Mean time of diffusion- and reaction-limited loading and unloading

Abstract

AbstractDirect determination of mean diffusion times from the Laplace transform of the spatial average of the diffusing species for $$p=0$$ p = 0 offers the advantage of yielding closed-form expressions rather than sum-type ones obtained otherwise from the time-dependent solution. This is made use of in the present work to determine the mean time of diffusion- and reaction-limited loading and unloading a species into or out of bodies of different shape (plate, cylinder, sphere) for the important type of boundary condition of fixed concentration in the surrounding. This approach particularly pays off for more complex cases when the calculation from the inverse of the Laplace transform becomes more and more laborious. As an example of such type, concomitant trapping and untrapping of the diffusing species within the object during unloading is considered. The obtained solutions are quantitatively discussed with examples from literature. The present concept of the mean time of loading or unloading is compared with other time constants, e.g., mean action time or time lag.