Dependence of cluster growth on the coefficient of restitution in a cooling granular fluid
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Dependence of cluster growth on the coefficient of restitution in a cooling granular fluid SUBIR K DAS1,2,*
and SUBHAJIT PAUL1,3
1
Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India 3 Institut fu¨r Theoretische Physik, Universita¨t Leipzig, 04009 Leipzig, Germany *Author for correspondence ([email protected]) 2
MS received 28 December 2019; accepted 7 July 2020 Abstract. Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the system exhibits a crossover to an inhomogeneous regime that is characterized by the formation and growth of particle-rich clusters. We present results on the time dependence of average mass of the clusters and that of average kinetic energy, obtained via event-driven molecular dynamics simulations, for a wide range of values for the coefficient of restitution (e), by fixing the overall density of particles in the system to a constant number. The time of onset of crossover from homogeneous to the inhomogeneous regime, as is well known, strongly increases as one moves towards the elastic limit. Nevertheless, our presented results suggest that the asymptotic growth is independent of e, for uniform definition of cluster, onset of which has a different e-dependence than the onset of above-mentioned crossover. In other words, not only the exponent but also the amplitude of the power-law growth, which is widely believed to be the form of the evolution, is at the most very weakly sensitive to the choice of e. While it is tempting to attribute this fact to the similar feature in the decay of energy, we caution that our current understanding is not matured enough to draw such a connection between cluster growth and energy decay in a meaningful manner. Keywords.
1.
Granular materials; growth dynamics; ballistic aggregation.
Introduction
Granular materials [1,2] consist of particles of varying shapes and sizes, and are very commonly observed in nature. Typical examples [1–4] are powders, drugs, sacks of rice or sugar grains, packets of coffee beans and cosmic dust, etc. Thus, knowledge of the behaviour of granular materials is of immense importance in many disciplines. Understanding of these, at different length and time scales, can be useful in the interpretation of the formation of planetary rings; has applications in industries like pharmaceutical, agriculture and mining; is of importance in the prevention of damages due to natural processes like landslide, erosion, etc. This, however, is challenging, a reason being that often these materials share properties of both fluids and solids [1,2]. Due to friction and inelastic collisions among particles these systems contin
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