Theory of surface deposition from a unary dilute vapor-containing stream allowing for condensation within the laminar boundary layer

Abstract

Deposition rates on targets cooled far below the dew point of undersaturated mainstreams have often been found to be surprisingly low and surface temperature dependent. A rational yet tractable theory to account for these observations is formulated and exploited in particular cases of current practical interest—e.g. the deposition of trace alkali sulfate vapors present in combustion products. The present physico-chemical model is based on the formation of a condensate aerosol near the deposition surface, with the resulting droplets (or particles) collected by the mechanism of thermophoresis [shown to be dominant, but previously neglected in related two-phase boundary layer (BL) analyses]. The vapor, assumed here to be in local equilibrium with the aerosol phase, is collected by the familiar mechanism of Fick (concentration) diffusion across the prevailing laminar BL(LBL), but the overly restrictive assumption D v ≌ α n (unity Lewis number) is not made. As by-products of the calculation of the total (aerosol + vapor) deposition rate the position of nucleation onset, as well as the structure of the LBL on either side of this “fog-locus”, are obtained. Encouraging agreement with limited available data on Na 2SO 4 deposition is obtained by assuming that the thermophoretic diffusivity of the resulting aerosol phase is about one decade smaller than the momentum diffusivity of the host combustion products.