Abstract
The theoretical model presented in this work allows quantitative prediction of the rate of Brownian coagulation of pollutant particles on a condensing aerosol droplet. The coupling of the processes of condensation and Brownian coagulation is established through the hydrodynamic-diffusiophoretic force acting upon the Brownian particles in the vicinity of the droplet. The new analytical approach is based on the Grad's moment method of solution to the Fokker Planck equation. The aerosol system is assumed to be isothermal and close to the thermodynamic equilibrium (i.e., the condensation and coagulation fluxes are small). The numerical predictions of the diffusiophoretic enhancement of Brownian coagulation rates are provided for NaCl-water droplets capturing small (primary) soot particles. The results of calculations show substantial enhancement (10 to 200 times) of the capture of soot particles by the condensing marine droplets for typical conditions that occur on the north-eastern coast of the U.S.A.
Highlights
The coupling of the processes of condensation and Brownian coagulation is established through the hydrodynamic-diffusiophoretic force acting upon the Brownian particles in the vicinity of the droplet
The numerical predictions of the diffusiophoretic enhancement of Brownian coagulation rates are provided for NaCl-water droplets capturing small soot particles
The presented theoretical model of Brownian coagulation in a presence of a hydrodynamic force allows estimating the rate of capturing (“filtering”) of particulates by fog droplets
Summary
The presented theoretical model of Brownian coagulation in a presence of a hydrodynamic (diffusiophoretic) force allows estimating the rate of capturing (“filtering”) of particulates by fog droplets. The Fokker-Planck equation with an external force has been reformulated in terms of Grad's thirteen-moments by Huang and Seinfeld (1990) for studies of Brownian coagulation of interacting aerosol particles. The above boundary conditions together with the derived by Huang and Seinfeld (1990) relations between the half-range fluxes and full-range moments for Brownian particles in an external force field, lead to the following set of equations for the dimensionless moments at the surface of the absorbing droplet (indicated with the subscript, s). In the condensation-free limit, b→0, the flow of Brownian particles in the vicinity of the aerosol droplet is expressed by the following equations:. This is a new formula for the potential-free Brownian coagulation flux. The above expression for the enhanced coagulation rate becomes of the same form as the one derived by Derjaguin and Dukhin (1959)
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