A new class of integro-partial differential equation models is derived for
the prediction of granular flow dynamics. These models are obtained using a
novel limiting averaging method (inspired by techniques employed in the de
rivation of infinite-dimensional dynamical systems models) on the Newtonian
equations of motion of a many-particle system incorporating widely used in
elastic particle-particle force formulas. By using Taylor series expansions
, these models can be approximated by a system of partial differential equa
tions of the Navier-Stokes type. The exact or approximate governing equatio
ns obtained are far from simple, but they are less complicated than most of
the continuum models now being used to predict particle flow behavior. Sol
utions of the new models for granular flows down inclined planes and in vib
rating beds are compared with known experimental and analytical results and
good agreement is obtained.