Abstract
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy a detailed balance-like condition when the CO,le 6. Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems.Graphic abstract
Highlights
Modelling self-organisation of dense granular matter (DGM) is essential to many natural phenomena and technological applications
The normalisation condition confines the dynamics to a line in the Q3-Q4 plane, with the steady state a unique stable fixed point on it, which is independent of the initial state
We have constructed master equations to describe the evolution of a key structural characteristic of granular media—the cell order distribution (COD)—from any initial state, given the cell merging and splitting rates
Summary
Modelling self-organisation of dense granular matter (DGM) is essential to many natural phenomena and technological applications. This is a key problem because both the dense flow dynamics and the large-scale properties of consolidated DGM, e.g. permeability [1], catalysis, heat exchange, fuel cell functionality [2], depend strongly on the particle-scale structure [1, 3,4,5,6,7] We address this issue and develop structural evolution equations for quasi-static two-dimensional (2D) particulate systems.
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