Chaotic mixing of finite-sized particles

Dynamical systems concepts have been used to analyze the behavior of rigid spherical finite-sized particles in chaotic flows in the eccentric annular system. If the particles are sufficiently small they follow the fluid streamlines. Then the dynamical system is Hamiltonian as a result of the presence of a streamfunction for the two-dimensional incompressible flow. The Stokes number characterizes the significance of particle inertia. It is shown that the bifurcations of the dynamical system can be harnessed for separating particles with different physical properties. These results are numerically obtained for finite-sized particles in Stokes flows.;Departure from Stokes flow toward higher Reynolds numbers results in longer transients in the fluid velocity field. It also changes the steady state pattern of the streamlines. Mixing under chaotic stirring procedures with up to ;Mixing in the eccentric annulus is applied to the problem of collecting fetal cells from maternal circulation of blood. Fetal cells were modeled as small spherical particles suspended in a Newtonian fluid filling the gap in a small eccentric annular mixing device. Two separate model collecting devices are used. The first model utilizes vertically placed and antibody coated fibers that adhere to fetal cells on contact. This model allows an analytic expression for the rate of collection for a perfectly mixed system (steady uniform distribution of fetal cells). Comparison with the results of the numerical model showed that the chaotic mixer is a very efficient randomizer of particle position. The second model utilizes the inner cylinder coated with antibody for collecting fetal cells. The numerically obtained collection rates are promising for clinical applications.