Mathematical Modeling of Jig Bed Stratification

"INTRODUCTIONIn a jig, which is primarily a coarse mineral concentration device, the bed of mineral particles is pulsated with a stream of water resulting in the particles of different specific gravities. It operates in a cyclic manner – the jig cycle consists of four stages, namely, inlet, expansion, exhaust and compression. In the inlet stage the bed lifts up en masse. Near the end of the lift stroke the particles at the bottom of the bed start falling resulting in the loosing of the bed which, in turn, causes its expansion or dilation. During the third and fourth stages the particle resettle through the fluid, and the bed collapses back to its original volume. The pulsation and suction are repeated to bring about stratification with respect to specific gravity across the bed height. Various parameters affecting the stratification process include amplitude and frequency of pulsation, bed thickness, rate of hutch water flow, and feed characteristics. This paper first presents a review of various jigging theories and then describes a new approach to mathematical modeling of jigging employing the discrete element method.JIG MODEL BASED ON DISCRETE ELEMENT METHOD (DEM) APPROACHThe jig models based on DEM essentially involve tracking the position of each particle incrementally, applying Newton’s law of motion and a force displacement law at the contact. The model presented here is based on a three dimensional mathematical description of solid-solid and fluid-solid interactions. In this model, the force balance on a particle is extended to account for the effect of continuously varying fluid on the particle. The total force on each particle is made up of a known external body force, fluid particle interaction force and particle-particle and/or particle-wall interaction force. The fluid-particle interactive force is primarily made of drag and buoyancy. Di Felice’s correlation is used to evaluate the drag force. Solid-solid interaction is described by treating particles as discrete elements that are indestructible but interact with each other and any other elements present, such as walls, when they make physical contacts. A pair of spring and dashpot represents a contact The contact forces are computed from the amount and the rate of overlap of the particles at the contact. The motion of the particle is due to movement of the fluid, which transmits its energy through the particle-particle contacts. A computer program incorporating both the contact and the fluid model has been developed. It takes the operating parameters such as amplitude and frequency of the pulsating fluid, pertinent data concerning particle properties and the geometry of the jig bed as inputs."