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Aerodynamic focusing of particles in a carrier gas

Published online by Cambridge University Press:  21 April 2006

J. Fernández De La Mora  and
P. Riesco-Chueca
J. Fernández De La Mora
Affiliation:
Yale University, Mechanical Engineering Department, Box 2159 Y.S., New Haven, CT 06520, USA
P. Riesco-Chueca
Affiliation:
Yale University, Mechanical Engineering Department, Box 2159 Y.S., New Haven, CT 06520, USA
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Abstract

The problem of whether a stream of microscopic particles may be concentrated into a focal point by entrainment within a carrier gas is considered for dilute particles linearly coupled to the velocity field of an incompressible gas. Typically, the dynamical behaviour of the particles is governed by a so-called Stokes number S, the product of their relaxation time and a characteristic value of the velocity gradient in the suspending fluid. An inequality due to Robinson (1956) is used to illustrate the natural tendency of potential flows to concentrate the particles. For geometries with planar or axial symmetry, with errors cubic in their initial distance to the axis, the trajectories of identical particles originating near an axis of symmetry are shown to cross it at a common focal point provided they have some initial convergence and their Stokes number is larger than a critical value S*. The position of the focal point of supercritical particles depends on their Stokes number, tending to infinity as S approaches S*. Particle trajectories originating far from the axis of symmetry are seen to cross the centreline at defocused positions, in analogy with the optical geometric aberration effect. The focusing phenomenon is illustrated numerically for two-dimensional potential flows through nozzles of several geometries and also analysed in the proximity of the axis of symmetry. For these examples, the threshold value S* of the Stokes number for focusing is of order one, over an order of magnitude larger than typical values of the familiar critical Stokes number marking the onset of particle impaction on solid surfaces. The focal width may be made over two orders of magnitude smaller than the nozzle diameter by restricting the region where particles are seeded to a moderate angle away from the axis. This angle may be higher than ¼π for the case of a jet exiting through a slit in an infinitely thin plate. There is also some discussion of the use of high-resolution focusing instruments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 1 - 21
Copyright
© 1988 Cambridge University Press

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