Concentration dependence of long-time tails in colloidal suspensions

Long-time tails in the velocity autocorrelation functions of colloidal particles immersed in fluid have been predicted for some time, and recently observed in experiments using diffusing-wave spectroscopy. We compute the linear effect of finite concentration of particles on the low-frequency (1/2) correction to the mobility of one colloidal particle, and hence the effect on the long-time tails, using a reflection method. The results are consistent with general arguments for the form of long-time tails in an effective medium.