SCARLET-1.0: SpheriCal Approximation for viRtuaL aggrEgaTes
Authors: Rossi Eduardo , Bonadonna Costanza 
Published: July 2021

Abstract. Aggregation of particles occurs in a large variety of settings and
is therefore the focus of many disciplines, e.g., Earth and environmental sciences, astronomy, meteorology, pharmacy, and the food industry. In particular, in volcanology, ash aggregation deeply influences the sedimentation of volcanic particles in the atmosphere during and after a volcanic eruption, affecting
the accuracy of model predictions and the evaluation of hazard and risk
assessments. It is thus very important to provide an exhaustive description
of the outcome of an aggregation process, starting from its basic
geometrical features such as the position in space of its components and the overall porosity of the final object. Here we present SCARLET-1.0, a MATLAB
package specifically created to provide a 3D virtual reconstruction for
volcanic ash aggregates generated in central collision processes. In
centrally oriented collisions, aggregates build up their own structure around
the first particle (the core), acting as a seed. This is appropriate for aggregates
generated in turbulent flows in which particles show different degrees of
coupling with respect to the turbulent eddies. SCARLET-1.0 belongs to the
class of sphere-composite algorithms, a family of algorithms that approximate 3D complex shapes in
terms of a set of sphere-composite nonoverlapping spheres. The conversion
of a 3D surface to its equivalent sphere-composite structure then allows for
an analytical detection of the intersections between different objects that
aggregate together. Thus, provided a list of colliding sizes and shapes,
SCARLET-1.0 places each element in the vector around the core, minimizing
the distances between their centers of mass. The user can play with
different parameters that control the minimization process. Among them the
most important ones are the cone of investigation (Ω), the
number of rays per cone (Nr), and the number of orientations of the
object (No). All the 3D shapes are described using the Standard Triangulation Language (STL) format, which is the
current standard for 3D printing. This is one of the key features of
SCARLET-1.0, which results in an unlimited range of applications of the
package. The main outcome of the code is the virtual representation of the
object, its size, porosity, density, and the associated STL file. In
addition, the object can be potentially 3D printed. As an example,
SCARLET-1.0 has been applied here to the investigation of
ellipsoid–ellipsoid collisions and to a more specific analysis of volcanic
ash aggregation. In the first application we show that the final porosity of
two colliding ellipsoids is less than 20 % if flatness and elongation are
greater than or equal to 0.5. Higher values of porosities (up to 40 %–50 %)
can instead be found for ellipsoids with needle-like or extremely flat
shapes. In the second application, we reconstruct the evolution in time of
the porosity of two different aggregates characterized by different inner
structures. We find that aggregates whose population of particles is
characterized by a narrow distribution of sizes tend to rapidly reach a
plateau in the porosity. In addition, to reproduce the observed densities,
almost no compaction is necessary in SCARLET-1.0, which is a result that suggests how
ash aggregates are not well described in terms of the maximum packing
condition.