DNA microarrays: design principles for maximizing ergodic, chaotic mixing

In this article we show that models of flows in DNA microarrays generated by pulsed source-sink pairs can be studied as linked twist maps. The significance of this is that it enables us to relate the flow to mathematically precise notions of chaotic mixing that can be realized through specific design criteria. We apply these techniques to three different mixing protocols, two of which have been previously described in the literature, and we are able to isolate the features of each mixer that lead to "good" or "bad" mixing. Based on this, we propose a new design to generate a "well-mixed" flow in a DNA microarray.