Rate and function to fill a theoretical vacuum

[laserdan]

I am trying to find a way to determine the rate and function that would describe how a theoretical vacuum (let's say a cubic centimeter) would repopulate with air if surrounded by ambient air at STP. Any suggestions? I am not very good with thermodynamic or kinetic theory.

My current work involves heating up the air with an infrared laser beam, by absorption and thermal relaxation of water vapor. This results in a barrier due to an abrupt change in compressibility in the path of the laser that can reflect sound waves off of it. We call this Thermally-induced Optical Reflection of Sound (THORS.) Recently we have been studying the temporal dynamics of THORS barriers, by measuring the efficiency of reflected ultrasonic pulses with respect to time after a 1 ms laser pulse was fired.

The decay in the reflection off the THORS barrier, with time, seems to fit an exponential decay. This would seem to be similar to molecular diffusion rates. I thought the rate of filling a vacuum might closely resemble the phenomenon.

Here is a link to our Latest publication on THORS. Help is much appreciated.

 

[Future Bruno]

https://www.mdpi.com/2072-6651/12/3/255/htmThe rate of air filling a vacuum can be described by Fick's Law. This law states that the rate of diffusion of a substance is proportional to the concentration gradient. The equation for this is: J = -D*(∂C/∂x)Where J is the rate of diffusion (cm^3/s), D is the diffusion coefficient of the gas (cm^2/s), and C is the concentration of the gas (mol/cm^3). So, if you know the diffusion coefficient of air at STP and the concentration gradient, you can calculate the rate of air filling the vacuum.