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.
Bibliographical noteFunding Information:
This work was funded by Donaldson Company (Bloomington, Minnesota, USA) and carried out at the University of Minnesota. We would like to thank Prof. Charles Schroeder, Dr. Anish Shenoy, and Dinesh Kumar from the University of Illinois at Urbana-Champaign (Chemical and Biomolecular Engineering, Mechanical Engineering), for help with setting up the Stokes trap and providing the code for MPC-based feedback control. We would also like to thank Dr. Benjamin Micklavzina (University of Minnesota), Dr. Yun Chen (University of Minnesota), and Prof. Andrew Metcalf (Clemson University) for helpful discussions. Rheological measurements were conducted at the Polymer Characterization Facility and pendant drop tensiometry measurements were conducted at the Coating Process Fundamentals Lab, both in the Chemical Engineering and Materials Science department at the University of Minnesota. Portions of this work were conducted in the Minnesota Nano Center, which is supported by the National Science Foundation through the National Nano Coordinated Infrastructure Network (NNCI) under Award No. ECCS-154220. There are no conflicts of interest to declare.