Modeling of solid particle formation during solution aerosol thermolysis: The evaporation stage

The evaporation state of solution aerosol thermolysis (SAT) was modeled to study the effect of various parameters on solid particle formation by solute precipitation. A comparison of the characteristic time constants for various processes demonstrated that droplet shrinkage and solute diffusion are the slowest processes, and that the fast processes, i.e., vapor diffusion and heat conduction in the gas phase and the liquid phase, can be assumed to have reached steady state. Differential equations for these faster processes were thus simplified and were solved numerically along with a modified solute diffusion equation, using an explicit first-order finite difference scheme. The computations were done until the solute concentration at the droplet surface reached the critical supersaturation. Then, if the solute concentration at the droplet center is higher than the equilibrium saturation, volume precipitation is proposed to occur. Solutes with a large difference between critical supersaturation and equilibrium saturation were observed to favor volume precipitation. High initial concentrations and low ambient temperatures were demonstrated to favor volume precipitation. Percolation theory was invoked to provide insights about the space filling capacity of the precipitated solids, and a second criterion, the percolation criterion, for solid particle formation was proposed; the solute concentration at the droplet center should be high enough so that the volume fraction of the precipitated solids is higher than the critical volume fraction. Volume precipitation only ensures that there are precipitated solids at the droplet center. The percolation criterion ensures that there is a sufficient volume of precipitated solids at the droplet center to form a coherent three-dimensional network. For solid particle formation by SAT, both the volume precipitation and the percolation criteria must be satisfied.