This work studies the influence of phoretic motion (thermophoresis and diffusiophoresis) of fine alumina particles ("smoke") produced during the combustion of aluminum. Direct numerical simulations on a single aluminum droplet burning in a quiescent environment suggest that thermophoresis is the main mechanism driving smoke back to the aluminum surface, hence a major contributor to the oxide lobe development. The presence of this lobe is found to distort the flowfield, which favors hot and smoke-rich regions closer to the lobe, thereby enhancing thermophoresis. This combination of aerodynamic and thermophoretic effects leads to a mass rate of deposited smoke which is consistent with experimental data. A simplified model, deduced from simulation results, is able to predict the size of the final oxide residue in good agreement with measurements. This study supports that aluminum oxide present on the burning aluminum particle is largely due to material formed in the flame, subsequently desposited by thermophoresis.