On the scaling of fragmentation and energy dissipation in collisions of dust aggregates

Fragmentation of granular clusters may be studied by experiments and by granular mechanics simulation. When comparing results, it is often assumed that results can be compared when scaled to the same value of $$E/E_{\mathrm{sep}}$$ E / E sep , where E denotes the collision energy and $$E_{\mathrm{sep}}$$ E sep is the energy needed to break every contact in the granular clusters. The ratio $$E/E_{\mathrm{sep}}\propto v^2$$ E / E sep ∝ v 2 depends on the collision velocity v but not on the number of grains per cluster, N. We test this hypothesis using granular-mechanics simulations on silica clusters containing a few thousand grains in the velocity range where fragmentation starts. We find that a good parameter to compare different systems is given by $$E/(N^{\alpha }E_{\mathrm{sep}})$$ E / ( N α E sep ) , where $$\alpha \sim 2/3$$ α ∼ 2 / 3 . The occurrence of the extra factor $$N^{\alpha }$$ N α is caused by energy dissipation during the collision such that large clusters request a higher impact energy for reaching the same level of fragmentation than small clusters. Energy is dissipated during the collision mainly by normal and tangential (sliding) forces between grains. For large values of the viscoelastic friction parameter, we find smaller cluster fragmentation, since fragment velocities are smaller and allow for fragment recombination. Graphic abstract

Influence of porosity on high-velocity mass-asymmetric collisions

ABSTRACT Using granular mechanics, we study the influence of porosity on the collisions of spherical granular aggregates with a mass ratio of around 60. At high filling factors, the projectile produces a crater on the target, similar to impacts on a granular bed. However, at low filling factors, the small projectile passes through the large target, strongly fragmenting it. By a consideration of the lateral grain velocities during the collision, we attribute this behaviour to the ‘piston effect’, in which the projectile loses momentum mainly to the grains below it. Due to an increase in grain–grain interactions as porosity decreases, the piston effect loses its importance for higher filling factors, ϕ ≳ 0.2. These results may prove useful in modelling collisions occurring in debris discs.