Nonelectrostatic interactions as random fields in charged liquids

We derive an equation capable of treating both electrostatic and nonelectrostatic interactions in charged liquids. The resulting equation is a complex version of the Poisson-Boltzmann equation, where nonelectrostatic interactions are represented as random fields through field theory. Consequently, the nonelectrostatic interactions of ions in charged liquids can be easily simulated by generating random numbers in accordance with these random fields. To solve the equation, we employ the finite element method. The nonelectrostatic interactions incorporated into the equation are general. In this study, we take the steric effect of ions as an example. The results show that the equation can capture the steric effect clearly. The steric effect excludes ions at the boundaries and alters the ion distribution within the bulk domain. In charged liquids with screening domains intersected, the steric effect in the bulk diminishes the steric effect at the boundaries.