Abstract

I will begin by talking briefly about what makes fluids mix (which has been known for a long time), and some examples of efforts to make this happen in practical devices. Then I will introduce the mathematical theory of mixing from ergodic theory and talk about why it is a useful guide, but why there are practical obstacles to applying the theory in “real life” and how this opens up a wealth of new mathematical questions. The mixers that I will mostly be concerned with are ‘’micromixers’’ and to motivate the general ideas that I wish to develop I will survey a number of micromixers with an idea of extracting the common features. This will provide a good entry for going back to the theory (a bit) and extracting “Eulerian and Lagrangian” aspects that influence mixing. Basically, what I would “ideally’’ like to do is completely bypass the Lagrangian aspect of mixing (which sounds contradictory, especially with respect to what I would have talked about earlier) but if it’s possible (and I will discuss the extent that it is) it offers great promise for a priori design, i.e. designing a mixer without simulating its mixing properties first. I will then give one or two examples from biotechnology (sensor arrays) where this approach can be practically implemented, and I will describe the advantages of this approach for “optimizing” the performance of a mixing device. The talk will emphasize ideas and not go into technical details. However, a general point that I hope to make in this talk is that many current designs for micromixers naturally fit into a common framework where (smooth) ergodic theory can not only yield practical results, such as design principles, but the design of the mixing devices themselves are suggesting interesting theorems and directions for research in ergodic theory.