I am measuring the moisture absorption of PET granules by measuring the mass over time. Is it possible to approximate numerically the integrated Fick's law (mass vs time) for the case of the sphere?
Hi Chiara and all.
Two questions rather than an answer.
Are PET individual granules porous particles? Or are you talking about a porous medium made with a large number of non-porous PET particles?
Thanks for answering @R.P.Peçanha
I'm talking about a single PET granule exposed to moisture environment. For PET sheets I use the integrated Fick's law approximated with numerical values as in
https://doi.org/10.1177%2F002199837601000101
My question is that in the case of a sphere and not a sheet I can use the same formula with the radius instead of the thickness.
Hi Chiara and all.
Equations holding for PET plane sheets will not work for PET spherical granules. In plane geometry, the cross-sectional area for the mass flux of water (water mass / (unit area x unit time)) is constant along the flux direction. In spherical geometry the flux varies along the flux direction (radial): inwardly, the area decreases and the flux increases. However, because of the progressive saturation of the PET granule with water, the process is unsteady (or transient): the overall absorption rate of water decreases with time. Maybe you can adapt an existing solution for chemical reaction inside a porous spherical particle of a catalyst, to the PET problem.
In this regard, have a look at § 17.6, p. 542 in the classical book Bird, R. B., Stewart, W. E. and Lightfoot, E. N., Transport Phenomena, John Wiley & Sons, Inc., 1960. There are newer editions and several printings: second edition (2002) and revised second edition (2006),
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