Particle condensation in evaporative flows

Abstract

The problem of the steady evolution of a particle-laden vapour, or condensation aerosol, by a source evaporating into an open, unreactive atmosphere is considered. A slip-flow model of energy and mass flow at the surface is combined with a stagnant boundary-layer model of flow in the gaseous continuum to obtain a set of parameters sufficient for the complete solution of the evaporation-condensation problem. These parameters are: the pressure, the source and sink temperatures, the sink concentrations and the flux density of heat or mass from the source. In an initial analysis the curve of vapour saturation ratio (S) against temperature (T) across the layer is obtained and compared to the critical saturation ratio (SR) of nucleation theory to find the conditions necessary for the incipience of particle formation by spontaneous nucleation. Data for zinc distilling into argon are summarized on energy and mass flux diagrams and on a nucleation threshold diagram (the ‘F-diagram’). Possible uses forF-diagrams are envisaged, for example, in the design of manufacturing processes in which particles are produced by aerosol condensation, or, alternatively, where particle-free evaporation is to be achieved. The problem of two-phase flow is tackled numerically. Starting with values at the nucleation threshold as initial conditions, the mass and energy equations are solved by introducing Becker and Doering’s formula for the nucleation rate and the Stefan diffusion model for particle growth to calculate the local depletion of vapour by aerosol condensation. The rise and fall of supersaturation and the evolution of the particle size distribution are revealed as the calculation proceeds along the flow coordinate. Results are given for various combinations of the experimental variables, again with zinc-argon as example. To test predictions in detail, measurements are required on heat or mass transfer rates in suitably designed experiments. Insufficient data are available as yet but a brief overview of reported trends in particle type, size and concentration in metallic condensation aerosols is given and some rationalization attempted. The formation of crystalline particles by the vapour-solid and vapour-liquid-solid routes, which can result in important morphological differences in aerosol precipitates, is shown to depend on several factors, including the mass and energy flux densities at the vapour source.