Hey! I'm working on a problem that tackles the uptake of water vapour in air bubbles (e.g. in a bubble column) and I'm having a surprisingly tough time getting some normal looking answers for the amount of water that is being diffused/absorbed into the bubble.
I thought that Fick's law of diffusion would be a very simple way to initially approximate this water uptake, but the amount of water that's being evaporated into the bubble greatly exceeds (e.g. bubble volume ~O(10e-9) m3, water vapour flow into bubble ~O(10e-5) kg/s) the mass of the bubble itself, so the numbers are just way off. The formula I'm using is the following:
Flow into bubble = 4*pi*D*(∆c)/(1/r - 1/R)
Where:
Flow into bubble = [kg/s]
D = diffusion coefficient ~O(10e-5) [m2/s]
∆c = change in concentration ~O(10e-2) [kg/m3] across gas/liquid film around bubble
r = inner radius of bubble ~O(10e-3) [m]
R = outer radius of bubble ~O(10e-3) [m] (e.g. r + film thickness)
I derived it from...
Flow into bubble = D*A*(-dc/dr) = D*4*pi*(r^2)*(-dc/dr)
... which is just Fick's second law applied to a spherical object.
I'm thinking that the huge water uptake might be an issue with the thin film, as the radial coordinates are inappropriate for the tiny thickness of the film which is ~O(10e-7).
Is there anything inherently wrong with the way I'm approaching this problem? Any help would be much appreciated!
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Topic: Fick's Law Diffusion of Water Vapour Into Bubble (Read 1583 times)