Polymer solutions under steady solvent flow between two semipermeable interfaces

Pressure differentials across polymer solutions cause fluid flow. We develop a theory for the spatial variation of polymer concentration in solutions under steady flow between two interfaces permeable to the solvent but not to the polymer. The balance between the external pressure gradient and the osmotic pressure gradient of the polymer solution determines the concentration profile, which increases from the solvent inlet towards the solvent outlet. We find that even if the solution is dilute on average, a semidilute region with overlapping polymers could develop near the outlet. Conversely, even if the solution is semidilute on average, a dilute region with non-overlapping polymers could develop near the solvent inlet. The spatial dependence of polymer concentration implies that polymer dynamics could be significantly slower at the outlet. We apply our theory to the distribution of mucin polymers in human airway mucus. This work suggests that although the average mucin concentration could be near overlap in healthy physiological conditions, water evaporation causes a layer of higher mucin concentration near the air-mucus interface and a dilute mucus layer near the cell surface. On the other hand, even if the average mucin concentration in some diseased states might compress the periciliary layer (PCL), the evaporation-driven redistribution of mucins could sufficiently decrease the concentration near the PCL, delaying the onset of PCL collapse and permitting mucociliary clearance.