Long-time decay of the translational/rotational velocity autocorrelation function for colloidal particles in two dimensions

In this work, the previously developed LB-DF/FD method has been extended to non-spherical particle suspensions in two dimensions. The calculated translational/rotational velocity autocorrelation function (VCF/RVCF) for the circular particles completely reproduces the theoretical predictions, i.e. the long-time decay of (t√lnt)−1 for the VCF and the long-time decay of t−2t−2 for the RVCF. Extensive numerical simulations of the elliptical and rectangular particles also confirm the theoretical results. On the basis of the reduced RVCFs and VCFs for the three kinds of particles, we conclude that the coefficients of the long-time tails of the RVCF and VCF are independent of the particle shape.