(534a) Reconciling the Pore Flow and Solution-Diffusion Description of Swollen Membrane Transport | AIChE

(534a) Reconciling the Pore Flow and Solution-Diffusion Description of Swollen Membrane Transport

Authors 

Hegde, V. - Presenter, Columbia University
Squires, T., University of California at Santa Barbara
Doherty, M. F., University of California
Membrane transport is treated by two distinct fundamental models. The Pore flow model treats membranes with identifiable permanent pores from a fluid momentum transport approach capturing pressure gradient driven convective flow. By contrast, the Solution-diffusion model, developed to treat transport through homogeneous non-porous membranes, takes a mass transport approach describing activity gradient driven solvent diffusion. While both models are clearly appropriate for the membranes they were designed to treat, there has long been controversy over non-porous, but highly-swollen membranes. As continuous fluid channels form within the highly swollen polymer network a momentum balance describes pressure gradient driven convective flow. At the same time, the osmotically active network diffusively swells against the percolating solvent and a mass balance describes activity gradient driven binary diffusion.

As both mass and momentum must be conserved, we argue that both approaches must be appropriate for swollen membranes, and demonstrate that both provide identical predictions of transport. To do so, we turn to the 2-phase Fluid-solid model, developed by the gel dynamics community, which captures the mechanical coupling between the flowing fluid and deformable polymer network, balancing stresses and thus conserving momentum. The fluctuation-dissipation theorem connects the membrane’s mechanical response to the thermodynamic fluctuations of the polymer network, which captures the binary diffusion of the two components. This connects the Fluid-solid model directly to the Solution-diffusion model, yet remains consistent with the mechanical approach adopted by the Pore flow model. Apparent discrepancies between the predictions of the two are likewise resolved: the Fluid-solid model reveals a pressure gradient within the fluid phase, and an equal and opposite stress gradient in the polymer phase. Thus, the total stress is constant across the membrane. At the same time a concentration gradient emerges via the compression of the swollen gel. These results are consistent with both classical models.

The Fluid-solid model not only provides a link between mass and momentum transport approaches for swollen membranes, but is also capable of treating complex membrane morphologies where neither classical approach alone seems appropriate.

Figure 1: Pressure and solvent activity gradients across a highly swollen polymer membrane