The electrical double layer in the Born-Green-Yvon equation

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Abstract
The first member of the Born-Green-Yvon hierarchy of integral equations is solved numerically for a system of charged hard spheres near a charged wall under two alternative closures. The first is analogous to the superposition approximation and yields results resembling those obtained from other integral equations. The second closure employs electroneutrality to approximate the dependence of the pair correlation function upon distances from the wall. This improved theory gives qualitatively different results which are in general agreement with the modified Gouy-Chapman theory over a wide range of charge densities on the wall.