Chaotic advection of inertial particles in two dimensional flows

TL;DR

This paper investigates the complex behavior of inertial particles in two-dimensional flows using a novel four-dimensional dissipative map, revealing distinct dynamical regimes and the ability to target specific particle behaviors.

Contribution

It introduces a new four-dimensional dissipative bailout embedding map based on the Maxey-Riley equation for modeling inertial particle dynamics in 2D flows.

Findings

Identification of three main dynamical regimes: periodic, chaotic, and mixed.

Construction of a phase diagram with Lyapunov exponents distinguishing regimes.

Ability to target specific particle behaviors in aerosol and bubble regimes.

Abstract

We study the dynamics of inertial particles in two dimensional incompressible flows. The Maxey-Riley equation describing the motion of inertial particles is used to construct a four dimensional dissipative bailout embedding map. This map models the dynamics of the inertial particles while the base flow is represented by a 2-d area preserving map. The dynamics of particles heavier than the fluid, the aerosols, as well as that of bubbles, particles lighter than the fluid, can be classified into 3 main dynamical regimes - periodic orbits, chaotic structures and mixed regions. A phase diagram in the parameter space is constructed with the Lyapunov characteristic exponents of the 4-d map in which these dynamical regimes are distinctly identified. The embedding map can target periodic orbits, as well as chaotic structures, in both the aerosol and bubble regimes, at suitable values of the dissipation parameter.