Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled
model with random initial inputs in the fine particle regime are proved in this
paper. Such a model is a system coupling the incompressible Navier-Stokes
equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with
distinct particle sizes. The main analytic tool is the hypocoercivity analysis
for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with
uncertainties, considering solutions in a perturbative setting near the global
equilibrium. This allows us to obtain the error estimates in both kinetic and
hydrodynamic regimes