The Discrete Element Method (DEM) replicates the movement and behaviour of particle flow. It was first described by Cundall and Strack in 1979 (see References) and has since been researched and refined extensively. Helix Technologies has developed its own calculation engine and interface based on this body of work.
When two moving objects collide, an impulsive force results that alters the velocity of one or both objects. Moving objects carry momentum as well as potential energy from their elevation.
An incremental force law is applied from F = ma, or a = F/m, where Kn is the normal stiffness of the material.
When two particles collide, their surfaces overlap slightly. Over a very small time step dt, the change in overlap dn is approximately v·dt. Acceleration is assumed constant over this small interval (a = F/m), and integrating over the interval gives v = (F/m)·dt. Mass is known and F and a can be calculated, so a velocity results. This is repeated for every particle at every time step, and summing the forces on each axis gives the resulting velocity. Gravitational acceleration is added to this, along with the effects of the co-efficient of restitution and friction between particles and surfaces.
The magnitude of the force acting on a particle depends on the normal stiffness and the size of the time step. If you increase the time step dt, you generally need to reduce the normal stiffness Kn to keep particle motion realistic. Changing particle diameter also changes particle mass (proportional to radius cubed) – it's this repulsive force that keeps particles from overlapping.
So the motion of particles depends on:
For any given particle density, diameter and time step, Kn needs to be tuned to give realistic results – see DEM Inputs and Settings and Fine Tuning DEM Inputs.