Critical pressure asymmetry in the enclosed fluid diode

Joint physically and chemically pattered surfaces can provide efficient and passive manipulation of fluid flow. The ability of many of these surfaces to allow only unidirectional flow mean they are often referred to as fluid diodes. Synthetic analogues of these are enabling technologies from sustainable water collection via fog harvesting, to improved wound dressings. One key fluid diode geometry features a pore sandwiched between two absorbent substrates, an important design for applications which require liquid capture while preventing back-flow. However, the enclosed pore is particularly challenging to design as an effective fluid diode, due to the need for both a low Laplace pressure for liquid entering the pore, and a high Laplace pressure to liquid leaving. Here, we calculate the Laplace pressure for fluid travelling in both directions on a range of conical pore designs with a chemical gradient. We show that this chemical gradient is in general required to achieve the largest critical pressure differences between incoming and outgoing liquids. Finally, we discuss the optimisation strategy to maximise this critical pressure asymmetry.