The flux decline during the unstirred ultrafiltration of dissolved macromolecular solutions such as polyethylene glycol and dextran solutions was measured at different pressures from I to 4 x 105 Pa and different bulk concentrations from 0.1 to 0.55 kg/m3 with three types of polysulfone membranes. On the basis of the concept that a concentrated solution layer (not a gel layer) is formed on the membrane surface, the hydraulic resistance of the boundary layer was defined with the help of solvent permeability of dissolved macromolecules. The cake filtration theory was employed to analyze the flux decline behaviour. This simple theory worked well and the effective boundary layer concentrations calculated with the boundary layer resistance model developed here were physically quite reasonable. The calculated boundary layer concentrations depend on the applied pressure. The origin of this dependency might be the step concentration profile assumed in the cake filtration theory.
Nakao, S., Wijmans, J. G., & Smolders, C. A. (1986). Resistance to the permeate flux in unstirred ultrafiltration of dissolved macromolecular solutions. Journal of membrane science, 26(2), 165-178. https://doi.org/10.1016/S0376-7388(00)80061-7