Solution of the Ornstein-Zernike equation in a hard-sphere Yukawa liquid containing an arbitrary-size hard sphere: a simple mean-spherical-approximation solution and free energy of forming a cavity

The simple mean-spherical-approximation solution of the Ornstein-Zernike equation in a hard-sphere Yukawa liquid containing an arbitrary-size sphere is presented. The surface density of liquid particles on the sphere is expressed in terms of a simple function of a set of parameters. On the basis of this density expression, the work of forming a cavity from the point cavity in the liquid is calculated, and expressions for the pressure, the surface tension and the Tolman length are obtained.