A DIRECT DERIVATION OF THE PROFILE EQUATIONS OF BUFF-LOVETT-MOU-WERTHEIM FROM THE BORN-GREEN-YVON EQUATIONS FOR A NONUNIFORM EQUILIBRIUM FLUID

A functional approach to the Born-Green-Yvon hierarchy is developed ou t of the observation that the configuration-space integral defining th e free energy of a non-uniform equilibrium fluid is invariant with res pect to local coordinate transformations. Interpreting such a coordina te transformation as a deformation leads to the identification of this hierarchy as a force balance relation between the inter-molecular for ces and the external forces representing the external constraints impo sed on the system. Using the invariance for translations and rotations of the inter-molecular forces, it is shown that the profile equations of Buff-Lovett-Mou-Wertheim can be obtained by taking appropriate mom ents of the Born-Green-Yvon equations.