Joint effect of advection, diffusion, and capillary attraction on the spatial structure of particle depositions from evaporating droplets

A simplified model is developed, which allows us to perform computer simulations of the particles transport in an evaporating droplet with a contact line pinned to a hydrophilic substrate. The model accounts for advection in the droplet, diffusion and particle attraction by capillary forces. The parameters chosen correspond to the experiments of Park and Moon [Langmuir 22, 3506 (2006)], where an annular deposition and snakelike chains of colloid particles have been identified. We find that the annular sediment is formed by advection and diffusion transport. The close packing of the particles in the sediment is possible if the evaporation time exceeds the characteristic time of diffusion-based ordering. The chains are formed by the end of the evaporation process due to capillary attraction of particles in the region bounded by a fixing radius, where the local droplet height is comparable to the particle size. At the beginning of the evaporation, the annular deposition is shown to expand faster than the fixing radius moves. However, by the end of the process, the fixing radius rapidly outreaches the expanding inner front of the ring. The snakelike chains are formed at this final stage.