Confined fluids at moderate densities

Replacing on the left side of this expression T /knT as before by employing again the equation of state in Eq. (4.28), it is a simple matter to show that 

However, in the limit p — 0, the mean-field treatment must be consistent with the one developed in Section 5.7.4. From Eq. (5.184) w e see that in this limit 

This latter expression can be derived independently by expanding in the mean-field equation of state (see Eq. (4.28)] the term 1/(1 — bp) bp 1) in a MacLaurin series according to 

Inserting this expansion into the mean-field equation of state and considering only terms up to second order in density, one can show that 

As we already demonstrated that the mean-field treatment developed in Section 4.2.2 is capable of describing, for instance, capillary condensation in nanoscopic porous media in a qualitatively correct fashion (see Section 4.2.4), the above discussion permits us to draw some important preliminary conclusions concerning the Joule-Thomson effect in confined fluids. These conclusions, bolstered further by corresponding MC data to be presented below in Sections 5.7.8 and 5.7.9, can be summarized as follows  

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