Title: Diffusion under confinement: hydrodynamic finite-size effects in simulation,
Abstract: We investigate finite-size effects on diffusion in confined fluids using
molecular dynamics simulations and hydrodynamic calculations. Specifically, we
consider a Lennard-Jones fluid in slit pores without slip at the interface and
show that the use of periodic boundary conditions in the directions along the
surfaces results in dramatic finite-size effects, in addition to that of the
physically relevant confining length. As in the simulation of bulk fluids,
these effects arise from spurious hydrodynamic interactions between periodic
images and from the constraint of total momentum conservation. We derive
analytical expressions for the correction to the diffusion coefficient in the
limits of both elongated and flat systems, which are in excellent agreement
with the molecular simulation results except for the narrowest pores, where the
discreteness of the fluid particles starts to play a role. The present work
implies that the diffusion coefficients for wide nanopores computed using
elongated boxes suffer from finite-size artifacts which had not been previously
appreciated. In addition, our analytical expression provides the correction to
be applied to the simulation results for finite (possibly small) systems. It
applies not only to molecular but also to all mesoscopic hydrodynamic
simulations, including Lattice-Boltzmann, Multi-Particle Collision Dynamics or
Dissipative Particle Dynamics, which are often used to investigate confined
soft matter involving colloidal particles and polymers.