.
[3] White, F.M. (2006) Viscous Fluid Flow Mc-Graw Hill, New York, P. 47.
 
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  • #2


Dear Goodman,

Thank you for bringing up this important topic for discussion. As you have correctly pointed out, the Reynolds number and Knudsen number play crucial roles in determining the slip/stick behavior of gases on walls. The Reynolds number, which is a measure of the ratio of inertial forces to viscous forces, is often used to characterize the flow regime. However, in the slip flow regime, it is not the only parameter that affects the slip/stick behavior. The Knudsen number, which is a measure of the ratio of the molecular mean free path to the characteristic length scale, also plays a significant role.

As you have mentioned, at high Reynolds numbers, the gas tends to stick to the wall due to the no-slip condition. On the other hand, at low Knudsen numbers, the gas molecules collide more frequently with the wall and thus, slip effects are negligible. However, at intermediate values of Knudsen number, slip effects become prominent and can significantly affect the flow behavior.

To address your first point, I agree that reducing the Knudsen number to zero may not be the only condition for reaching the continuum regime. In addition, a higher Reynolds number may also be necessary to mitigate the slip effects and approach the continuum regime. This is because, at higher Reynolds numbers, the gas particles have higher momentum and are able to overcome the slip effects to some extent.

Regarding your second point, I believe that the Reynolds number can both intensify and mitigate the slip rarefaction effects depending on its value and the Knudsen number. At low Knudsen numbers, increasing the Reynolds number may indeed mitigate the slip effects, but at intermediate Knudsen numbers, it may intensify the slip effects. This is because, at intermediate Knudsen numbers, the slip effects are more significant and the increased momentum of the gas particles can lead to a higher degree of slip.

In conclusion, I agree with your views that the Reynolds number represents two different physics in the slip flow regime - fluid inertia and slip rarefaction effects. The interaction between these two factors determines the slip/stick behavior of gases on walls. I hope this clarifies the problem for you and I am happy to discuss this further with you.
 
  • #3


Dear Goodman,

Thank you for your interesting insights on the relationship between Reynolds number and Knudsen number. I agree with your points that the Reynolds number can have a similar effect to the Knudsen number in terms of slip/stick behavior of gases on walls.

As you mentioned, the Reynolds number represents two different physics - fluid inertia and slip rarefaction effects. This is an important factor to consider when studying gas flow in microchannels, as the slip rarefaction effects become more significant at small scales.

I also agree with your first point that reducing the Knudsen number to zero may not be the only condition to reach the continuum regime. The Reynolds number can also play a role in mitigating the slip rarefaction effects, and a new nonzero value for the Knudsen number may be needed to fully characterize the flow.

However, I have a different perspective on your second point. While it may seem counterintuitive, there have been studies that have shown the Reynolds number can intensify the slip rarefaction effects at high velocities and low Knudsen numbers (Zuppardi et al., 2007). This is due to the increased interaction between gas particles and the wall at higher velocities, leading to more frequent collisions and thus stronger slip effects.

Overall, your thoughts and questions on this topic are valid and worth further investigation. Thank you for bringing this to our attention and I hope we can continue to explore this topic together.
 

1. What is the Reynolds number and the Knudsen number?

The Reynolds number is a dimensionless quantity used to determine the type of flow (laminar or turbulent) of a fluid over a surface. The Knudsen number is also a dimensionless quantity used to determine the type of flow (continuum or rarefied) of a gas in a confined space.

2. How does the Reynolds number affect the flow of a fluid?

The Reynolds number is used to predict the transition from laminar to turbulent flow. Higher Reynolds numbers indicate a more turbulent flow, while lower Reynolds numbers indicate a more laminar flow. The transition point varies depending on the shape and surface characteristics of the object, as well as the fluid properties.

3. How does the Knudsen number affect the flow of a gas?

The Knudsen number is used to predict the transition from a continuum flow (governed by fluid mechanics) to a rarefied flow (governed by molecular dynamics) in a confined space. Higher Knudsen numbers indicate a more rarefied flow, while lower Knudsen numbers indicate a more continuum flow. The transition point varies depending on the gas properties and the size and geometry of the confined space.

4. Can the Reynolds number and Knudsen number have a similar effect on flow?

Yes, in certain cases, the Reynolds number and Knudsen number can have a similar effect on flow. This is because both numbers are used to predict the transition from one type of flow to another. However, the physical mechanisms behind this transition are different for fluids and gases, as they are governed by different principles.

5. How can the Reynolds number and Knudsen number be related?

The Reynolds number and Knudsen number can be related through the concept of non-dimensionalization, where physical quantities are expressed in terms of dimensionless parameters. In this case, the Knudsen number can be seen as a non-dimensionalized version of the Reynolds number for gas flows in confined spaces. However, they still have distinct meanings and applications in fluid and gas dynamics.

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