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We study the dynamics of inertial particles in two dimensional incompressibleflows. The Maxey-Riley equation describing the motion of inertial particles isused to construct a four dimensional dissipative bailout embedding map. Thismap models the dynamics of the inertial particles while the base flow isrepresented by a 2-d area preserving map. The dynamics of particles heavierthan the fluid, the aerosols, as well as that of bubbles, particles lighterthan the fluid, can be classified into 3 main dynamical regimes - periodicorbits, chaotic structures and mixed regions. A phase diagram in the parameterspace is constructed with the Lyapunov characteristic exponents of the 4-d mapin which these dynamical regimes are distinctly identified. The embedding mapcan target periodic orbits, as well as chaotic structures, in both the aerosoland bubble regimes, at suitable values of the dissipation parameter.

Chaotic advection of inertial particles in two dimensional flows