Deflection of a dilute stream of particles

Abstract

We consider a two-dimensional system in which a dilute stream of particles collides with an oblique planar wall. Both collisions between particles and collisions between particles and the wall are inelastic. We investigate the effective force experienced by the rigid boundary and show that a number of surprising phenomena can occur in dilute systems. One may naively imagine that a larger angle between the wall and the particle stream implies a larger velocity component perpendicular to the wall. We refer to this as a geometric effect. Hence the wall experiences a larger force. This is the case in a dense particle stream. However, we perform numerical simulations in two dimensions and show that in dilute systems the mean force experienced by the wall can be a nonmonotonic function of the angle between the wall and the particle stream. We show that this occurs because particles that rebound from the wall can collide with incoming particles and be scattered. This kind of particle-particle collisions can reduce the force experienced by the wall. We refer to this effect as shielding. The behavior of the mean force is a result of the competition of the geometric effect and the shielding effect. Furthermore, we show that the force experienced by the wall may be an increasing, decreasing or non-monotonic function of the restitution coefficient in particle-particle collisions. We show that when glancing collisions are predominant, a larger restitution coefficient in particle-particle collisions makes the shielding effect stronger, and thus the mean force will decrease as the restitution coefficient increases. However, when head-on collisions are predominant, a larger restitution coefficient in particle-particle collisions makes the shielding effect weaker, and thus the mean force will increase as the restitution coefficient increases. We derive an exact solution for the mean force on the wall if the system is dilute, and the theoretical prediction is found to be in good agreement with our numerical results. The theory allows us to explicitly quantify the effects of geometry and shielding, and thus to explain a number of interesting features. The theory also generally provides a useful upper bound for the mean force on the wall.

Date of Award	4 Oct 2010
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Jonathan James WYLIE (Supervisor) & Qiang ZHANG (Co-supervisor)