ISSN:
1432-1467
Keywords:
settling of aerosol particles
;
singular perturbation
;
invariant manifold
;
heteroclinic break-up
;
symmetric map
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary This paper presents a proof that given a dilute concentration of aerosol particles in an infinite, periodic, cellular flow field, arbitrarily small inertial effects are sufficient to induce almost all particles to settle. It is shown that when inertia is taken as a small parameter, the equations of particle motion admit a slow manifold that is globally attracting. The proof proceeds by analyzing the motion on this slow manifold, wherein the flow is a small perturbation of the equation governing the motion of fluid particles. The perturbation is supplied by the inertia, which here occurs as a regular parameter. Further, it is shown that settling particles approach a finite number of attracting periodic paths. The structure of the set of attracting paths, including the nature of possible bifurcations of these paths and the resulting stability changes, is examined via a symmetric one-dimensional map derived from the flow.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01275644
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