Inertial Self-Assembly Dynamics of Interacting Droplet Ensembles in Microfluidic Flows

The multiphase flow of droplets is widespread and used for both biological and nonbiological applications alike. However, the ensemble interactions of such systems are inherently nonlinear and complex, compounded by interfacial effects, making it a difficult many-body problem. In comparison, the self-assembly dynamics of solid particles in flow have long been studied and exploited in the field of inertial microfluidics. Here, we report novel self-assembly dynamics of liquid drops in microfluidic channels that contrast starkly with the established paradigm of inertial microfluidics, which stipulates that higher inertia leads to better spatial ordering. Instead, we find that ordering can be negatively correlated with inertia, while Dean flow can achieve long-range spatial periodicity on length scales at least 3 orders of magnitude greater than the drop diameter. Experimentally, we decouple droplet generation from ordering, enabling independent and systematic variation of key parameters, especially in ranges practical to droplet microfluidics. We find the inertia-dependent emergence of preferred drop separations and show that surfactant effects can influence the longitudinal ordering of multidrop arrays. The dynamics we describe have immediate utility to droplet microfluidics, where the ability to order drops is key to the streamlined integration of on-chip incubation with deterministic drop manipulation downstreamtwo important functions for biological assays. To this end, we demonstrate the use of passive inertial drop self-assembly to combine a delay line with picoinjection. These results not only present a largely unexplored direction for inertial microfluidics but also show the practical benefit of its unification with the versatile field of droplet microfluidics.