Hydrostatic pressure in granular environment

Abstract

The problem is that to date there is no general theory of the granular state of matter in a closed form. However, there are some well-developed models that use, for example, the representation of a continuous environment. Typical bulk material is a large conglomeration of micro-mechanical particles of different sizes and shapes that interact with each other and the walls contain containers by mainly repulsive forces in direct mechanical contact (by nature it is forces of electromagnetic origin – dry and viscous friction forces, as well as traction).
In the proposed work to study the pressure in a multiparticle micro-mechanical system, a model of a lattice gas in a gravitational field is considered. Analysis of the determination of free energy and entropy allowed us to establish the corresponding equilibrium density profile, which is described by a Fermi-type function. The Fermi profile in the form of a density field was used to find the vertical hydrostatic pressure for which the analytical expression was obtained. Hydrostatic pressure was different from the known relations derived from the theory of condensed matter. The obtained results are confirmed by experimental observations, which indicate a complex, anisotropic significantly different from the known from the theory of condensed matter distribution of even vertical pressure in large conglomerations of discrete micro-mechanical particles. Which really repeats the Fermi distribution. The obtained results stimulate the revision of typical ratios of hydrostatics of continuous media, such as Pascal's laws. Torricelli, Archimedes and Bernoulli in the case of discrete micro-mechanical (granular) systems. The conclusions of the work can be significant in the design and evaluation of operating parameters of storage, release and transportation of bulk cargo, which consist of discrete micro-mechanical conglomerations with different degrees of compaction and compaction.