A Numerical Determination of the Efficiency with Which Spherical Aerosol Particles Collide with Spherical Water Drops Due to Inertial Impaction and Phoretic and Electrical Forces

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  • 1 Department of Atmospheric Sciences, University of California, Los Angeles 90024
  • | 2 Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada
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Abstract

A theoretical model to compute the efficiency with which aerosol particles of radius 0.5≤r≤10 μm collide with water drops of radius a=42, 72, 106, 173, 309 and 438 μm falling at terminal velocity in air is presented. Inertial impaction, thermophoresis, diffusiophoresis and electrical effects are considered. The computations were carried out for ambient conditions of 10°C, 900 mb, and 100%, 95% and 75% relative humidity. The drops and particles were assumed to carry electric charges of 0.2 a2 and 0.2 r2 [esu], respectively, and charges of 2.0 a2 and 2.0 r2 [esu], respectively, where a and r are expressed in centimeters. The external electric field strengths were assumed to range between 0≤E0≤3×105 V m−1. The results of our computations show 1) that the efficiency E with which aerosol particles collide with the drops considered is significantly raised by phoretic and electric forces over and above the efficiency resulting from inertial impaction, this effect being the more pronounced the smaller the collector drop; 2) hydrodynamic effects as well as phoretic effects tend to promote particle capture in the rear of a drop if particles are sufficiently small, resulting in a minimum of E versus r which lies in the “Greenfield gap” region and thus reinforces the gap; 3) electrical effects tend to eliminate this gap reinforcement; and 4) computations which consider phoretic effects only without simultaneously taking account of the particles’ motion due to the hydrodynamic flow around the collector drop significantly overestimate E for r≲1.5 μm.

Abstract

A theoretical model to compute the efficiency with which aerosol particles of radius 0.5≤r≤10 μm collide with water drops of radius a=42, 72, 106, 173, 309 and 438 μm falling at terminal velocity in air is presented. Inertial impaction, thermophoresis, diffusiophoresis and electrical effects are considered. The computations were carried out for ambient conditions of 10°C, 900 mb, and 100%, 95% and 75% relative humidity. The drops and particles were assumed to carry electric charges of 0.2 a2 and 0.2 r2 [esu], respectively, and charges of 2.0 a2 and 2.0 r2 [esu], respectively, where a and r are expressed in centimeters. The external electric field strengths were assumed to range between 0≤E0≤3×105 V m−1. The results of our computations show 1) that the efficiency E with which aerosol particles collide with the drops considered is significantly raised by phoretic and electric forces over and above the efficiency resulting from inertial impaction, this effect being the more pronounced the smaller the collector drop; 2) hydrodynamic effects as well as phoretic effects tend to promote particle capture in the rear of a drop if particles are sufficiently small, resulting in a minimum of E versus r which lies in the “Greenfield gap” region and thus reinforces the gap; 3) electrical effects tend to eliminate this gap reinforcement; and 4) computations which consider phoretic effects only without simultaneously taking account of the particles’ motion due to the hydrodynamic flow around the collector drop significantly overestimate E for r≲1.5 μm.

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