  Liquid diodes are surface structures that facilitate the flow of liquids in a
specific direction. When these structures are within the capillary regime, they
promote liquid transport without the need for external forces. In nature, they
are used to increase water collection and uptake, reproduction, and feeding.
While nature offers various one-dimensional channels for unidirectional
transport, networks with directional properties are exceptional and typically
limited to millimeters or a few centimeters. In this study, we simulate, design
and 3D print liquid diode networks consisting of hundreds of unit cells. We
provide structural and wettability guidelines for directional transport of
liquids through these networks, and introduce percolation theory in order to
identify the threshold between a connected network, which allows fluid to reach
specific points, and a disconnected network. By constructing well-defined
networks that combine uni- and bi-directional pathways, we experimentally
demonstrate the applicability of models describing isotropically directed
percolation. By varying the surface structure and the solid-liquid interfacial
tension, we precisely control the portion of liquid diodes and bidirectional
connections in the network and follow the flow evolution. We are, therefore,
able to accurately predict the network permeability and the liquid's final
state. These guidelines are highly promising for the development of structures
for spontaneous, yet predictable, directional liquid transport.
