Investigation of the staggered herringbone mixer with a simple analytical model.

An analytical model is presented for the three-dimensional flow in the recently introduced staggered herringbone mixer for microchannels. In this model, the flow in the cross-section of the channel is treated as a lid-driven cavity flow. The model is shown to reproduce the advection patterns that were observed experimentally in the staggered herringbone mixer. The model is then used to study the quality of mixing in this flow as a function of geometry. Analysis is performed with Poincaré maps, mixing simulations, and residence time distributions. A range of optimal geometries is identified.