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

## TL;DR

This paper develops a macroscopic model to understand how compounds redistribute during droplet evaporation on thin polymer films, revealing power law regimes and deposit profiles consistent with experimental patterns.

## Contribution

It introduces a combined evaporation and diffusion model accounting for compound leaching, evaporation, and precipitation effects on thin polymeric films, which was not previously modeled in this detail.

## Key findings

- Identifies three power law regimes for deposit size based on initial conditions.
- Predicts deposit profiles with pronounced edges and linear decay towards the center.
- Model results align with experimental concentration patterns.

## Abstract

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 ongoing leaching in combination with 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, characterised by a pronounced edge and a linearly decaying profile towards the centre of the stain. Our predictions for the concentration profile within the solid substrate resemble patterns found experimentally.