Diffusion of Solute Atoms in an Evaporated Liquid Droplet

Controlling the evaporation of a solvent has made it possible to grow crystals, nanoparticles, and microparticles from liquid droplets. At the heart of this process is the evaporation-induced diffusion of solute atoms, causing the liquid solution of the solute atoms to be in a supersaturated state. In this work, we analyze the mass transport in a spherical liquid droplet, which experiences the loss or evaporation of the solvents across the droplet surface. Using a pseudo-steady-state method, two approximate solutions are derived for the moving boundary problem: one is a linear function of the square of radial variable with a constraint to the loss rate of the solvent, and the other is an exponential function of the square of radial variable without any constraint to the loss rate of the solvent. The numerical results obtained from both approximate solutions are in accord with the numerical results from the finite element method, validating the approximate solutions. The results reveal that a small evaporation/loss rate of the solvent is needed to maintain a relatively uniform distribution of solute atoms in a liquid droplet during the solvent evaporation/loss.