Dissipative Dynamics of Granular Materials

Abstract

Granules are inelastic particles, undergoing dissipative and repulsive forces on contact. A granular state consists of a conglomeration of discrete, non-Brownian particles in a combined state of solid, liquid, and gas. Modern theoretical physics lacks general theories for the granular states. Simulation methods for particle dynamics include molecular dynamics (MD), Brownian dynamics (BD), Stokesian dynamics (SD), dissipative particle dynamics (DPD), and dissipative hydrodynamics (DHD). These conventional methods were originally designed to mimic the small-particle motion being less influenced by the gravitational force. There are three reasons that a conventional method cannot be directly applied to investigate granular dynamics. First, volume exclusion forces between colliding particles are often disregarded due to strong repulsive forces between negatively charged colloids and nanoparticles. Second, the gravitational force is not significant as applied to small, light particles, and therefore it is often discarded in force/torque calculations. Third, energy conservation in an equilibrium state is not guaranteed for the granular system due to the inelastic and frictional nature of the granular materials. In this light, this chapter discusses the fundamentals of particle dynamics methods, formulates a robust theoretical framework for granular dynamics, and discusses the current applications and future directions of computational granular dynamics.

A Coupling Algorithm of Computational Fluid and Particle Dynamics (CFPD)

“…Dissipative hydrodynamics (DHD) has all the features required to be a universal simulation method for particle dynamics by taking specific advantages from MD, BD, SD, DPD, and DEM. A detailed review can be found elsewhere [14].…”

“…After an instantaneous collision, the two particle have the following velocities [14]: where 0 ≤ ε n ≤ 1 and À1 ≤ ε t ≤ 1 are restitution coefficients in the normal and tangential directions, respectively, μ ij is a reduced mass defined as…”

“…Stokesian dynamics (SD) uses the grand mobility matrix to include the far-field hydrodynamic forces/torques [13]. In-depth comparative analyses of present particle dynamic methods can be found elsewhere [14]. This mobility matrix is inverted and updated by adding differences between near-field lubrication forces and farfield two-body interactions.…”

“…DHD is a generalized method of which special cases converge to MD, BD, DPD, and SD by turning on or off specific force mechanisms. Details of DHD can be found elsewhere [14][15][16]. CFD and PHD were developed and applied without strong mutual influences.…”