The dynamics of nanoparticles in complex fluids are of great interest for applications in drug delivery, oil recovery, and materials processing. Particle mobility is well described by the generalized Stokes-Einstein (GSE) relation when the nanoparticles are much larger than the polymers. Violations of GSE predictions are observed, however, when the size of nanoparticles is comparable to or smaller than length scales in polymer solutions . We investigate the microscopic origin of this anomalous behaviour using multi-particle collision dynamics (MPCD) , an advanced algorithm for rigorously modelling solvent-mediated hydrodynamic interactions in coarse-grained, mesoscale simulations. We apply MPCD to study transport in nanoparticle-polymer systems and the effects of many-body hydrodynamic interactions on this behaviour. We demonstrate that the translational centre-of-mass motions of both nanoparticles and polymers are sub-diffusive on short times before transitioning into a diffusive regime on longer time scales . The long-time diffusivities of nanoparticles collapse according to scaling predictions , in accord with recent experiments . The sub-diffusive behaviour predicted by MPCD simulations, by contrast, agrees with experiments , but significantly deviates from theoretical predictions. We show that this disagreement is due to a hitherto unreported transport mechanism characterized by the tight coupling of the translational motions of the nanoparticle and polymer centres-of-masses, which is not accounted for in current theories. Finally, we investigate the influence of polymer flexibility on particle transport. As the persistence length of the polymers increases, the nanoparticle dynamics become more subdiffusive and decouple from the dynamics of the polymer chain centre-of-mass .
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