High throughput estimates of surface tension using steady droplet deformation in pressure-driven fluidic flows

Advances in fluidic droplet generation both necessitate and enable accessible, high throughput methods to optimize formulations by measuring surface tension. One fluidic approach involves creating extensional flow using constrictions. Droplets deform within a constriction, and then experience extensional flow upon exiting into a wider channel. Transient relaxation of the deformed droplets, coupled with the details of the extensional flow, can be used to measure surface tension. We propose an alternative, arguably simpler approach: we use steady deformation within a constriction to measure surface tension. Our approach is motivated by the linear theories that describe droplet deformation in steady flows. These theories, encompassing both clean and surfactant covered drops in unbounded and bounded shear flows, show that droplet deformation is linear with the capillary number for small deformations. Interestingly, this steady deformation approach to estimating the capillary number, and thus, surface tension, has not been tested in pressure driven microfluidic flows. We generate and flow emulsion droplets through a series of increasingly narrow constrictions and use steady deformation to measure surface tension. We investigate both water-in-oil and oil-in-water droplets, stabilized by three different surfactants over a range of concentrations. In a subset of experiments, we vary the viscosity ratio by adding polyethylene glycol diacrylate to water droplets. Validation using both the transient deformation fluidic approach and pendant drop measurements on individual droplets demonstrates the viability of using linear scaling behavior to estimate surface tension. Our results suggest steady state deformation in pressure driven flows can be used to measure surface tension even when droplets are slightly confined. This steady droplet deformation approach to surface tension measurements represents a readily-accessible option for those using fluidic droplet generators to perform biomedical or other assays, or to investigate or optimize emulsion formulations.