Computing accumulation density of particles on a line with parabolic trajectories

Authors:
Yu-Kumg Chen;Shuo-Yan Chou
Affiliations:
Department of Electronic Engineering, Huafan University 1 Huafan Road, Shihtin Hsiang, Taipei Hsien, Taiwan 223, R.O.C.;Department of Industrial Management National Taiwan University of Science and Technology 43 Keelung Road, Section 4, Taipei, Taiwan 10672, R.O.C.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2001

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Deriving the accumulation density function with parabolic trajectories of particles for arbitrary lines

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Abstract

In this paper, an ideal particle accumulation problem is studied, in which particles are emitted from a fixed point at the same emission velocity onto a plane with a negative y-intercept. Since particles acted on by gravity travel in space via parabolic trajectories, by studying such families of parabolas, the accumulation of particles on a plane can be deduced. An analytical equation, namely the accumulation density function, is subsequently established for representing particle accumulation on such a plane. This accumulation function provides a basis for simulating accumulation of materials on the surfaces in applications such as chemical vapor deposition and spray painting.