Flows of Highly Energetic Particles through Funnels with Frictional Effects

The researchers will study the phenomena that occur when frictional, inelastic, spherical particles fall under gravity through a symmetric funnel. The researchers will focus on the case in which the particles enter the funnel with a large amount of energy and so rapidly experience collisions with their neighbors and with the funnel walls. Such systems are extremely important in numerous industrial processes in which streams of rapidly moving particles must be steered into a narrow channel. Typically these systems are extremely complicated and obtaining a detailed understanding gives rise to a number of extremely challenging problems. Immediately after entering the funnel, particles are highly agitated and experience binary collisions and do not experience sustained contacts. However, the dissipative nature of such systems means particles rapidly lose their energy and therefore may come into sustained contact with other particles. In this regime, friction between particle and between particles and the walls becomes important. The researchers will perform careful simulations that track the motions of individual particles and determine the details of the dynamics. Of particular interest are questions such as when the funnel can become blocked, what is the average time spent in the funnel by a particle and what are the forces experienced by the funnel walls. The researchers will consider a dilute theory and determine the effects of friction between the particles and the funnel walls. This will allow them to determine the important physical mechanisms and gain a solid understanding of the underlying processes. This will have major importance for understanding design criteria for a broad range of industrial equipment.