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Can someone please explain to me in a simplified way, what exactly does a well-recognized Danckwerts boundary condition do to the concentration profile of adsorption phenomena? I just cannot find a relevant source - everyone says they used this condition in their simulation, but never mention any explanation.

As far as I know, the definition of the Danckwerts boundary condition says that after the gas is introduced into the column, the convection transport mechanism is associated with the diffusion, which causes a concentration step change at the inlet. However, when I went through multiple peer-reviewed articles of adsorption modelling, I haven't noticed any effects of the concentration change at inlet on the plotted graphs like I would expect if the Danckwerts boundary condition was used, e.g.,

enter image description here

This pictures (taken from this article) shows a concentration profile in the gas phase along the adsorption column length (Danckwerts B.C. was assumed).

Here, on the next picture is a concentration profile at column inlet/outlet, which describes what one should expect (taken from this presentation). The Danckwerts condition is at the left side for the column inlet...

enter image description here

Why I cannot see something like this on the first picture (I wouldn't expect a different measuring scale of both curves to neglect the Danckwerts B.C. in the first picture)?

My point is also my current work - in my model, I have specified that the concentration at the column inlet is constant (given by the Dirichlet B.C.) such that the concentration at inlet equals the concentration of component in the feed gas (concentration before the gas enters column).

How much of a error do I get by assuming this?

Thank You!

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