An electrokinetic mixer driven by oscillatory cross flow

Abstract

An electrokinetic mixer driven by oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and throughput mixing configurations. The flow is analyzed using numerical simulation of the unsteady Navier–Stokes equations combined with the tracking of single and multi-species passive tracer particles. First, the case of confined flow mixing is studied in which flow in the perpendicular channels of the oscillatory mixing element is driven sinusoidally, and 90° out of phase. The flow is shown to be chaotic by means of positive effective (finite time) Lyapunov exponents, and the stretching and folding of material lines leading to Lagrangian tracer particle dispersion. The transition to chaotic flow in this case depends strongly on the Strouhal number (St), and weakly on the ratio of the cross flow channel length to width (L/W). For L/W = 2, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 0.32, and the transitional value of St increases slightly with increasing aspect ratio. A peak degree of mixing on the order of 85% is obtained for the range of parameter values explored here. In the second phase of the analysis, the effect of combining a fixed throughput flow with the oscillatory cross channel motion for use in a continuous mixing operation is examined in a star cell geometry. Chaotic mixing is again observed, and the characteristics of the downstream dispersion patterns depend mainly on the Strouhal number and the (dimensionless) throughput rate. In the star cell, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 1, slightly higher than for the case of cross cell. The star cell mixing behavior is marked by the convergence of the degree of mixing to a plateau level as the Strouhal number is increased at fixed flow rate. Degree of mixing values from 70 to 80% are obtained indicating that the continuous flow is bounded by the maximum degree of mixing obtained from the confined flow configuration.