Ballone-Pastore-Galli-Gazzillo

The Ballone-Pastore-Galli-Gazillo (BPGG) (1986) (Eq. 3.8 Ref. 1) closure relation, developed for mixtures of hard spheres, is given by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(r)=\left[ 1+s\gamma \left( r\right) \right] ^{1/s}-1-\gamma \left(r\right) }

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=15/8} . It has its origins in the Martynov-Sarkisov closure ($s=2$). The value of $s$ can be determined by a self-consistency condition. Notice that for $s=1$ the BPGG approximation reduces to the hyper-netted chain closure.

References

1. P. Ballone; G. Pastore; G. Galli; D. Gazzillo "Additive and non-additive hard sphere mixtures" Molecular Physics, 59 pp. 275-290 (1986)