We study, turbophoresis--the clustering properties of heavy inertial
passive particles in a inhomogeneous turbulent flow--by direct
numerical simulation of inhomogeneously forced turbulence in a
periodic box without walls. The forcing is a periodic function of one
coordinate direction. The inertial particles cluster near the minima
of the turbulent kinetic energy. Drawing analogy with Soret effect in
near-equilibrium thermodynamics, we can describe the flux of particles
as a sum of two fluxes, described by two turbulent transport
coefficients, turbulent diffusion of particles and turbophoretic
coefficient. The second (turbophoretic) flux is assumed to be
proportional to the gradient of turbulent intensity. The ratio of
these two coefficients would be analogous to Soret coefficient, hence
we call this the turbulent Soret coefficient. Our numerical
calculation show that such a description is a good description of our
data. Furthermore, we find that the turbulent Soret coefficient is a
non-monotonic function of the particle inertia (described by the
Stokes number); i.e. beyond a critical Stokes number the clustering of
the particles decreases, but in a smooth manner.
