  We derive from the first principles Smoluchowski-Euler equations, describing
aggregation kinetics in space-inhomogeneous systems with fluxes. Starting from
Boltzmann equations, we obtain microscopic expressions for the aggregation
rates for clusters of different size, and observe that they significantly
differ from the currently used phenomenological rates. Moreover, we show that
for a complete description of aggregating systems, novel kinetic coefficients
are needed. These may be called ``flux-reaction'' and ``energy-reaction''
rates, as they appear, respectively, in the equations for fluxes and energy. We
report microscopic expressions for these coefficients. We solve numerically the
Smoluchowski-Euler equations for two representative examples -- aggregation of
particles at sedimentation, and aggregation after an explosion. The solution of
the novel equations is compared with the solution of currently used
phenomenological equations, with phenomenological rate coefficients. We find a
noticeable difference between these solutions, which manifests unreliability of
the phenomenological approach and the need of application of new,
first-principle equations.
