A hydrogel in a solute gradient moves. Solute molecules interact differently with the polymer network than with the surrounding water, creating osmotic pressure differences that drive internal flows and deform the gel. This is diffusiophoresis โ motion driven by chemical gradients rather than external force. At small strains, the theory is linear and the speeds are modest.
Katke and Kaplan develop a nonlinear poroelastic theory for large diffusiophoretic strains. The coupling between polymer-solute interactions, network elasticity, and solvent transport produces amplification effects invisible at small deformation. Varying the stimulus concentration can increase strain rate up to four times. Changing solute particle size amplifies it up to roughly 25 times. Imposing flow amplifies it up to approximately 40 times. The nonlinearity is not a correction to linear behavior โ it is a separate regime where small changes in input produce disproportionate changes in output.
The theory also handles gels that generate their own solute gradients โ polyacrylic acid hydrogels producing internal chemical fields that drive autonomous deformation without external stimulus.
The through-claim is about where the amplification lives. In the linear regime, strain rate scales proportionally with the gradient, and doubling the input doubles the output. In the nonlinear regime, the gel's large deformation changes its permeability, which changes the internal flow, which changes the deformation โ a feedback loop that amplifies the response beyond proportionality. The amplification is not in the stimulus. It is in the material's response to its own response. The gel is not being pushed harder. It is changing into something that moves more easily.