  We investigate the large-scale transport properties of
quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean
periodic or steady ergodic flows. We show how to compute large-scale indicators
such as the inertial-particle terminal velocity and eddy diffusivity from first
principles in a perturbative expansion around the limit of added-mass factor
close to unity. Physically, this limit corresponds to the case where the mass
density of the particles is constant and close in value to the mass density of
the fluid which is also constant. Our approach differs from the usual
over-damped expansion inasmuch we do not assume a separation of time scales
between thermalization and small-scale convection effects. For general
incompressible flows, we derive closed-form cell equations for the auxiliary
quantities determining the terminal velocity and effective diffusivity. In the
special case of parallel flows these equations admit explicit analytic
solution. We use parallel flows to show that our approach enables to shed light
onto the behavior of terminal velocity and effective diffusivity for Stokes
numbers of the order of unity.
