  Particulate flows have been largely studied under the simplifying assumptions
of one-way coupling regime where the disperse phase do not react-back on the
carrier fluid. In the context of turbulent flows, many non trivial phenomena
such as small scales particles clustering or preferential spatial accumulation
have been explained and understood. A more complete view of multiphase flows
can be gained calling into play two-way coupling effects, i.e. by accounting
for the inter-phase momentum exchange between the carrier and the suspended
phase, certainly relevant at increasing mass loading. In such regime, partially
investigated in the past by the so-called Particle In Cell (PIC) method, much
is still to be learned about the dynamics of the disperse phase and the ensuing
alteration of the carrier flow.
  In this paper we present a new methodology rigorously designed to capture the
inter-phase momentum exchange for particles smaller than the smallest
hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. In fact,
the momentum coupling mechanism exploits the unsteady Stokes flow around a
small rigid sphere where the transient disturbance produced by each particle is
evaluated in a closed form. The particles are described as lumped, point masses
which would lead to the appearance of singularities. A rigorous regularization
procedure is conceived to extract the physically relevant interactions between
particles and fluid which avoids any "ah hoc" assumption. The approach is
suited for high efficiency implementation on massively parallel machines since
the transient disturbance produced by the particles is strongly localized in
space around the actual particle position. As will be shown, hundred thousands
particles can therefore be handled at an affordable computational cost as
demonstrated by a preliminary application to a particle laden turbulent shear
flow.
