Droplet microfluidics provides a versatile tool for measuring interfacial tensions between two immiscible fluids owing to its abilities of fast response, enhanced throughput, portability and easy manipulations of fluid compositions, comparing to conventional techniques. Purely homogeneous extension in the microfluidic device is desirable to measure the interfacial tension because the flow field enables symmetric droplet deformation along the outflow direction. To do so, we designed a microfluidic device consisting of a droplet production region to first generate emulsion droplets at a flow-focusing area. The droplets are then trapped at a stagnation point in the cross junction area, subsequently being stretched along the outflow direction under the extensional flow. These droplets in the device are either confined or unconfined in the channel walls depending on the channel height, which yields different droplet deformations. To calculate the interfacial tension for confined and unconfined droplet cases, quasi-static 2D Darcy approximation model and quasi-static 3D small deformation model are used. For the confined droplet case under the extensional flow, an effective viscosity of the two immiscible fluids, accounting for the viscosity ratio of continuous and dispersed phases, captures the droplet deformation well. However, the 2D model is limited to the case where the droplet is confined in the channel walls and deforms two-dimensionally. For the unconfined droplet case, the 3D model provides more robust estimates than the 2D model. We demonstrate that both 2D and 3D models provide good interfacial tension measurements under quasi-static extensional flows in comparison with the conventional pendant drop method.
Full linear Phan-Thien–Tanner fluid model: Exact analytical solutions for steady, startup, and cessation regimes of shear and extensional flows