Spider egg sacs reveal how pockets of air can be used to conserve water

Controlling water transport across surfaces is essential for all living organisms. Spider egg sacs are multifunctional membranes that protect eggs and spiderlings from the external environment. Past research gives conflicting results about whether these mats of silk fibers reduce evaporation of water in part because the diffusive resistance of any membrane cannot be measured independently of the system in which it is studied. We developed a model to describe water vapor transport across porous surfaces that includes the important roles of the gap space underneath the membrane and the boundary layer on the outside of the membrane in controlling water vapor flux, in addition to the relative impermeability of the membrane itself. The model accurately predicts diffusive resistance of a variety of synthetic surfaces from empirical studies, as well as the egg sacs of the black widow Latrodectus hesperus and the garden spider Argiope aurantia. We show that 'typical' spider egg sac membranes offer surprisingly low diffusive resistance to water because they are highly porous at microscopic scales. However, silk egg sacs still play key roles in controlling water loss by preserving and defining an internal region of stagnant air that often dominates the diffusive resistance of the whole system. Our model provides a tool to explore diverse spider egg sac geometries, but can also be adopted to fit a variety of systems to facilitate comparison and engineering of diffusive resistance across membranes.