The Maxey-Riley ͓Phys. Fluids 26, 883 ͑1983͔͒ particle equation of motion is considered without the history term and for an asymptotically small Stokes number. The equation admits a globally attractive invariant manifold identified as the Eulerian particle velocity field asymptotically close to the unperturbed fluid velocity field, thus suppressing the inconsequential initial transients. A recursive asymptotic scheme is obtained for the calculation of the invariant manifold in any order of accuracy. The dimension of the particle equation on the invariant manifold is reduced by half, which considerably facilitates the analysis of its motion in physical space. Structural stability theory provides comprehensive qualitative description of the particle motion.In the limit of zero Reynolds number the equation governing rigid spherical particle motion ͑position, x, and velocity, v͒ in arbitrary unperturbed host flow field, u, is the equation finalized by Maxey and Riley, 1where a is particle radius; fluid viscosity, m f = f V and m p = p V, V is particle volume, f , p are fluid and particle densities, respectively, and g is gravitational acceleration. Since its appearance, the Maxey-Riley equation has been the subject of extensive study. Motion of dense 2,3 and neutrally buoyant 4 particles was investigated in cellular flows. In these studies chaotic large-scale motion was observed for sufficiently large Stokes ͑St͒ numbers in specific two dimensional configurations. The settling of dense, aerosol particles was investigated in flow fields modeling turbulence. [5][6][7] Strictly analytical studies were conducted by linearizing the external flow near singular points to investigate the local behavior for Stϳ O͑1͒ ͑Ref. 8͒ and to study stability of stationary points. [9][10][11] Equation ͑1͒ was also considered in the past in order to study the importance of various terms in the equation. Studies of the dispersion of dense particles in isotropic turbulence found that the history, added mass, buoyancy, and pressure are negligible. 12,13 The effect of the history term was found negligible in the case of a particle introduced impulsively into the fluid. 14 Vojir and Michaelides 15 found that the history term has small contribution to the particle motion whenever the particle is denser than the fluid.Thus particle motion in nonlinear flow fields is mostly investigated numerically for specific configurations. No systematic attempt has been made to solve the equation for general spatially varying flow fields. In this respect several results can be cited. Druzhinin 16 and Dodin and Elperin 17 used successive approximations on the aerosol limit of Eq. ͑1͒, v = -1 ͑u − v͒ + g, ͑2͒to obtain the particle velocity up to third ͑and second, including gravity in Dodin and Elperin 17 ͒ order precision ͑the dot denotes differentiation with respect to time and is the Stokes response time͒. However, in these studies the problem of the stability of the particle velocity was not addressed. Maxey 5 used classical asymptotic analysis on ͑2͒ and n...

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Novel experimental results on the hydrodynamic forces acting on a small heated particle at low Reynolds and Grashof numbers are presented. The temperature difference between the particle and the ambient causes free convection flow around the particle. As a result, the drag force exerted on the particle by forced flow deviates significantly from the Stokes law. This deviation is represented quantitatively for three basic directions of forced flow, namely assisting, opposing, and crossing with respect to free convection flow. Validity of the Stokes formula at mixed-convection creeping flow conditions is discussed.