RSOZ for polydisperse systems

For a polydisperse fluid, composed of $n_{f}$ components, in a polydisperse matrix, composed 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 n_m} components, written in matrix form in Fourier space (see Eq. 18 of Ref. 1):

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 \tilde H_{mm} = \tilde C_{mm} + \rho_m \tilde C_{mm} \tilde H_{mm}}

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 \tilde H_{fm} = \tilde C_{fm} + \rho_m \tilde C_{mm} \tilde H_{fm} + \rho_f \tilde C_{fm} \tilde H_{ff} - \rho_f \tilde C_{12} \tilde H_{fm} }

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 \tilde H_{ff} = \tilde C_{ff} + \rho_m \tilde C_{fm}^T \tilde H_{fm} + \rho_f \tilde C_{ff} \tilde H_{ff} - \rho_f \tilde C_{12} \tilde H_{12}}

${\tilde {H}}_{12}={\tilde {C}}_{12}+\rho _{m}{\tilde {C}}_{fm}^{T}{\tilde {H}}_{fm}+\rho _{f}{\tilde {C}}_{ff}{\tilde {H}}_{12}+\rho _{f}{\tilde {C}}_{12}{\tilde {H}}_{ff}-2\rho _{f}{\tilde {C}}_{12}{\tilde {H}}_{12}$

Note: 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 c_{fm} = c_{mf}^T} and 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 h_{fm} = h_{mf}^T} .

(PD. I am not sure about the equation 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 \tilde H_{fm}} )

References

1. S. Jorge; Elisabeth Schöll-Paschinger; Gerhard Kahl; María-José Fernaud "Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix", Molecular Physics 101 pp. 1733-1740 (2003)