A comprehensive model is proposed for multiphase DNS simulations of gas-solid systems involving particles of size comparable to the mean free path of the gas and to that of the bounding geometry. The model can be implemented into any multiphase Direct Numerical Simulation (DNS) method. In the current work, the Volume of Fluid (VOF) method is used, and it is extended to allow for the incorporation of rarefaction effects. For unbounded flow, the model is in excellent agreement with experimental data from the literature. For flows in closed conduits, the model outperforms the alternate approach of using a slip boundary condition at the particle surface for the most relevant degrees of rarefaction and confinement. The proposed model is also able to correctly handle particle-particle interception. The model is intended for low particle Reynolds number flows, and can be applied to resolve in great detail phenomena in a large number of industrial applications (such as filtration of fine particles in porous media). (C) 2011 Elsevier Ltd. All rights reserved.