EFFECT OF SURFACE HETEROGENEITIES ON CONDENSATION ON AN AEROSOL PARTICLE

Aerosol particles undergo a multitude of interactions with background gases and vapors as a result of their comparatively large surface areas and long residence times in suspension. These interactions, in turn, modify the physical and chemical properties of the particles, including those properties that affect their toxicity. While the importance of these interactions has always been recognized, the subject has assumed even greater importance with the recent recognition of PM-2.5 inhalation related effects. Here, the comparatively larger surface areas of the smaller particles dictate the existence of a quasi-two-dimensional diffusion/adsorption mechanism at the gas–surface boundary. This implies a strong dependence of particle growth rates on the local nature of the often complex and highly variable surface properties of the particles as well as on their morphologies. Both natural and anthropogenic aerosols are equally affected. We develop a mathematical formulation based on the diffusion model approximation which permits the introduction of surface heterogeneities via a surface-dependent jump boundary condition. This boundary condition for the particle surface expresses the diffusant concentration in terms of the product of a surface dependent “jump” function and the normal derivative of the diffusant concentration (i.e. the condensation current). Then, a Green’s function technique is applied to reduce the 3-D problem to a 2-D problem for the particle surface. Here, singularity removal is used to formulate an integro-differential equation which can be solved by numerical techniques. In particular, a numerical formulation based on Gauss–Legendre quadratures of the surface is applied to a spherical particle with an axisymmetric distribution of alternating rings of high and low adsorption. In addition to the global condensation rate on a sphere, local condensation currents at solution sites determined by the nodes of Gauss–Legendre quadratures were calculated. The results demonstrate consistency with a related investigation in which Berg and Purcell calculated the diffusive intake current for a bio-aerosol with a uniform distribution of perfect sink absorption sites sparsely distributed throughout the cell wall ( Biophysical J. 20, 193–218, 1977).