The diffusion length is the characteristic length scale for diffusion problems. It increases as the square root of the time. For semi-infinite regions, the solution looks the same for all times if the length is scaled by the appropriate diffusion constant for that time. Note that the relevant time used to find the diffusion length will often be the residence time of gases in the reactor. If the diffusion length is much shorter than the system size, concentrations can differ drastically from one part of the reactor to another.
Gradients can be very large, and concentrations are highly time-dependent.
Large changes in concentration in one region in the reactor will have no effect on other regions if the time involved is short enough that the diffusion length is small. The diffusion length is our first introduction into a characteristic scale for a problem. Therefore in this tutorial we'll usually use length and time scales, but we'll try to remember to translate them into Chemical Engineerese to help the reader access the technical literature. This problem was originally studied in connection with catalysis in porous media, in which the consumption of species occurs not through deposition but through conversion into products.