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We postulated that the major reason for the failure of the aeration method was that the air bubbles were not easily accessible to much of the dissolved gas volume in the solution. The size of dissolved gas molecule is on the order of 10 ^-10 m, while the Aeration Apparatus has an inner diameter of 10.12 cm. To reach the air bubbles infused into the reactor, the bulk of the dissolved gas molecules in reactor would have had to travel over a few centimeters. To validate this reasoning, we used the equation presented below to predict the time an oxygen molecule would need to travel a distance of 1 cm - 10 cm.

{latex}
$$
x \approx \sqrt {D_m t} 
$$
{latex}

where
x = distance traveled (in m)
t = time required
D _m = molecular diffusion coefficient of the dissolved gas

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