  We consider coupled models for particulate flows, where the disperse phase is
made of particles with distinct sizes. We are thus led to a system coupling the
incompressible Navier-Stokes equations to the multi-component
Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical
scheme to approximate the system. The scheme is based on suitable implicit
treatment of the stiff drag force term as well as the Fokker-Planck operator,
and can be formally shown to capture the hydrodynamic limit with time step and
mesh size independent of the Stokes number. Numerical examples illustrate the
accuracy and asymptotic behavior of the scheme, with several interesting
applications.
