A mathematical model for trapping skinning in polymers

When saturated polymer films are desorbed, a thin skin of glassy polymer can form at the exposed surface, inhibiting desorption. In addition, trapping skinning, in which an increase in the force driving the desorption decreases the accumulated flux, can also occur, These behaviors cannot be described by the simple Fickian diffusion equation, The mathematical model presented for the system is a moving boundary-value problem with a set of coupled partial differential equations that cannot be solved by similarity variables, Therefore, integral equation techniques are used to obtain asymptotic estimates for the solution. It is shown that although increasing the driving force will increase the instantaneous flux, the time of accumulation will decrease, thus reducing the overall flux. In addition, the model is shown to exhibit sharp fronts moving with constant speed, another distinctive feature of non-Fickian polymer-penetrant systems.