This project explores basic mechanisms of introducing chaotic advection to enhance mixing in a hydrodynamic model of a nanoliter-scale batch reactor. A combined analytical, numerical and experimental approach will be used, which brings together two novel features: (1) a non-contact experimental method of precisely moving, merging, and mixing nanoliter-sized droplets using temperature-induced surface tension gradients, and (2) a convenient theoretical model based on the Stokes equation for the fluid coupled with the advection equation for the solute concentration that is suitable for making quantitative predictions of mixing behaviors observed in the experiments. The central focus of this research is on fundamental understanding of nonperturbative effects in time-dependent flow, which are most likely to lead to effective mixing in practical applications. The main idea of our approach is based on using the invariants, or functions preserved along the streamlines of the flow, which arise due to a high symmetry of typical flows in microdroplets. As streamlines cannot cross the invariant surfaces, destruction of all invariants is the key to achieving good mixing. The nonperturbative corrections that arise naturally from non-ideal aspects of any experimental implementation are therefore essential ingredients in the mixing process as they change the symmetry of the flow and thus affect the existence and number of invariants. The obtained results will be used to design an effective procedure for controlling mixing that should be applicable to a broad class of flows involving the mixing of discrete quantities of fluid.
Miniaturization holds great promise for novel applications, such as chemical and biological sensors, drug discovery, and clinical tests, bringing radical improvements in speed, throughput, and sensitivity. This project focuses on the fundamental problem of fluid mixing, which plays a crucial role in most microfluidic technologies, yet becomes increasingly difficult at small scales. The study of chaotic mixing in liquid microdroplets is an integral part of a broader study of opto-microfluidics, a novel approach for handling liquids at the microscale using optical methods. This approach will allow construction of a new generation of microfluidic devices free of many drawbacks of conventional microchannel-based technology. Such highly integrated dynamically reprogrammable reusable devices could be used to design complete "labs-on-a-chip" with a potential to revolutionize the way chemical and biological assays are done.
