Ballone-Pastore-Galli-Gazzillo
The Ballone-Pastore-Galli-Gazillo (BPGG) (1986) (Eq. 3.8 Ref. 1) closure relation, developed for hard sphere mixtures, 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 (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=2} ). The value of 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} can be determined by a self-consistency condition. Notice that for 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=1} the BPGG approximation reduces to the hyper-netted chain closure.