Volcanic Particle Aggregation: A Fast Algorithm for the Smoluchowski Coagulation Equation

Abstract:

Particle aggregation is a key process that significantly affects dispersal and sedimentation of volcanic ash, with obvious implications for the associated hazards. Most theoretical studies of particle aggregation have been based on the Smoluchowski Coagulation Equation (SCE), which describes the expected time evolution of the total grain-size distribution under the hypothesis that particles can collide and stick together following specific mathematical relations (kernels). Nonetheless, the practical application of the SCE to real erupting scenarios is made extremely difficult – if not even impossible - by the large number of Ordinary Differential Equations (ODE) which have to be solved to study the typical sizes of volcanic ash (1 micron to 1 mm). We propose an algorithm to approximate the discrete solutions of the SCE, which can describe the time evolution of the total grain-size distribution of the erupted material with an increased computational efficiency. This algorithm has been applied to observed volcanic eruptions (i.e., Eyjafjallajokull 2010, Sakurajima 2013 and Mt. Saint Helens 1980) to see if the commonly used kernels can explain field data and to study how aggregation processes can modify the tephra dispersal on the ground. Different scenarios of sticking efficiencies and aggregate porosity have been used to test the sensitiveness of the SCE to these parameters. Constraints on these parameters come from field observations and laboratory experiments.