One of the most restricting uncertainties in the use of the two-fluid models in multiphase computations comes from the solid phase boundary conditions. Typically, the fluid boundary condition at a solid wall is the so called no-slip condition, which has become the cornerstone of single-phase fluid dynamics. By analogy, similar no-slip conditions or variations of them, such as partial slip, are also applied as the boundary conditions of the solid phase (or phases) at impermeable walls in two-fluid model computations. However, and given that the solid phase is subject to the gravitational force, there is not a physical reason as to why the no-slip condition should apply to fine or coarse particles and there are no detailed experiments or simulations that support such a hypothesis. We have undertaken a study, to determine what is the behavior of particles near solid, impermeable walls and what are the velocities of the particles at the plane where their boundary conditions are prescribed (one particle radius far from the wall). This will help prescribe the correct boundary conditions for the solid phase of a multiphase mixture and will remove a cause of uncertainty in particulate modeling. The study is based on Direct Numerical Simulations (DNS) of a dense particulate flow and the results pertain to both dilute and dense mixtures. Since the model of particle-wall interactions/collisions is important in the results, the computations include the parameters of the particle-wall interaction model of DNS. The results show that the solid-phase velocity at a vertical wall is clearly negative, in the direction of gravity, and that the absolute value of the velocity depends primarily on the size of the particles. (c) 2011 Elsevier BM. All rights reserved.