A syringe pump (Fusion 4000, Chemyx) was fitted with two syringes (1-ml Luer-Lok, BD, 309628), one to infuse media into the inlet spot (Dinlet = 1 mm) and another to withdraw from the outlet spot (Doutlet = 3 mm). Both syringes had 18-gauge (Φinlet = Φoutlet = 1 mm) blunt tip needles (SAI Infusion Technologies, B18-150) attached with 18-gauge polytetrafluoroethylene tubing (Component Supply, SWTT-18-C) leading to the microchannels. The needle on the inlet for fluid delivery was treated with PDMS-silane to obtain double ELR (with the same treatment as PDMS-grafted glass was performed), stabilizing TCL and thus limiting the capillary wicking of media along the outer wall of the needle. The needle on the outlet was untreated. The inlet tubing was cleared of air by depressing the syringe. The inlet needle was held perpendicularly above the inlet spot at a height of 1 mm (hinlet = 1 mm).
The outlet needle was placed in the same way as the inlet but with 3 mm (houtlet = 3 mm) between the outlet spot and the needle. The syringe pump was set to start at a small flow rate (0.1 to 1 μl/min, depending on the channel width tested), and the microchannel was allowed to equilibrate for at least 1 min. Flow rates were then stepped up every 30 s (0.2 μl/min for 200-μm-wide microchannels, 2 μl/min for 500-μm-wide microchannels, and 100 μl/min for 1000-μm-wide microchannels). The maximum flow rate was determined by recording the point at which accumulation of aqueous fluid at the inlet occurred (Fig. 4). Each replicate was performed with a new microchannel. Images of the microchannels tested were taken on a Nikon Eclipse Ti with 2-NBDG solution (2 mM in media) using the bright field and 485-nm/525-nm (Ex/Em) (exposure time, 2 s) channels.
Under the tested condition, the inlet microdroplet takes a torus shape to minimize the radius of curvature [Rinlet = 2/(1/Rinlet-1 + 1/Rinlet-2) = 0.67 mm, where Rinlet-1 = hinlet, Rinlet-2 = hinlet/2], and the outlet microdroplet is the shape of a spherical cap with a radius of curvature Routlet= 1.88 mm (defined by Doutlet and houtlet). ΔP is defined by the Laplace pressure differential between the inlet and outlet spots (i.e., 2γoil/media/Rinlet − 2γoil/media/Routlet, where γoil/media is the oil-media interfacial tension, about 41.8 mN/m at 25°C) (table S1) (18). The radius of curvature of the microchannel (Rchannel) at t0 (i.e., immediately after the microchannels filled with a solution by under oil sweep) can be calculated as Rchannel = 2/(1/Rchannel ⊥ + 1/Rchannel ∥) = 2 Rchannel ⊥ (table S2 and fig. S5), where Rchannel ⊥ (defined by channel width, w, and height, h) and Rchannel ∥ (∞) are the radius of curvature from the cross section of the microchannel perpendicular (i.e., a circular segment) and parallel to the flow (i.e., a rectangle). Je’Xperiment (JEX) was used to measure the width, w, and length, l, of each connecting channel. A power-law dependence of Q on w was estimated (i.e., Q ∝ w^a, fitting data to find “a”). This was performed in R/RStudio by plotting log10(Q) versus log10(w) with the “lm” function to calculate the slope parameter, “a = 5.22.”