Abstract

Super-absorbent polymers placed in water can form hydrogels with polymer fractions of less than 1% by volume, with the water molecules being adsorbed by the hydrophilic polymer to form an elastic material. They are used in disposable diapers, for soil remediation, for controlled drug delivery and as actuators in microfluidic devices. Hydrogels are also a component part of the xylem, through which water is transported upwards in trees. The water is not fixed in place but can flow through the porous polymer scaffold to drive swelling, drying and transpiration. We have developed a new mathematical approach to model super-absorbent hydrogels, which allows for strongly nonlinear swelling while remaining linear in deviatoric strains, in effect treating hydrogels as instantaneously incompressible, linear elastic materials with inhomogeneous elastic properties related to the differential swelling states. I will describe this model and illustrate its features by solving simple examples of swelling spheres and transpiration through cylinders, and by analysing different instabilities that can arise during swelling and drying. I will also introduce a hypothesis for a potential role of hydrogels in pumping water up very tall trees.