Buckling of swelling gels

TL;DR

This paper investigates the patterns formed by swelling gels, combining experiments and linear elasticity theory to understand the instability and wavelength of the resulting buckling patterns as a model for tissue growth.

Contribution

It provides a combined experimental and theoretical analysis of buckling patterns in swelling gels, linking pattern wavelength to swelling rate and stability analysis.

Findings

Waves form in swelling gels when the swelling rate exceeds a critical value.

Theoretical predictions of wavelength match experimental measurements.

Instability analysis explains the transition from flat to buckled states.

Abstract

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern which wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.