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

Abstract

Deposition rates on solid targets cooled far below the dew point of undersaturated, dilute binary vapor and hot gas mainstreams have recently been found to be reduced and sharply surface temperature dependent compared to their pure vapor deposition counterparts. A rational yet tractable theory to account for such observations is formulated and exploited in particular cases of current practical interest; e.g. the deposition of trace multiple alkali sulfate vapors present in flowing combustion products. Our physicochemical model is based on the formation of a binary solution condensate aerosol near the deposition surface, with the resulting droplets collected by the mechanism of thermophoresis. The binary vapors, assumed here to be in local equilibrium with the solution aerosol phase, are collected by the familiar mechanism of Fick (concentration) diffusion across the prevailing laminar boundary layer (LBL) but we do not make the restrictive assumption that the Fick diffusivities are equal to the energy diffusivity of the carrier gas. As by-products of our calculation of the total (aerosol + vapor) deposition rate we obtain the BL position of condensation onset, as well as the structure of the LBL on either side of this binary “fog-locus”. Illustrative predictions are shown for the effects of Na 2SO 4(g) addition on salt deposition rates from combustion product streams containing a fixed amount of K 2SO 4(g), on the assumption that the resulting Na 2SO 4 + K 2SO 4 droplets form nearly ideal solutions, having droplet thermophoretic diffusivities within two decades of the host gas momentum diffusivity, v. With systematic corrections for the effects of (a) alkali salt vapor dissociation/equilibrium chemical reaction with the hydrocarbon combustion products and (b) slight solution non-ideality, the present theoretical formalism should be useful in accounting for binary nucleation onset effects observed in recent deposition rate experiments using alkali-seeded atmospheric pressure flat flames.