A study of mixing by chaotic advection in two three-dimensional open flows

Mixing by chaotic advection is studied in two types of three-dimensional open flows. The first flow is spatially periodic, it consists of a cylindrical tube with a finite number of static mixer elements inside. Mixing in this 3-D flow with no moving parts is studied by numerically solving the momentum equations using computational fluid dynamics. Using Lagrangian particle tracking simulations, we determine the number of elements necessary to mix a blob of passive tracer over the entire exit cross-section of the mixer and to examine the influence of the initial blob location. The second mixer considered here is the time-periodic 3-D flow between two confocal elliptic cylinders whose inner and outer boundaries glide at constant or variable velocity. This flow consists of axial Poiseuille flow superimposed on the 2-D cross-sectional flow between two concentric, confocal ellipses whose walls can glide along their elliptical circumference while keeping the geometry invariant. This flow has moving parts, but induces a lower pressure drop and, as we shall demonstrate, can be controlled by varying the motion of the two boundaries or by modifying the axial flow rate. It is shown that this boundary motion is feasible by comparing streaklines obtained from experiments to numerical results based on the analytical solution of the Stokes equations for this flow. It is also shown that there is a certain range of modulation frequencies for which mixing is enhanced; outside of this range the flow is practically regular.

► Mixing by chaotic advection is studied in two types of 3-D open flows.
► In one geometry—the Kenics KM static mixer—the flow is spatially periodic.
► In the other geometry—the 3-D confocal elliptic mixer—the flow is time periodic.
► Symmetry can provoke or inhibit chaotic advection depending on the flow.