The paper is concerned with the prediction of the deposition rate of small particles from two-dimensional turbulent gas flows onto solid boundaries using a fully-Eulerian two-fluid approach. Density-weighted averaging is used to derive the ensemble-averaged particle equations which are closed with simple models for the particle turbulence correlations. A possible inconsistency in the modelling is discussed. A special method of handling the equations provides much clearer insight into the physical processes governing deposition. The solution procedure uses a formulation which can automatically capture particle-free regions and can predict surface deposition rates which may vary by several orders of magnitude. This is illustrated via calculations of deposition from turbulent channel-flow which also allow prediction of the inlet region where the particle flow is not fully-developed. Deposition from turbulent boundary layers is also considered and calculations showing the interaction between velocity slip (caused by streamline curvature), viscous drag, diffusion and turbophoresis are presented. The ability to handle complex geometries is illustrated by a calculation of deposition in a gas turbine cascade. This also provides an illustration of how inertial and diffusional deposition mechanisms work in concert and how the sum of the contributions considered separately does not represent the total deposition rate. Some preliminary calculations and experimental data on the effect of thermophoresis in non-isothermal flows are also presented. (C) 2003 Elsevier Science Ltd. All rights reserved.