Editing RSOZ
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Given and Stell (Refs 1 and 2) provided '''exact''' | Given and Stell (Refs 1 and 2) provided '''exact''' OZ equations for two-phase random media | ||
based on the original work of Madden and Glandt (Refs 3 and 4). | based on the original work of Madden and Glandt (Refs 3 and 4). | ||
For a two-species system, for the <math>(s+1)</math> replicated system one has (see Eq.s 2.7 --2.11 Ref. 2): | For a two-species system, for the <math>(s+1)</math> replicated system one has (see Eq.s 2.7 --2.11 Ref. 2): | ||
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:<math>h_{ff} = c_{ff} + \rho_m c_{fm} \otimes h_{mf} + \rho_f c_{ff} \otimes h_{ff} + (s-1) \rho_f c_{12} \otimes h_{12}</math> | :<math>h_{ff} = c_{ff} + \rho_m c_{fm} \otimes h_{mf} + \rho_f c_{ff} \otimes h_{ff} + (s-1) \rho_f c_{12} \otimes h_{12}</math> | ||
:<math>h_{12} = c_{12} + \rho_m c_{fm} \otimes h_{mf} + \rho_f c_{ff} \otimes h_{12} + \rho_f c_{12} \otimes h_{ff} + (s-2) \rho_f c_{12} \otimes h_{12} </math> | :<math>h_{12} = c_{12} + \rho_m c_{fm} \otimes h_{mf} + \rho_f c_{ff} \otimes h_{12} + \rho_f c_{12} \otimes h_{ff} + (s-2) \rho_f c_{12} \otimes h_{12} </math> | ||
In the limit of <math>s \rightarrow 0</math> these equations from the | In the limit of <math>s \rightarrow 0</math> these equations from the ROZ equations (see Eq.s 2.12 --2.16 Ref. 2): | ||
:<math>h_{mm} = c_{mm} + \rho_m c_{mm} \otimes h_{mm}</math> | :<math>h_{mm} = c_{mm} + \rho_m c_{mm} \otimes h_{mm}</math> | ||
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describes correlations between fluid particles in the same cavity and the | describes correlations between fluid particles in the same cavity and the | ||
function <math>h_b(x)</math> describes correlations between particles in different cavities. | function <math>h_b(x)</math> describes correlations between particles in different cavities. | ||
==References== | ==References== | ||
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#[http://dx.doi.org/10.1007/BF01028471 W. G. Madden and E. D. Glandt "Distribution functions for fluids in random media", J. Stat. Phys. '''51''' pp. 537- (1988)] | #[http://dx.doi.org/10.1007/BF01028471 W. G. Madden and E. D. Glandt "Distribution functions for fluids in random media", J. Stat. Phys. '''51''' pp. 537- (1988)] | ||
#[http://dx.doi.org/10.1063/1.462726 William G. Madden, "Fluid distributions in random media: Arbitrary matrices", Journal of Chemical Physics '''96''' pp. 5422 (1992)] | #[http://dx.doi.org/10.1063/1.462726 William G. Madden, "Fluid distributions in random media: Arbitrary matrices", Journal of Chemical Physics '''96''' pp. 5422 (1992)] | ||
[[Category: Integral equations]] | [[Category: Integral equations]] |