For microfluidic mixing devices, it is necessary to quantify its mixing effectiveness and optimize its design. For this purpose, we are working on multiscale mixing measures for arbitrary domains and the design of optimal mixing protocols.

Efficient mixing of fluids is a necessary step in many microfluidic processes. The advent of new microfluidic technologies that make use of phenomena such as dielectrophoresis and electro-osmosis make it possible to generate arbitrarily time-varying velocity fields, thus opening the possibility of using the tools of optimal control theory to design optimal microfluidic mixing protocols. In our previous work, we proposed multiscale mixing measures for toroidal domains and developed algorithms to compute optimal mixing protocols in the case of zero diffusion. Currently, we are working on extending these multiscale mixing measures to arbitrary domains and we are also studying the effects of diffusion on the optimal controls for mixing.