Diffusion in elongated membranes

Abstract

ABSTRACT:The model proposed by Cohen and collaborators is used to describe the process of diffusion through polymeric membranes subjected to externally applied extensions. This continuum mechanics approach is compared with a model developed via a mesoscopic theory. Experimental data on a variety of polymer/solvent systems are successfully described by the model. It was found that the flux-versus-time curves for deformations up to 80% elongation could be reduced to a master curve.

Viscoelastic (Non‐Fickian) Diffusion

“…The ratio between parameters γ 1 , and γ 2 provides an indication as to whether the transport is stress controlled or driven by molecular diffusion. Liu et al 58,59 used a dimensionless time (a Deborah number) that characterizes the relaxation of the polymer. Figure 2 shows quantitative agreement between experimental data and the theory.…”

Diffusion through swelling membranes with a Robin boundary condition

“…Figure 3 shows the effect of γ 1 on the flux versus time profile. As previously discussed,1, 7 γ 1 is associated with the effect of polymer swelling on the diffusion process. To show the significant role of γ 1 , we choose $ \gamma_{2} =1, \gamma_{3} =0, \alpha = -1 $ .…”

“…The other dimensionless time γ 3 is associated with a polymer retardation time,1, 7 related to creep behavior 11, 12. Thus, γ 3 is a time scale associated with the swelling process, whereas γ 2 , is associated with the relaxation process.…”