Statistical physics methods are applied to analyze a fluid particles flow in an attempt to avoid the over-detailed knowledge of the hydrodynamic interactions. The fluid is considered as a steady source of energy which controls the particle agitation, like a thermostat in molecular physics. This method was applied to a flow previously studied with the help of three-dimensional visualizations in which spherical particles fell down into a fluid in a square section channel. This flow is characterized by a solid volume fraction of 5% and a particle Reynolds number around 4. Schematically the beads are divided into free beads and beads involved in chain caused par wakes interactions. These wake effects explain the non-Maxwellian behavior of the solid phase. The wall influence on the normal velocity component is taken into account by an interaction potential related to the kinetic energy and the distance from the wall. (c) 2007 Elsevier B.V. All rights reserved.