“…Conical pores, or pores with a variation in cross-sectional width have been shown in microfluidic fields to enable effective passive regulation of fluid flow, with a key application being the capillary burst valve [15,19,20,21]. Furthermore, substantial progress has been made in calculating the maximum Laplace pressures for liquid entering physically textured surfaces, see for example [22,23], as well as liquid exiting physically textured surfaces of axisymmetric and non-axisymmetric cross sections [24,25]. However, the enclosed geometry, efficacy at preventing back-flow, and the impact of chemical patterning have never been discussed.…”