A model of Brownian dynamics for colloidal suspensions

A model for the exact treatment of a suspension of heavy particles is presented. The model consists of a one-dimensional set of suspended particles in a harmonic oscillator assembly. It is shown that in the double limit as the ratio of the masses (M) of the heavy particle to the particle of the medium goes to infinity and as the time t goes to infinity, such that τ = t/M is finite, the suspended particles are described by Langevin equations. The interaction between the suspended particles and the harmonic interaction matrix are completely arbitrary. The friction and diffusion constants are obtained in terms of the value at zero frequency of the spectrum of normal modes of the assembly, a quantity that depends on the distribution of the suspended particles.