Premium
Diffusion of low molecular weight substances into a fiber with skin‐core structure—rigorous solution of the diffusion in a coaxial cylinder of multiple components
Author(s) -
Fukuda Mitsuhiro,
Kawai Hiromichi
Publication year - 1994
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760340415
Subject(s) - penetrant (biochemical) , materials science , fick's laws of diffusion , coaxial , cylinder , diffusion equation , sorption , diffusion , analytical chemistry (journal) , thermodynamics , chemistry , physics , chromatography , geometry , mathematics , organic chemistry , economy , service (business) , adsorption , electrical engineering , economics , engineering
The diffusion equation of low molecular weight substances (penetrant) into a coaxial cylinder of multiple components ( m ) was formulated in general and solved rigorously. As the simplest but a practical case of m = 2, which corresponds to the diffusion of penetrant into fibrous material with skin and core structure, the diffusion of penetrant was analyzed in detail. That is, changes in the penetrant concentration distribution within the coaxial dual cylinder of skin and core components and the total amount of penetrant sorbed within the cylinder both with time after exposing the cylinder to atmosphere of fixed penetrant concentration of C out were calculated with variation of the diffusion coefficient ratio ( D 1 / D 2 ) and the radius ratio ( R 2 / R 1 ), where D 1 and D 2 are the diffusion coefficients of penetrant in the core and the skin, and R 2 and R 1 are the radii of the fibrous material and the core, respectively. Keeping ( R 2 / R 1 ) at a constant value of 1.2 but varying ( D 1 / D 2 ) from 10 4 to 10 −2 , the penetrant concentration distribution was calculated and found to be much different particularly within the core between ( D 1 / D 2 ) > 1 and ( D 1 / D 2 ) < 1. The sorption curves were also found to deviate in their respective ways from that of Fickian curve of a homogeneous cylinder with ( D 1 / D 2 ) = 1 except at initial stage of sorption. Further, by keeping ( D 1 / D 2 ) constant but varying ( R 2 / R 1 ) from 1.1 to 1.5, the effects of relative skin thickness upon the sorption curve were studied.