Perturbation theory of large-particle diffusion

A new theory is developed to study the effects of the granularity of a liquid on the diffusion of a large particle in the liquid. Inhomogeneous Langevin equations are expanded in powers of the size ratio between the solvent and large particles. From the expansion, we obtain hydrodynamic equations with new boundary conditions on the surface of the large particle in the first order. The new boundary conditions can be obtained from the radial distribution function between diffusing and solvent particles. The present theory is formulated by perturbation expansion and can thus deal with a large particle. In addition, using analytical solutions of hydrodynamic equations, we consider the effects of solvent particles at an infinite distance in contrast to the case for other methods. The theory is applied to a model radial distribution function, a hard-sphere system, and a Kihara potential system.