The Nernst-Planck-Poisson finite difference method is used to simulate the dynamic evolution of a water-nitrobenzene system with initially equimolar concentrations of a monovalent salt present in both liquids. The effect of single ion partition coefficients on the evolution of the liquid junction is investigated. The results from simulations reveal two separable components of the potential difference, similar to the behavior observed in recent works on the dynamic theory of membrane potentials [Ward, K. R; et al. J. Phys. Chem. B 2010, 114, 10763-10773]: a localized static component purely dependent on the ratio of single ion partition coefficients and a dynamically expanding diffuse component dependent on the mean salt partition coefficient and the diffusion coefficients of the constituent ions.