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 means they are often termed 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 that 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 traveling 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 optimization strategy to maximize this critical pressure asymmetry.