Model for the Kinematics of Polymer Dissolution

A review of polymer dissolution

“…Tu and Ouano [83] proposed one of the first models for polymer dissolution, assuming Fickian solvent diffusion into the polymer followed by the establishment of two distinct boundaries characterized by sharp changes in the concentration of the solvent. They also assumed that the conditions of constant chain disassociation concentration and rate are established immediately upon wetting the polymer surface and that the solvent and the polymer are incompressible.…”

“…Experimental data from the literature [83] was compared with the model predictions with good results.…”

Asymptotic and Numerical Results for a Model of Solvent-Dependent Drug Diffusion through Polymeric Spheres

“…Equations (3.12)-(3.13) show explicitly how the flux of drug from the polymer ball is O(1) and the normalized drug release is O(t) in the small-time limit, and the effect the kinetic parameter μ has on these processes. In particular, the kinetic boundary condition (2.9) (which leads to the so-called Case II diffusion of solvent through the polymer) dictates the scalings of drug release for small time, and without this empirical law the time-dependence would be qualitatively different (as in [26,39,41,51,52], for example). Clearly (3.12)-(3.13) break down in the limit μ → 0 + , and in fact (3.11)-(3.13) are valid only for t = O(μ 2 ) in this limit (see the related discussion in section 2.3).…”

“…There exists a number of mathematical models for the above processes, including the early studies [2,21,39,26,51,52] and good reviews by [37,38]. Here we are interested in those mathematical models for which the glassy-rubbery inter-face is described by a moving boundary whose kinetics is governed by an empirical law that relates the concentration of solvent there to the velocity of the interface.…”

“…In section 2 we formulate the model for a spherical polymeric particle (as in Lin et al [29]), so that the glassy-rubbery interface moves toward the center of the sphere. By applying formal asymptotics in section 2.3, we are able to determine a number of terms in the small-time expansion and observe the transition to a completely different qualitative behavior (which has the interface initially moving with infinite speed) as the important kinetic parameter vanishes, the implication being that models that do not apply the kinetic law on the glassy-rubbery interface (such as [26,39,41,51,52], for example) cannot recover the appropriate small-time behavior. The moving boundary problem is solved numerically using a front-fixing transformation together with a finite volume spatial discretization (section 2.4).…”