Scavenging in weakly electrified saturated and subsaturated clouds, treating aerosol particles and droplets as conducting spheres

The effects of electric charge on collision rate coefficients for scavenging of aerosol particles by droplets are evaluated, as appropriate to weak electrification conditions in clouds. Variations in charges on droplets and particles in clouds are proportional to the flow of current in the global electric circuit through gradients in resistivity, which are determined by gradients in droplet concentration and humidity. We obtain the collision rate coefficients by "trajectory model" calculations for spherical aerosol particles and droplets using the exact electrical force equation, with its long-range repulsion and short-range attraction, interacting with drag, inertia, and phoretic forces. The use of the exact electric force gives rate coefficients up to a factor of two greater than previous image charge calculations for particles in the "Greenfield Gap". Rate coefficients for scavenging by Brownian diffusion are obtained by the analytic expression for "flux model" calculations. Rate coefficients for combined effects of electric and phoretic scavenging are given, as appropriate for scavenging of droplets evaporating to residual particles while temporarily retaining the original droplet charge. For particles of radii below about 0.1 mm and with charges typical of residues of freshly evaporated droplets, the long-range repulsive electrical force reduces the collision rate coefficients below those for phoretic scavenging in subsaturated air and below the rates for Brownian scavenging. Time constants for scavenging of particles are given for selected values of droplet size, particle and droplet charges, and particle density, and the applications to observed effects in the atmosphere are discussed.