Self-oscillations of hydrogels driven by chemical reactions

A model is developed for the mechanical response of hydrogels whose deformation is accompanied by swelling-shrinkage driven by the Belousov-Zhabotinsky reaction. A hydrogel is treated as a compressible network of flexible chains with a time-dependent reference (stress-free) state whose evolution is driven by oxidation of a catalyst pendent to chains. The model involves three components: stress-strain relations for deformation of a polymer network coupled with swelling, kinetic equations for chemical reactions with diffusing species, and relations connecting changes in the reference configuration with concentration of oxidized catalyst. Results of simulation confirm the ability of the model to describe autonomous oscillations of a hydrogel layer under constrained swelling. The effect of material parameters on amplitude and frequency of oscillations is studied numerically. In agreement with the available experimental data, it is shown that amplitude of oscillations decreases and their period increases when (i) elastic modulus of the polymer network grows, (ii) a good solvent is replaced with a poor one, (iii) concentration of a catalyst is reduced, (iv) size of a sample decreases, and (v) diffusivities of solvent and activator grow.