Looking for help solving the following diffusion problem. All guidance, references and/or exact solutions are welcome!
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You are given a small capsule containing CO2, at pressure P, at time, t = 0. The volume of this capsule is denoted by V and remains constant for all time. The capsule is at room temp, and the ambient environment is STP.
A circular, Aluminum membrane with diameter d, and thickness h is sealing the capsule. Assume that the membrane is mechanically sound (i.e. does not fail as a result of the pressure). Furthermore, assume that the CO2 can only diffuse through the membrane (not other walls, or interfaces in the capsule).
Calculate the pressure, P, in the enclosed capsule as a function of time. Please provide an explanation if possible.
Assume that the previously noted properties have the following values:
P = 20 Bar (@ 0 seconds)
h = .125 mm
V = 300 mm^3
d = 1 mm
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