Droplet-Based Microfluidics Droplet Transport and Spatiotemporal Dynamics in Microfluidic Networks            Currently, microfluidic devices can produce millions of nanoliter-scale droplets in an hour  allowing high throughput encapsulation of single biomolecules and cells. Given the complexity of  biological analysis, these droplets often need to be shuttled through a network of fluidic channels  so that they can be merged with other reagent-loaded droplets, then sorted and eventually  analyzed. Realizing this vision of an ultrafast fluidic bioprocessor in the laboratory is quite a  daunting task because akin to car traffic on congested highways, collective hydrodynamic  interactions between drops in interconnected networks precludes full control over the position  and timing of droplets. For example, as shown in the figure below, decision making of the  droplets arriving at the junction can be quite complex.                    We are pursuing a combined experimental and computational approach to understand droplet  traffic in fluidic networks. We are currently quantifying the hydrodynamic resistance of drops in  microchannels and incorporating that knowledge to understand and model the spatiotemporal  dynamics of drops in simple fluidic networks. In the long term, we aim to develop a rational  framework for the design of large-scale droplet-based fluidic processors.              Nanoliter-Scale Droplet Arrays for Biological Analysis              Multi-well plates combined with robotics are currently the gold standard for conducting high  throughput screening assays in biology and medicine. This approach uses microliter volumes of  reagents and limits the throughput and the level of combinatorial screening that can be achieved  in applications such as drug discovery. Droplet-based microfluidics has the potential to reduce  the volumes down to nanoliters. However an engineering challenge is to develop ways to either  array or store droplets on a chip.               We are currently engineering fluidic networks on a chip that can generate two-dimensional  arrays of drops. The advantage of 2D arrays lies in alleviating the need for indexing since drops  are stored at predefined locations. We are pursuing scientific studies to understand the factors  that regulate the production of 2D drop arrays that will enable us to robustly generate droplet  arrays not only with homogeneous composition but also with varying compositional gradients of  reagents.              Crystallization and Partial Coalescence in Oil-in-Water Emulsions            A relatively unexplored and poorly understood route to designing soft materials is forcing  emulsions containing crystallizable oils to undergo a process known as partial coalescence.  Partial coalescence occurs when the interfacial crystals of one fat droplet penetrate a second  droplet. The mechanical strength of the crystalline network linking the droplets is capable of  overcoming the Laplace pressure and maintains the aggregate shape as shown in Figure 1.  From a practical perspective, this mechanism has been exploited in ice cream manufacture for  nearly three centuries and has found additional applications in cosmetics, pharmaceutical  creams, and phase change materials. Technological control of partial coalescence in these  applications requires scientific understanding of crystallization transitions and the kinetics of  partial coalescence in oil-in-water emulsions.              Direct experimental characterization of out-of-equilibrium phenomena such as crystallization and  partial coalescence requires investigating statistically large ensembles of well-controlled droplet  sizes. Our principal approach is to deploy microfluidic technology to create organized arrays  containing several hundred monodisperse single droplets and doublets for probing nucleation  and kinetics of partial coalescence under quiescent conditions. In addition, we are designing  microfluidic devices to probe shear-induced kinetics of partial coalescence. This microfluidic-  based bottom-up approaches and direct visualization methods are expected to fill fundamental  gaps in the current understanding of partial coalescence in emulsions.