Approximate analytical solutions to the condensation-coagulation equation of aerosols

TL;DR

This paper derives more general analytical solutions to the aerosol condensation-coagulation equation, enabling better understanding of aerosol behavior and sensitivity in atmospheric conditions.

Contribution

It provides new analytical solutions that extend previous models, including a coagulation limit with condensation correction, and compares them with numerical results.

Findings

Solutions effectively estimate cloud condensation nuclei sensitivity.

Analytical solutions match numerical results under various limits.

Enhances understanding of aerosol dynamics in the atmosphere.

Abstract

We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical solutions. For example, we provide an analytic solution to the coagulation limit plus a condensation correction. Our solutions are then compared with numerical results. We show that the solutions can be used to estimate the sensitivity of the cloud condensation nuclei number density to the nucleation rate of small condensation nuclei and to changes in the formation rate of sulfuric acid.