Understanding the relationship between internal kinetic energy and injected energy in granular materials is a challlenge that unites the efforts of a wide and diversified research community: from theoretical and experimental physicists to engineers and industrial developers. On one hand, the energy transfer to a granuar medium is an instance of the more general problem of the response of nonequilibrium systems when driven beyond the linear regime; on the other hand it is an important issue for many applications in food and pharmaceutical industry.
A common way to give energy to a granular medium is through a sinusoidal vibration of the walls that confine it.
The external source of energy is thus parametrized by the amplitude A and the frequency f of these vibrations while the internal kinetic energy K is proportional the mean quadratic velocity of the grains. Depending on the specific combination of A and f a granular system can achieve a wide range of dynamical states. At the same time, the dynamical state of the system affects the interaction with the source of external energy. In this complex scenario, one of the most interesting aspects is the occurrence of maximization/minimization conditions for the energy tranfer.
Here we present a proposal for a systematic experimental and numerical study of the energy diagram of a dense granular packing. We want understand how the regions where maximal/minimal energy transfer occurs are distributed in the A-f space, how they depend on the material properties of the grains and how they are related to the dynamical state of the system.
Experiments consist on measuring the mean kinetic energy of an intruder immersed in a dense granular packing vibrated through an elecrodynamic shaker. The numerical study will be performed by DEM (Discrete Element Method) simulations of the same setup allowing the study of the unaccessible observables through experiments.
Up to our knowledge, a combined study of kinetic energy and granular phases for a dense vibrated granular medium in the two-dimensional space of driving parameters has never been addressed in the systematic way that we propose. In addition, our particular attention to the optimal energy tranfer conditions is promising both for applications and theoretical aspects of non-equilibrium physics.
From previos studies a complex scenario of phase successions and non-monotonic behaviors of the energy is emerged with different features in different regions of the driving parameters plane. From Fig. 1 of the above section is clear that our experimental and numerical analysis has the potential to unify these previous results and explain theri connections.
Moreover, once aquired such a great amount of informations about this phenomena will try to propose some phenomenological models in order to rationalize the observed phenomenology. This is an important aspect because, also without the full derivation from fundamental theories, an empirical model in good agreement with our data may help us to undrstand what are the key ingredients for the occurrence of maximization of the energy transer.
We also note that every phase achieved by a vibrated granular system is a non-equilibrim steady state in which the mechanisms of input and output energy are balanced. These kind of situations are also crucial in many other fields as active matter, biology and chemistry. In view of this, our study will offer interesting interdisciplinary perspectives.