Chaotic advection in particle laden flows

Experiments by Maric and Macosko show that the addition of a small number of balls into a mini-mixer significantly improves the dispersion characteristics in polymer blends. Their results show that the balls enhance the circulation of materials from low to high shear rate regions and promote breakup of drops. In this work, we examine the direct influence of the addition of such a ball on distributive mixing. We study chaotic advection of fluids in a simple cavity flow containing freely suspended inertia less rigid particles by the dynamical systems theory and numerical simulations. We concentrate on the understanding of the mechanism how the presence of the particle affects the dynamical system of the flow. Unlike the work done by Vikhansky, we show that even a regular periodic motion of a single particle can induce chaotic transports of the fluid particle, as a result of the superimposed hyperbolic flow from the existence of the freely rotating solid particle. In fact, stretching and folding of the fluid elements are guaranteed by the occurrence of the hyperbolic flow centered at the particle and by the rotation of the freely suspended particle, respectively. The fluid-solid flow problem has been solved by a new fictitious-domain/finite-element method based on the rigid-ring description of the solid particle. Results are shown for a single particle system which is studied in detail in view of the dynamical systems theory and then extended to two- and three-particle systems.