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Title:  Deflection of a dilute stream of particles 
Other Titles:  Xi shu li zi liu de pian zhuan 稀疏粒子流的偏轉 
Authors:  Deng, Yuhui (鄧宇輝) 
Department:  Department of Mathematics 
Degree:  Doctor of Philosophy 
Issue Date:  2010 
Publisher:  City University of Hong Kong 
Subjects:  Particles  Mathematical models. Granular materials  Mathematical models. 
Notes:  CityU Call Number: TA418.78 .D46 2010 v, 81 leaves : ill. 30 cm. Thesis (Ph.D.)City University of Hong Kong, 2010. Includes bibliographical references (leaves 7681) 
Type:  thesis 
Abstract:  We consider a twodimensional 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 particleparticle 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 nonmonotonic function of the restitution coefficient in particleparticle
collisions. We show that when glancing collisions are predominant, a larger restitution
coefficient in particleparticle collisions makes the shielding effect stronger, and thus
the mean force will decrease as the restitution coefficient increases. However, when
headon collisions are predominant, a larger restitution coefficient in particleparticle
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. 
Online Catalog Link:  http://lib.cityu.edu.hk/record=b3947869 
Appears in Collections:  MA  Doctor of Philosophy

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