[Paper Review] A hyperelastic theory for nonlinear hydrogel diffusiophoresis

Chinmay Katke, C. Nadir Kaplan|arXiv (Cornell University)|Mar 2, 2026

Hydrogels: synthesis, properties, applications0 citations

TL;DR

The paper develops a nonlinear poroelastic (hyperelastic) theory of hydrogel diffusiophoresis for large deformations in two models, showing how external or internally generated solute gradients drive rapid, large gel deformations. Model II indicates strain rates can be boosted by manipulating stimulus concentration, solute size, and flow.

ABSTRACT

Hydrogel diffusiophoresis is the deformation of a hydrogel due to a solute gradient that leads to a gradient of pairwise interactions between the solute particles and the hydrogel polymers to trigger osmotic flux. Unlike typical osmosis, it occurs without any interface selectivity of the gel to the solute and can overcome the diffusive swelling without any structural modifications to the gel. We have recently shown this effect for linear deformations of a chemically responsive polyacrylic acid (PAA) hydrogel that releases ions upon arrival of a stimulus (acid), thus internally generating the solute gradient required for diffusiophoresis [Phys. Rev. Lett. 132, 208201 (2024)]. Here we develop a nonlinear poroelastic theory for large diffusiophoretic gel strains in two models: Model I considers deformations of a generic gel when an external solute gradient is imposed. In Model II, the gel generates the solute gradient internally, motivated by the coupled PAA gel, solute (copper), and stimulus (acid) system. In Model II, we investigate the nonlinear deformations for high stimulus concentrations or by changing the solute particle size to boost steric polymer-solute interactions, as well as under a stimulus flow through the gel driven by a pressure drop across the domain. Model I indicates that deformations can be stored while the stimulus gradient persists. Compared to the experimental strain rates in Katke [Phys. Rev. Lett. 132, 208201 (2024)], Model II demonstrates that varying the stimulus concentration can increase the strain rate up to four times, changing the solute particle size up to $\sim 25$ times, and imposed flow up to $\sim 40$ times. Our theory couples nonlinear poroelasticity, polymer-solute interactions, and reaction-transport dynamics to predict large and fast diffusiophoretic gel deformations, which may find applications in hydrogel-based soft robotics and drug delivery.

Motivation & Objective

• Extend gel diffusiophoresis theory from linear to nonlinear (large) deformations.
• Couple nonlinear poroelasticity with polymer–solute interactions and reaction–transport dynamics.
• Develop two models: external solute gradient (Model I) and internally generated gradient (Model II) for a PAA gel system.
• Explore how stimulus concentration, solute size, and flow affect deformation rates.
• Provide a framework applicable to hydrogel actuation and intelligent drug delivery systems.

Proposed method

• Use a nonlinear poroelastic (hyperelastic) framework with Flory-type free energy for the polymer network.
• Define nominal (First Piola–Kirchhoff) and Cauchy stresses including poroelastic, entropic, and diffusiophoretic contributions.
• Introduce a diffusiophoretic stress tensor tied to polymer–solute interactions and a scalar diffusiophoretic coefficient for uniaxial cases.
• Couple deformation with solvent flow via Darcy’s law in the material frame and mass conservation in the material frame.
• Formulate two models: Model I with an externally imposed solute gradient, Model II with an internally generated gradient (copper/acid system).
• Derive dimensionless forms and boundary conditions to solve for displacement, solute fractions, and interfacial pressures.

Experimental results

Research questions

• RQ1 How do nonlinear (large-strain) poroelastic effects modify gel diffusiophoresis under external solute gradients?
• RQ2 How does an internally generated solute gradient from chemical stimuli drive nonlinear gel deformations in Model II?
• RQ3 How do stimulus concentration, solute size, and imposed flow influence diffusion-driven deformation rates?
• RQ4 What is the role of polymer–solute interactions and diffusion in controlling the time evolution of gel height and internal stresses?

Key findings

• Model I shows deformations can be stored while the external stimulus gradient persists.
• Model II shows that increasing stimulus concentration can raise the strain rate up to four times.
• Increasing solute particle size can boost diffusiophoretic effects by up to ~25 times.
• Imposed flow can amplify deformation rates by up to ~40 times.
• The theory integrates nonlinear poroelasticity, polymer–solute interactions, and reaction–transport dynamics to predict large, fast diffusiophoretic gel deformations.
• Predictions may inform hydrogel-based soft robotics and drug delivery applications.