Mean Free Path of Gases with Bulk Velocities

[nrivera494]

Hello all,

I'm modeling a situation in which a gas moves through a pressure gradient established by a quartz frit with 40-100 μm sized pores. What I'm interested in finding out is how the mean free path of the gas changes after it exits the frit region, if at all.

I think that the mean free path of the gas should increase. I say this based off of a limiting case in which the bulk velocity of the gas (x direction) becomes far greater than the average y and z components of the velocity meaning in a given time interval, the particles travel much farther along x than along y and z, making the mean free path infinite.

What I think is happening here is that the maxwell distributions (for speeds) in the y and z direction are untouched but that the maxwell distribution in the x component gets shifted. What I think this means is that for the y and z directions, the distances traveled before collisions remain the same but in the x direction the distance that the molecules travel increases by a factor of v_exit/v_enter, meaning the total mfp changes by a factor of norm(<v_exit, v_y, v_z>)/norm (<v_enter, v_y, v_z>)

Could someone help me understand this. It would be greatly appreciated

 

[Valerie Park]

. Thanks!</code>Yes, the mean free path of the gas should increase. This is because when a gas passes through a pressure gradient, it accelerates due to the decrease in pressure. This means that the particles move faster and thus, they can travel farther before they collide with each other. The increase in the mean free path is related to the difference in velocities before and after passing through the pressure gradient. Specifically, it is proportional to the ratio of the norm of the post-gradient velocity vector to the pre-gradient velocity vector. In terms of the Maxwell distribution, the maxwell distributions for the y and z directions are unaffected by the pressure gradient. However, the maxwell distribution in the x component is shifted. This shift is related to the increase in the mean free path since the molecules can travel further in the x direction due to the increased velocity. Hope this helps!