March 2013
Intermediate to advanced
406 pages
14h 48m
English
Content preview from Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
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192 Perturbation Theories for Fluids and Solids
7.5.2 PERCUS–YEVICK THEORY FOR ADDITIVE HARD-SPHERE
FLUID MIXTURES
The solution of the PY theory for the RDF and the EOS of a pure HS fluid was
generalized by Lebowitz (1964) to an m-component mixture of AHS. The PY closure
(4.15) for mixtures transforms into
c
ij
(
r
)
= f
ij
(
r
)
y
ij
(
r
)
, (7.77)
where f
ij
= e
−βu
ij
(r)
−1 is the Mayer function for the pairs ij. For an AHS mixture,
f
ij
(
r
)
=
0, r < σ
ij
1, r > σ
ij
. (7.78)
Taking into account this relationship, together with the definition of the cavityfunction
y
ij
(r) = g
ij
(r)e
βu
ij
(r)
for pairs ij, from Equation 7.77 the following conditions, similar
to those in Equation
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