Analytical structure factor of a two-species polydisperse Percus-Yevick fluid with bimodal Schulz distributed diameters

An analytic expression is obtained for the static structure factor $S(k)$ of a two-species polydisperse fluid of hard spheres in the Percus-Yevick approximation. The size polydispersity is included via a bimodal Schulz distribution. The derived expression is used to study the effects on $S(k)$ of the size polydispersity in a equiatomic binary mixture of hard-spheres. The main features of the effects are (1) the damping of the oscillations in $S(k)$ beyond its principal peak and larger values of $S(k)$ in the long-wavelength limit, relative to the monodisperse case; and (2) the stronger effect of the species with the larger average particle size.