The combustion of nano-aluminum and water mixtures is studied theoretically for a particle size of 80 nm and over a pressure range of 1-10 MPa. Emphasis is placed on the effects of entrainment and agglomeration of particles on the burning rate and its dependence on pressure. The flame thickness increases by a factor of similar to 10, when particle entrainment is considered. This lowers the conductive heat flux at the ignition front, thereby reducing the burning rate. The pressure dependence of the burning rate is attributed to the changes in the burning time and velocity of particles with pressure. In the diffusion limit, the pressure exponent increases from 0 to 0.5, when the entrainment index increases from 0 to 1.0. A similar trend is observed in the kinetics-controlled regime, although the corresponding value exceeds the diffusion counterpart by 0.5. The kinetics-controlled model significantly over-predicts the burning rate and its pressure exponent, depending on the entrainment index. The present analysis suggests that nano-particles formed closely-packed agglomerates of diameter 3-5 mu m, which may burn under diffusion-controlled conditions at high pressures. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved