General theory of tracer-diffussion in colloidal suspensions

In this work we derive a generalized Langevin equation that describes the translational Brownian motion of a tracer particle which interacts with other diffusing particles in the system. The direct interactions of the tracer with these other diffusing particles give rise to memory effects described by a time-dependent friction. The main result of this work is a general and exact expression for this friction function which admits the possibility that the tracer is non-spherical, and that the particles diffusing around it are not of a single species, although they are assumed spherical.