Droplet shape relaxation in a four-channel microfluidic hydrodynamic trap

Two-phase liquid-liquid systems are prevalent in a range of commercial and environmental applications. Understanding the behavior of liquid-liquid systems under various processing conditions requires the study of droplet dynamics under precisely controlled flow fields. Here we trap and control the position of droplets in a microfluidic trap to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented Stokes trap by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. Using the hydrodynamic trap, confined droplet dynamics in response to perturbation are studied by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation time is obtained from the shape decay curves, for aqueous glycerol droplets of varying viscosities in the dispersed phase with light and heavy mineral oils in the continuous phase. Systems were chosen to provide similar equilibrium interfacial tensions (5-10 mN/m) with wide variations of viscosity ratios. It is found that the droplet shape relaxation in the moderately confined regime shows a strong dependence on droplet radius, and a weaker dependence on the ratio of dispersed to continuous phase viscosity. An empirical scaling relationship is developed, and relaxation times from the experiments are compared to theoretical relaxation times for the limiting regime of unconfined droplets. The droplet response in the moderately confined regime differs from both limiting regimes of unconfined and highly confined droplets with regards to the radius scaling. Droplet shape relaxation time can be used inform the response of droplets in an emulsion when subjected to transient flows in various processing conditions. Finally, an application of this platform for directly visualizing droplet coalescence in planar extensional flow is presented. The microfluidic four-channel hydrodynamic trap can thus be applied for studying the fundamental physics of droplet deformation and droplet-droplet interactions on the microscale.