Abstract

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 \(E/E_{\mathrm{sep}}\), where E denotes the collision energy and \(E_{\mathrm{sep}}\) is the energy needed to break every contact in the granular clusters. The ratio \(E/E_{\mathrm{sep}}\propto v^2\) 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 \(E/(N^{\alpha }E_{\mathrm{sep}})\), where \(\alpha \sim 2/3\). The occurrence of the extra factor \(N^{\alpha }\) 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

中文翻译：

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尘埃聚集体碰撞中破碎和能量耗散的尺度

摘要

可以通过实验和通过颗粒力学模拟研究颗粒团簇的破碎。在比较结果时，通常假设将结果缩放到\（E / E _ {\ mathrm {sep}} \）的相同值时可以比较结果，其中E表示碰撞能量，而\（E _ {\ mathrm {sep }} \）是打破粒状簇中每个接触所需的能量。比\（E / E _ {\ mathrm {sep}} \ proto v ^ 2 \）取决于碰撞速度v，而不取决于每个簇的晶粒数N。我们使用颗粒力学模拟在破碎开始的速度范围内包含几千个晶粒的二氧化硅簇上测试了这个假设。我们发现\（E /（N ^ {\ alpha} E _ {\ mathrm {sep}}）\）给出了一个比较不同系统的好参数，其中\（\ alpha \ sim 2/3 \）。多余因子\（N ^ {\ alpha} \）的出现这是由于碰撞过程中的能量耗散造成的，因此大型簇需要比小簇更高的冲击能量才能达到相同的破碎水平。碰撞过程中的能量耗散主要是由晶粒之间的法向和切向（滑动）力造成的。对于较大的粘弹性摩擦参数值，我们发现较小的簇碎片，因为碎片速度较小，并允许碎片重组。

图形摘要