Surface wrinkles of swelling gels under arbitrary lateral confinements

Based on perturbation analysis, this study investigates surface wrinkling of a gel layer under arbitrary lateral confinements in the equilibrium state of swelling. Gels containing incompressible polymer networks and solvents may incur large deformations and increase the volume by several times after swelling. Owing to the restrictions on lateral expansions and surface imperfections, the instabilities may appear in the form of wrinkling. Wrinkling is strongly governed by the compressibility of swollen gel, confinements and gel thickness. Additionally, gel compressibility is attributed to the migration of solvent under stress at the confined-swelling state, and can be expressed in terms of a confined-swelling volume ratio. This work also discusses possible gel-solvent systems of wrinkling under different confinements. At equal biaxial confinements, the wrinkle pattern is a combination of plane waves with the same wavelength in all directions. Meanwhile, at non-equal biaxial confinements, the wrinkle pattern may be a sum of plane waves with dissimilar wavelengths and corresponding directions.