Using Chaos for Fluid Mixing in Pulsed Micro Flows

Even though mixing is crucial in many microfluidic applications where biological and chemical reactions are needed, efficient mixing remains a challenge since the Reynolds number of these flows is typically low, thus excluding turbulence as a potential mechanism for stirring. While various approaches relying on clever geometries, cross-flows, miniature stirrers or external fields have been used in the past, our work has focused on generating stirring in microchannels of simple geometry by merely pulsing flow rates at the inlets through which the two fluids are brought into the device. Flow visualizations from experiments, as well as numerical simulations, have indicated that the majority of the mixing takes place in the confluence region. Even though it has been shown in previous work that good mixing can be achieved at relatively large scales using this technique, one of the challenges is to make sure that mixing occurs at small scales (i.e., particle scales) as well. To address this issue, we carefully study the dynamics of tracer particles using both computational fluid dynamics and dynamical systems theory, and explore the parameter space in terms of the Reynolds number, Strouhal number and phase difference between the two inlet flows. Specifically, we generate a bifurcation diagram in which both regular and chaotic dynamics occur. As expected, the chaotic regime exhibits stretching and folding of material lines at all (large and small) scales, and is thus promising as an effective mixing tool.