Density profiles of hard spheres in a cylinder filled with disordered matrix: application of the Born–Green–Yvon equation

Local densities of a hard sphere fluid in a cylindrical pore filled with quenched disordered hard-sphere matrix are calculated using Born–Green–Yvon equation with Fisher–Methfessel approximation. The solution of replica Ornstein–Zernike equation in the Percus–Yevick approximation for a fluid in a homogeneous matrix is used as an input. A comparison of the density profiles with simulation data shows that the theory works satisfactorily for the considered matrix and fluid densities.