  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.
