Hindered transport of spherical particles in cylindrical pores: The role of structural heterogeneity in rejection-permeability trade-offs

Abstract

Membrane separations rely on balancing rejection and permeability. Extensive work has clarified how pore structure and operating conditions control each quantity in idealized or weakly heterogeneous systems. However, it remains unclear how this trade-off emerges in strongly heterogeneous media, where coupled distributions of pore and particle sizes shape the local balance between advection and diffusion and generate substantial variability in performance among distribution realizations. Here we present a steric hindered-transport framework for spherical particles in cylindrical pores that explicitly resolves both single and coupled dual heterogeneity in size distributions. We show that the ensemble-averaged rejection increases with the particle-pore aspect ratio $\lambda$ and with the P\'eclet number $Pe$, while advection enhances steric exclusion by up to $\sim$20\% at intermediate $\lambda$. Dual heterogeneity broadens the distribution of effective $Pe$, increases the variability and incidence of anomalous rejection trends, while systematically shifting the rejection-permeability trade-off toward higher permeability at fixed rejection. These results suggest that controlled heterogeneity can serve as a design lever to expand the attainable operating space for simultaneous high selectivity and high throughput.