Chaotic mixing in microfluidic devices driven by oscillatory cross flow

The kinematics of oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and continuous throughput flow configurations. The flow is analyzed using numerical simulation of the unsteady Navier-Stokes equations combined with tracking of single and multispecies passive tracer particles. Two characteristics of chaotic flow are demonstrated: the stretching and folding of material lines leading to particle dispersion and a positive "effective" Lyapunov exponent. The primary mechanism for the generation of chaotic flow is a periodic combination of stretching (which occurs via shear in the channels) and rotation (which occurs via the timing of the oscillations), making these systems effective tendril-whorl type flows. First, the case of confined mixing is studied. It is shown that chaotic flow is generated in a cross-cell device when sinusoidally driven, out-of-phase, perpendicular fluid streams intersect in the flow domain. Calculations indicate that the flow becomes chaotic in the center region starting at a Stroultal number on the order of 1. A degree of mixing based on a relative mixing entropy as high as 91% is obtained. Approximately 10-15 sinusoidal cycles are needed in order to effectively mix different groups of passive tracer particles. In the second phase of the analysis, the cross flow mixing mechanism is utilized in a continuous operation by combining a throughput channel flow with an oscillatory cross flow in a configuration called the star-cell geometry. It is shown that the oscillatory flow remains chaotic even in combination with the throughput flow, and a degree of mixing in the 80%-90% range is obtained for the range of parameters studied here.