Extended Data Fig. 4: Assessment of the stability of the leading barrier.

a, During longitudinal flow, the hydraulic pressure (P_hydraulic) increases as the hydraulic resistance (R_hydraulic) increases with the distance travelled by the liquid. The leading barrier is able to preserve the longitudinal flow as long as the pinning forces (P_Laplace) can balance the increasing hydraulic pressure and the pressure exerted by the resistance to wetting (R_wetting). In order to investigate this effect, the width (W = 75, 100, 125, 150, 175 or 200 µm) and the height (H = 30, 45 or 90 µm) of the longitudinal flow area and the filling flow rate (Q_in = 0.75, 1.5 or 3.0 µl min⁻¹) were varied. During experiments, the maximum distance along which the liquid remains pinned was measured. b, Bright-field (left) and SEM (right) images of devices in which stability-assessment experiments are performed. c, Experimental data support theoretical predictions that: first, a smaller liquid–vapour interface can bear a higher hydraulic pressure; second, the hydraulic radius of the longitudinal flow area needs to be large in order to fill deeper structures or for high filling flow rates; and third, the flow rate challenges the stability of the leading barrier. Data points are means of experiments (n = 8 or more; error bars represent standard error of the mean). Conditions in which the liquid was not pinned at the CPL (longitudinal flow length = 0  mm) or the liquid travelled to the end of the test device (longitudinal flow length = 65 mm) are excluded from the plot.