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

Roland Würschum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Direct determination of mean diffusion times from the Laplace transform of the spatial average of the diffusing species for 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.
Original languageEnglish
Article number53
JournalApplied Physics A: Materials Science and Processing
Issue number1
Publication statusPublished - Jan 2023


  • Characteristic time constant
  • Diffusion-reaction model
  • Hydrogen diffusion
  • Laplace transform

ASJC Scopus subject areas

  • General Chemistry
  • General Materials Science

Fields of Expertise

  • Advanced Materials Science


Dive into the research topics of 'Mean time of diffusion- and reaction-limited loading and unloading'. Together they form a unique fingerprint.

Cite this