Micellar ultrafiltration in an unstirred batch cell at constant flux

Abstract

An unsteady mass-transfer model is developed to describe the ultrafiltration of micellar surfactant solutions in an unstirred batch cell at constant flux. Excellent agreement between the model and new experiments for asymmetric polyethersulfone membranes [5000 and 50,000 molecular weight cutoff (MWCO)] with aqueous hexadecyl (=cetyl)pyridinium chloride (CPC) solutions in 0.01 M NaCl allows quantitative characterization of the intrinsic membrane rejection properties for both surfactant monomer and micelles, and supports the physics at the membrane surface presumed in the model. The 5000 MWCO membrane rejects all of the micelles (hydrodynamic radius ≈2.5 nm) and most of the singly dispersed surfactant molecules, or monomers (hydrodynamic radius ≈0.42 nm); the intrinsic rejection coefficient of this membrane for micelles is 1.0 and for monomers 0.80. For the 50,000 MWCO membrane, two pore types are necessary to explain the observations. The small-pore intrinsic rejection coefficients for monomers and micelles are 0.75 and 1.0, respectively, while the large-pore rejection coefficients are 0.4 and 0.85, respectively. At least 88% of the permeate flow for the 50,000 MWCO membrane is through pores that completely reject micelles. More of the monomers and micelles are sieved by the membranes than is expected from their advertised molecular weight cutoffs. Calculations of intrinsic rejection using estimates of pore and solute size indicate qualitatively that repulsive electrostatic interactions and surfactant adsorption significantly influence rejection.