Premium
A mathematical model for a dissolving polymer
Author(s) -
Edwards David A.,
Cohen Donald S.
Publication year - 1995
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690411102
Subject(s) - viscoelasticity , nonlinear system , boundary value problem , similarity solution , polymer , constant (computer programming) , fick's laws of diffusion , perturbation (astronomy) , dissolution , mathematical analysis , penetrant (biochemical) , mechanics , diffusion , mathematics , materials science , physics , boundary layer , thermodynamics , chemistry , computer science , quantum mechanics , programming language , organic chemistry , composite material
In certain polymer‐penetrant systems, nonlinear viscoelastic effects dominate those of Fickian diffusion. This behavior is often embodied in a memory integral incorporating nonlocal time effects into the dynamics; this integral can be derived from an augmented chemical potential. The mathematical framework presented is a moving boundary‐value problem. The boundary separates the polymer into two distinct states: glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. Asymptotic solutions are obtained where sharp fronts move with constant speed. The resultant profiles are quite similar to experimental results in a dissolving polymer. It is then demonstrated that such a model has a limit on the allowable front speed and a self‐regulating mass uptake.