CO2 gas diffusion into a cell factory

[soe236]

I have to pick the best cell culture vessel:
For my experiments, the vessel initially contains 0% CO2. Then it's placed in an incubator set to 37 degreesC and 5% CO2. There is a 1 micron filter i can attach to a port in the vessel that can be 10mm wide or a .2 micron filter can be attached to a port that is 26mm wide. Experimentally the vessel with the 26mm port proves to be better as more cells survive--probably because CO2 diffuses quicker (I assume)--and 5%CO2 is necessary for the cells. I'm just not able to justify the result--can anyone please explain why this might be occurring based on any theories like brownian motion or bernoulli's principle maybe?? Basically I need some kind of an equation that justies that the volumetric flow rate is much faster/better in the vessel that has a 26mm port instead of the 10mm ports (regardless of the filter device--which probably acts as resistance).

 

[jbsteele]

The difference in the volumetric flow rate between the 10mm and 26mm ports is due to a phenomenon known as laminar flow. In laminar flow, the fluid (in this case CO2) moves in a straight line within the vessel. The larger the port, the more space for the CO2 to move, creating an increased flow rate. This increased flow rate leads to more CO2 being able to reach the cells, resulting in more surviving. The equation that justifies this is the Hagen-Poiseuille equation which states that the volumetric flow rate (Q) is directly proportional to the radius of the pipe (r) to the fourth power:Q = (πr^4)/8*L*ηwhere L is the length of the pipe and η is the viscosity of the fluid. The increased radius in the 26mm port thus increases the volumetric flow rate, as seen in the equation.