Figure 1. Neck pinch-off in microfluidics.

(a) Experimental setup. (b) Image of a drop discharged from ejection nozzle. D_n, D_min and Z₀ are the nozzle diameter, minimum neck diameter and location of the minimum neck, respectively. Scale bar, 100 μm. (c,d) Snapshots of (c) unperturbed and (d) perturbed neck thinning versus time τ remaining to pinch-off (see supplementary Movies S1,S2,S3,S4,S5). In time period 0 < τ < 6.16 ms before pinch-off, the difference in neck diameter for perturbed case (ε₀= 2 mm) is larger than that for unperturbed case, showing the enhancement of pinch-off by mechanical perturbation. A suction of inner fluid towards the nozzle in (d) characterizes the last stage of neck pinch-off modulated by perturbation. The viscosity ratio of fluid system is λ = 0.157. Inner and outer fluid flow rates are Q_i = 0.3 mL h⁻¹ and Q_o = 1 mL h⁻¹, respectively. Scale bars, 100 μm. (e) Plot of minimum neck diameter D_min versus time τ for unperturbed two-fluid pinch-off with various viscosity ratios. Neck thins faster for fluid system with smaller viscosity ratio. (f) Scaling law for unperturbed neck pinch-off with different viscosity ratios. In Stokes regime, linear scaling gives . Inset: minimum neck diameter D_min versus time τ plotted in a log-log plane. The error comes from the limiting resolution in the captured image.