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

Abstract

[1] 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.

A review of volcanic ash aggregation

“…in the vertical column, as aggregation due to the presence of ice seems is less effective. Costa et al (2010) also demonstrated how wet aggregation strongly depends on the ratio between the residence time of aggregating particles within the cloud region where liquid water exists and the time required for aggregates to form. As a result, aggregation processes are likely to be more effective in moderate explosions and small plumes than in vigorous Plinian and sub-Plinian eruptions characterized by fast ascending plumes.…”

“…Such a model was then implemented by Folch et al (2010) with good agreement. The models proposed by Costa et al (2010) and Folch et al (2010) demonstrate that wet aggregation is limited to the cloud region characterized by temperatures above the freezing point of water, i.e. in the vertical column, as aggregation due to the presence of ice seems is less effective.…”

“…The availability and abundance of water in the eruption cloud exerts a dominant control on aggregation (Gilbert and Lane, 1994;Veitch and Woods, 2001;Costa et al, 2010;Folch et al, 2010;Textor et al, 2006a and b). Initial fragmentation, particle collisions, mixed phase clouds and particle separation all lead to particle charging (Mather and Harrison, 2006) which influences particle collisions and may provide binding forces in the absence of water (more relevant for clouds 1000s km from source or >24 hours in age).…”

“…Costa et al (2010) developed a model of wet aggregation based on the classical theory of Smoluchowski (1916) using a fractal relationship to describe the rate at which particles form aggregates based on three different collision mechanisms (i.e., Brownian motion, ambient fluid shear, and differential sedimentation). Both the effects of magmatic water and atmospheric water are considered as well as the effects of water in a liquid or solid state on aggregation.…”

“…Most volcanic ash finer than 125 µm settles out of the atmosphere as particle aggregates that have higher settling velocities than individual constituent particles (Carey and Sigurdsson, 1982;Sorem, 1982;Lane et al, 1993). While aggregation exerts a first order control on the dispersal of fine ash within eruption clouds, the physical and chemical processes involved are not completely understood despite significant progress over the past twenty years (Schumacher and Schmincke, 1995;Gilbert and Lane, 1994;James et al, 2002James et al, , 2003Textor et al, 2006a and b;Costa et al, 2010). Fine airborne particles adhere to each other as a result of electrostatic attraction, moist adhesion between particles (e.g., Sorem, 1982;Gilbert and Lane, 1994;Schumacher andSchmincke, 1991, 1995;James et al, 2002) and hydrometeor formation (e.g., Veitch and Woods, 2001;Textor et al, 2006a;.…”