Rapid nonlinear hydrogel diffusiophoresis

Chemically responsive hydrogels can store and release chemical signals, such as polyacrylic acid (PAA) gels storing copper or calcium divalent ions and freeing them upon adding acid. While a hydrogel interface is often fully permeable to the ions and acid, interactions between the free ions and the gel polymer network can lead to a diffusiophoretic gel actuation at a rate faster than the characteristic poroelastic deformation rate. We have recently shown this effect theoretically and experimentally by focusing on linear deformations of a PAA gel [1]. However, in light of potential applications such as hydrogel-based soft robotics and drug delivery, comprehending large hydrogel deformations is imperative for increased strain rates and power output. We present a nonlinear poroelastic theory to model large diffusiophoretic gel swelling induced by high stimulus concentrations or by a steady stimulus flow at arbitrary rates. We also establish enthalpic origins of the diffusiophoretic stress by considering variation in the hydrogel free energy. Our theory incorporates the interplay between nonlinear poroelasticity, dynamic hydrogel permeability, and diffusiophoretic swelling along with the transport dynamics of chemical agents within the gel.