# Reynolds number may have a similar effect to the Knudsen number

1. Jan 9, 2008

### Goodman

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.