Mesoscopic modeling of mass transport in viscoelastic phase-separated polymeric membranes embedding complex deformable interfaces

Layered Double Hydroxides (LDHs)

“…According to this model, the permeation in polymers consists of three steps as illustrated in Figure 18a (i) sorption of the permeant from the high concentration side onto the membrane/film surface, (ii) diffusion of the permeant along the concentration gradient through the membrane and (iii) desorption through evaporation from the low concentration surface of the membrane. When the permeating molecule interacts with the polymer, then the deviations from a gradient with a straight line can be observed and is known as non-Fickian diffusion explained by the diffusion-relaxation model [164,165].…”

The effect of the embedded interface dynamics on mass transport in immiscible polymer blends

“…To ensure such a coupling, the diffusion mass flux expression has been extended to include stresses, [7][8][9][10][11][12][13][14][15][16]18,19,24 conformation or Finger tensor 13,14,16,18,19 regarded thus as independent state variables. It has then become possible to successfully describe, to some extent, several experimental deviations from the classical Fickian behavior including Case II, 7,8,12,13 two-stage sorption, 10,23,24 overshoot, 6,13,23,24 and swelling. 13,18,19,23,24 Nonetheless, most of the abovementioned studies did not examine solvent diffusion into immiscible polymer blends embedding a deformable interface.…”

“…It has then become possible to successfully describe, to some extent, several experimental deviations from the classical Fickian behavior including Case II, 7,8,12,13 two-stage sorption, 10,23,24 overshoot, 6,13,23,24 and swelling. 13,18,19,23,24 Nonetheless, most of the abovementioned studies did not examine solvent diffusion into immiscible polymer blends embedding a deformable interface. In this context and inspired by past rheological models, [27][28][29] mesoscopic models have been proposed during the last two decades, 17,[20][21][22][23] in which the coupling arising among flow, diffusion, and interface deformation has been incorporated into the governing equations.…”

“…13,18,19,23,24 Nonetheless, most of the abovementioned studies did not examine solvent diffusion into immiscible polymer blends embedding a deformable interface. In this context and inspired by past rheological models, [27][28][29] mesoscopic models have been proposed during the last two decades, 17,[20][21][22][23] in which the coupling arising among flow, diffusion, and interface deformation has been incorporated into the governing equations.…”

“…Our goal in this contribution is to examine the unsteady isothermal mass transport of a solvent into a blend of two immiscible polymers embedding a macroscopic interface that deforms. In order to render past models, 17,[20][21][22][23] tractable for simulation techniques and easily confronted to available experimental data, we here offer, using the GENERIC formalism, [30][31][32] a phenomenological coarse-grained reformulation of previous models [20][21][22][23] based on the use of the area tensor N (see Appendix A and the section 3). The section 3 is devoted to the investigation of a unidirectional mass transport occurring in thin films through scaling analysis, numerical solutions, and comparison with sorption data selected from the literature.…”