Settling and asymptotic motion of aerosol particles in a cellular flow field

SummaryThis 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.

[1]  M. Maxey On the advection of spherical and non-spherical particles in a non-uniform flow , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[2]  Kurt Wiesenfeld,et al.  Suppression of period doubling in symmetric systems , 1984 .

[3]  Martin R. Maxey,et al.  Gravitational Settling of Aerosol Particles in Randomly Oriented Cellular Flow Fields , 1986 .

[4]  Amable Liñán,et al.  On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow , 1993, Journal of Fluid Mechanics.

[5]  A. Crisanti,et al.  Passive advection of particles denser than the surrounding fluid , 1990 .

[6]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[7]  Knobloch,et al.  Chaotic advection by modulated traveling waves. , 1987, Physical review. A, General physics.

[8]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[9]  Martin R. Maxey,et al.  The motion of small spherical particles in a cellular flow field , 1987 .

[10]  Camassa,et al.  Chaotic advection in a Rayleigh-Bénard flow. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[11]  Neil Fenichel Geometric singular perturbation theory for ordinary differential equations , 1979 .

[12]  Y. Pomeau,et al.  Free and guided convection in evaporating layers of aqueous solutions of sucrose. Transport and sedimentation of solid particles , 1991 .

[13]  Neil Fenichel Persistence and Smoothness of Invariant Manifolds for Flows , 1971 .

[14]  T. D. Burton,et al.  Chaotic dynamics of particle dispersion in fluids , 1992 .