Diffusion in polymer–solvent systems. A study of numerical methods of simulation

Abstract

Fickian and non‐Fickian diffusion into polymer‐solvent systems were simulated on both analog and digital computers. Methods were evaluated to solve the descriptive nonlinear ordinary and partial differential equations. Analog methods published previously have been expanded. It was shown that discrete time solutions are superior to discrete distance solutions for partial differential equations, as hardware requirements are small. Also, accuracy problems on some of the smaller installations can be reduced by reverse time integration. For highly nonlinear equations, analog methods are superior to digital in stability and effort required. Digital solutions can be require extensive preliminary work to define computation parameters. However, the errors introduced by the finite difference equations are small in moderately nonlinear equations and much more accurate solutions are possible. Generalized solutions for polymer‐solvent diffusion with exponential concentration dependence are presented for the Fickian cases. Also, typical solutions are demonstrated for all known types of non‐Fickian diffusion.

Computer Simulations of Transport Processes

“…The reported studies on extrusion (20, 50), injection (10), and drying (30,40) of polymeric materials have all used a digital computer as a process simulator. On the other hand, the simulations of three basic types of regenerators, fixed-bed (IQ, 2Q, 4Q, 5Q), moving-bed (3Q, 6Q), and thermal re-Ind.…”