The Hydrodynamic Radius of Particles in the Hybrid Lattice Boltzmann-Molecular Dynamics Method

We address the problem of the consistency of different measures of the hydrodynamic radius of solid point and composite solute particles incorporated into the hybrid lattice Boltzmann--molecular dynamics (LBMD) multiscale method. The coupling between the fluid and the particle phase is naturally implemented through a Stokesian type of frictional force proportional to the local velocity difference between the two. Using deterministic flow tests such as measuring the Stokes drag, hydrodynamic torques, and forces we first demonstrate that in this case the hydrodynamic size of the particles is ill-defined in the existing LBMD schemes. We then show how it is possible to effectively achieve the no-slip limit in a discrete simulation with a finite coefficient of the frictional force by demanding consistency of all these measures, but this requires a somewhat modified LB algorithm for numerical stability. Having fulfilled the criteria, we further show that in our consistent coupling scheme particles also obey the macroscopically observed fluctuation-dissipation theorem for the diffusion coefficient of a single particle without any adjustable parameters. In addition, we explicitly show that diffusion alone is not a good criterion for calibration of the frictional coupling.Peer reviewe