Gas mixing

Conditions:

: sphere of diameter 5 mm  = 6.54e-8 m^3

: cylinder of 40 mm diameter , 750 mm long =9.42e-4 m^3

Suppose we replace part of material of volume  repeatedly, every mixing corresponds to the volume density change of the original material:

And

Solving N, one gets:

Now we use

, corresponding to nitrogen gas in the air.

Below is a table of impurity level and time.

Below is the time dependence of the impurity level as a figure.

Finally, let’s emphasize that the assumptions 1) the input bubble are 100% pure.; 2) the mixing is complete, meaning the gas is homogeneous before the bubble is released.