MIXING ENHANCEMENT BY FREQUENCY-SELECTIVE CHAOTIC ADVECTION IN A 3-D TIME-PERIODIC STOKES FLOW

A new 3-D periodic Stokes flow has been imagined and realized experimentally. It consists of axial Poiseuille flow superimposed on the 2-D tangential motion between two confocal ellipses that glide circumferentially so that the geometry is invariant. Chaotic streak lines obtained experimentally are compared to numerical simulations of this time-periodic flow. We next turn our attention to the problem of determining how to move the boundaries in order to obtain the most efficient mixing. Using a numerical experiment to study the advection of a passive scalar, we show that for a given 3-D mixer geometry and flow rate there is an optimum modulation frequency of the boundary displacement protocol for which the mixing process is most efficient. Furthermore, it is shown that chaotic advection can be regarded as a frequency-selective amplifier. This behavior is similar to that of fluid instability where external perturbations are amplified for a certain frequency range. For values above or below this range, perturbations are damped and the system is stable.