Eur. Phys. J. E (2006) 20: 119-124
https://doi.org/10.1140/epje/i2005-10124-5

Regular Article

Buckling of swelling gels

Laboratoire de Physique Statistique de l'École Normale Supérieure, 24, rue Lhomond, 75231, Paris Cedex 05, France

^* e-mail: boudaoud@lps.ens.fr

Received: 15 April 2005
Accepted: 19 April 2006
Published online: 16 June 2006

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 whose 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.