  Hydrogels have a distinct combination of mechanical and water-transport
behaviors. As hydrogels stiffen, they become less permeable. Here, we combine
semi-dilute polymer theory with the Kozeny-Carman equation to develop a simple
scaling law describing the relationship between hydraulic permeability and
mechanical stiffness. We find that these properties are dictated by the polymer
strand spacing, explained via analogy of a bowl of noodle soup. We find a
remarkably close agreement between our scaling law and experimental results
across four different polymer families with varied crosslinkings.
