A new method for the fabrication of well-defined nanostructured deposits by evaporation-driven directed self-assembly of nanoparticles is proposed and studied theoretically. The technique comprises a film of suspended nanoparticles drying with its surface in contact with a topographically patterned membrane which promotes spatially varying evaporation, resulting in a patterned deposit. Membrane thickness and topography (in conjunction with the initial film height and concentration) allow the feature and residual layer dimensions to be controlled independently. Numerical solutions of equations governing the dynamics of the process show how the concentration profile evolves as a result of flow driven by heterogeneous evaporation. Analysis yields bounds on the dimensions of the dried deposit, and provides processing parameters to achieve specific patterns. It is estimated that films with 10 nm to 100 μm features can be fabricated with a drying time of 0.1-10 seconds per 10 μm of feature height above the residual layer (depending on membrane thickness), making this a promising method for high throughput pattern deposition.