- #1
jencam
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Hi
I am reading and trying to comprehend the article "Dispersion of soluble matter in solvent flowing slowly through a tube", Sir Geoffrey Taylor, Proceedings of the Royal Society of London, 1953.
I am particularly interested in cases A2 and B2, where a concentrated solution is injected into one end of a tube filled with solvent only.
Case A2 handles the (average) concentration at different positions in the tube disregarding diffusion, which happens to become a linear decrease in concentration.
Case B2 generalizes the model to include radial diffusion still ignoring axial diffusion. The solution in this case becomes a symmetric erf function, which principally extends infinitely in both directions.
What bothers me is that when flow increases or coefficient of diffusion decreases, case B2 should in my opinion asymptotically fall back to case A2. Principally I would think the concentration profile should be limited in length - we have no axial diffusion so the concentrated part shouldn't be able to extend beyond case A2.
I don't know if I am plain stupid or if this is due to some assumptions that are not fulfilled at low-D.
Can anyone please give me a hint?
Regards
--Jens
I am reading and trying to comprehend the article "Dispersion of soluble matter in solvent flowing slowly through a tube", Sir Geoffrey Taylor, Proceedings of the Royal Society of London, 1953.
I am particularly interested in cases A2 and B2, where a concentrated solution is injected into one end of a tube filled with solvent only.
Case A2 handles the (average) concentration at different positions in the tube disregarding diffusion, which happens to become a linear decrease in concentration.
Case B2 generalizes the model to include radial diffusion still ignoring axial diffusion. The solution in this case becomes a symmetric erf function, which principally extends infinitely in both directions.
What bothers me is that when flow increases or coefficient of diffusion decreases, case B2 should in my opinion asymptotically fall back to case A2. Principally I would think the concentration profile should be limited in length - we have no axial diffusion so the concentrated part shouldn't be able to extend beyond case A2.
I don't know if I am plain stupid or if this is due to some assumptions that are not fulfilled at low-D.
Can anyone please give me a hint?
Regards
--Jens