Compound redistribution due to droplet evaporation on a thin polymeric film: Theory

A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to continuous leaching in addition to the evaporation of the droplet. This may eventually lead to an inversion of the transport process and a redistribution of the compounds within the thin film. In order to gain an understanding of the compound redistribution, we apply a macroscopic model for the evaporation of a droplet and combine that with a diffusion model for the compound transport. In the model, material deposition and the resulting contact line pinning are associated with the precipitation of a fraction of the dissolved material. We find three power law regimes for the size of the deposit area as a function of the initial droplet size, dictated by the competition between evaporation, diffusion, and the initial compound concentrations in the droplet and the thin film. The strength of the contact line pinning determines the deposition profile of the precipitate, characterized by a pronounced edge and a linearly decaying profile toward the center of the stain. Our predictions for the concentration profile within the solid substrate resemble patterns found experimentally.