A model for wet aggregation of ash particles in volcanic plumes and clouds: 1. Theoretical formulation

Abstract

We develop a model to describe ash aggregates in a volcanic plume. The model is based on a solution of the classical Smoluchowski equation, obtained by introducing a similarity variable and a fractal relationship for the number of primary particles in an aggregate. The considered collision frequency function accounts for different mechanisms of aggregation, such as Brownian motion, ambient fluid shear, and differential sedimentation. Although model formulation is general, here only sticking efficiency related to the presence of water is considered. However, the different binding effect of liquid water and ice is discerned. The proposed approach represents a first compromise between the full description of the aggregation process and the need to decrease the computational time necessary for solving the full Smoluchowski equation. We also perform a parametric study on the main model parameters and estimate coagulation kernels and timescales of the aggregation process under simplified conditions of interest in volcanology. Further analyses and applications to real eruptions are presented in the companion paper by Folch et al.