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wallytutor committed Apr 16, 2024
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This expression has a very straightforward interpretation. If there is no creation rate $B_{s}$ at the interface, flux is continuous across interface; otherwise some arbitrary form of discontinuity should arise, whose form would depend on the volume governing equations at each side of $S$.

## Conservation at moving interfaces



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As a side note, it is worth mentioning here that in analytical methods the $b_{\infty}$ is treated as constant because otherwise analysis could grow exponentially in complexity. For the numerical solution of models it can be often treated as an explicit time function. For instance, imagine a material treatment where pulses of a reacting species are controlled and their concentration in the reactor is known in time; if modeling the solid state uncoupled from the reactor - what is generally the case due to computational time limitations - then the value of $b_{\infty}$ can be provided explicitly, keeping in mind that $h$ can also be a function of this value or surface concentration, depending on the closure model used for the specific simulation.

## Microscopic models of diffusion


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