Despite the widespread use of screw feeders in industry for the transport of
particulate materials, there has been no attempt to derive a detailed, mechanics-based
model. Such a model would assist in optimal design of screw feeders. In this investigation,
we have studied powder flow in a single-screw feeder, as the first step towards modelling
flow in a twin-screw feeder.
We first constructed a mechanics-based model by enforcing the balances of linear
and angular momentum on a suitably chosen continuum element. With the assumptions
that the granular medium moves as a rigid body that slips along the surfaces of the screw
and barrel, and neglecting the effects of gravity and friction on the screw surface, we obtain
the discharge rate for a given angular velocity and screw geometry. We show that the
discharge can be maximized by setting the ratio of the screw pitch p to barrel diameter d
to a specific value. Thus, despite the assumptions that simplify the analysis, the model
yields a non-trivial result that could be useful in the design of screw feeders.
We then studied the detailed flow within the screw feeder for non-cohesive particles
by particle dynamics simulations using the discrete element method (DEM). Our
simulations show that a significant fraction of the material does indeed exhibit solid body
motion, in agreement with the assumption of the model. We find the prediction of the
model to be in excellent agreement with the results of the DEM simulations for a
frictionless screw in the absence of gravity. We then assess the effect of relaxing the
conditions of no friction at the screw surface and no gravity, employed in the model. We
find that the discharge rate exhibits the same qualitative trend, in that there is an optimum
value of p/d at which the feed rate is maximum. Thus, the qualitative dependence of the
volumetric discharge rate on the geometry of the feeder is not altered by the introduction
of gravity and friction at the screw surface.
Our ongoing work is to model dynamical changes in the feed rate, due to
fluctuations in the inlet flow or spontaneous fluctuations within the screw – this was the
request of several IFPRI members at the GBM. For this, we are implementing a non-local
constitutive model for the stress that accounts for dilatancy. We have recently built an
experimental screw feeder assembly to test our model predictions, provide insight into the
detailed flow, and motivate further refinement in our modelling efforts.