Size-Sieving Separation of Hard-Sphere Mixtures through Cylindrical Pores

The collision dynamics of hard spheres and cylindrical pores is solved exactly, which is the minimal model for a regularly porous membrane. Nonequilibrium event-driven molecular dynamics simulations are used to show that the permeability $P$ of hard spheres of size $\sigma$ through cylinderical pores of size $d$ follow the hindered diffusion mechanism due to size exclusion as $P \propto (1-\sigma/d)^2$. Under this law, the separation of binary mixtures of large and small particles exhibits a linear relationship between $\alpha^{-1/2}$ and $P^{-1/2}$, where $\alpha$ and $P$ are the selectivity and permeability of the smaller particle, respectively. The mean permeability through polydisperse pores is the sum of permeabilities of individual pores, weighted by the fraction of the single pore area over the total pore area.