For a very dense binary liquid of hard spheres the dependence of the veloci
ty-autocorrelation function (VAF) of tagged particles and of the self-diffu
sion coefficient on system size is derived from the coupling of self diffus
ion to modes of collective flow. Collective flow is described by longitudin
al and transverse current-current correlation functions for different wavev
ectors which are obtained by molecular dynamics simulation. The size depend
ence of the VAF is reproduced rather accurately for longer times t > 7 tau,
where tau is the mean time of free flight. The result for the size depende
nce of the self-diffusion coefficient is in satisfactory agreement with a d
irect calculation, but this result also depends on the VAF's at shorter tim
es.